#include "../../../include/lammp/impl/prime_table.h"
#include "../../../include/lammp/impl/mparam.h"
#include "../../../include/lammp/impl/inlines.h"
#include "../../../include/lammp/impl/tmp_alloc.h"

prime_table.c 的引用(Include)关系图:

结构体
struct	prime_int
	Copyright (C) 2026 HJimmyK(Jericho Knox) 更多...

宏定义
#define	G global_prime_int_table

#define	IDX(p) ((p) >> 1)

#define	set_not_prime(p, i) p[i / LMMP_BITSET_BITS] &= not_mask_64[(i % LMMP_BITSET_BITS)]

#define	set_prime(p, i) p[i / LMMP_BITSET_BITS] \|= (1ULL << (i % LMMP_BITSET_BITS))

类型定义
typedef struct prime_int	prime_int
	Copyright (C) 2026 HJimmyK(Jericho Knox)

函数
int	lmmp_is_prime_table_ (uint p)
	根据全局素数表判断一个数是否为素数

void	lmmp_prime_cache_free_ (prime_cache_t *cache)
	释放素数表缓存

void	lmmp_prime_cache_init_ (prime_cache_t *cache, uint n)
	初始化素数表缓存

void	lmmp_prime_cache_next_ (prime_cache_t *cache)
	素数表缓存更新（从小到大遍历全局质数表）

ushort	lmmp_prime_cnt16_ (ushort n)
	计算小于等于 n 的素数数量

void	lmmp_prime_int_table_free_ (void)
	释放全局素数表

void	lmmp_prime_int_table_init_ (uint n)
	初始化全局素数表

static uint	prime_table_size (uint n)

变量
static _Thread_local prime_int	global_prime_int_table

static const lmmp_bitset_t	not_mask_64 [(64)]

const ushort	prime_short_table [6542]

const lmmp_bitset_t	r35711_mask_map [19]

static const lmmp_bitset_t	wheel_mask [105]

结构体说明

◆ prime_int

struct prime_int

This file is part of LAMMP.

LAMMP is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed WITHOUT ANY WARRANTY.

See https://www.gnu.org/licenses/.

在文件 prime_table.c 第 22 行定义.

prime_int 的协作图:

成员变量
lmmp_bitset_p restrict	map
uint	map_size
uint	max

宏定义说明

◆ G

#define G global_prime_int_table

在文件 prime_table.c 第 34 行定义.

◆ IDX

#define IDX ( p ) ((p) >> 1)

在文件 prime_table.c 第 120 行定义.

◆ set_not_prime

#define set_not_prime	(	p,
		i
	)	p[i / LMMP_BITSET_BITS] &= not_mask_64[(i % LMMP_BITSET_BITS)]

在文件 prime_table.c 第 121 行定义.

◆ set_prime

#define set_prime	(	p,
		i
	)	p[i / LMMP_BITSET_BITS] \|= (1ULL << (i % LMMP_BITSET_BITS))

在文件 prime_table.c 第 122 行定义.

类型定义说明

◆ prime_int

typedef struct prime_int prime_int

This file is part of LAMMP.

LAMMP is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed WITHOUT ANY WARRANTY.

See https://www.gnu.org/licenses/.

函数说明

◆ lmmp_is_prime_table_()

int lmmp_is_prime_table_ ( uint p )

根据全局素数表判断一个数是否为素数

参数

p 待判断的数

警告: p>1, p%2==1

注解: 若 p 超过了当前全局素数表的范围，则返回 -1

返回: 1 素数，0 合数，-1 超出质数表范围

在文件 prime_table.c 第 207 行定义.

                                 {
    if (p < PRIME_SHORT_TABLE_N) {
        ushort i = lmmp_prime_cnt16_(p);
        if (prime_short_table[i - 1] == p)
            return 1;
        return 0;
    } else if (p > G.max) {
        return -1;
    } else {
        // p>=3
        lmmp_param_assert(p > 1);
        lmmp_param_assert((p & 1) == 1);
        uint idx = IDX(p);
        return (G.map[idx / LMMP_BITSET_BITS] >> (idx % LMMP_BITSET_BITS) & 1);
    }
}

引用了 G, IDX, LMMP_BITSET_BITS, lmmp_param_assert, lmmp_prime_cnt16_(), n, prime_short_table , 以及 PRIME_SHORT_TABLE_N.

被这些函数引用 lmmp_is_prime_uint_() , 以及 lmmp_is_prime_ulong_().

函数调用图:

这是这个函数的调用关系图:

◆ lmmp_prime_cache_free_()

void lmmp_prime_cache_free_ ( prime_cache_t * cache )

释放素数表缓存

参数

cache 缓存结构体

在文件 prime_table.c 第 303 行定义.

                                                  {
    lmmp_free(cache->pp);
    cache->pp = NULL;
}

引用了 lmmp_free() , 以及 n.

被这些函数引用 lmmp_odd_2factorial_uint_(), lmmp_odd_factorial_uint_(), lmmp_odd_multinomial_uint_(), lmmp_odd_nCr_uint_(), lmmp_odd_nPr_uint_() , 以及 lmmp_primefac_().

函数调用图:

这是这个函数的调用关系图:

◆ lmmp_prime_cache_init_()

void lmmp_prime_cache_init_	(	prime_cache_t *	cache,
		uint	n
	)

初始化素数表缓存

参数

cache	缓存结构体
n	遍历素数表的范围（超过n时或者遍历到全局质数表末尾，is_end 置为 1）

在文件 prime_table.c 第 224 行定义.

                                                          {
    lmmp_param_assert(n > 2);
    lmmp_param_assert(n <= G.max);
    cache->pp = ALLOC_TYPE(PRIME_CACHE_SIZE, uint);
    cache->size = 0;
    cache->start_idx = 0;
    uint max_bit_idx = (n - 1) / 2;
    cache->end_num = n;
    cache->end_idx = max_bit_idx / LMMP_BITSET_BITS;
    cache->is_end = 0;
}

引用了 ALLOC_TYPE, G, LMMP_BITSET_BITS, lmmp_param_assert, n , 以及 PRIME_CACHE_SIZE.

被这些函数引用 lmmp_odd_2factorial_uint_(), lmmp_odd_factorial_uint_(), lmmp_odd_multinomial_uint_(), lmmp_odd_nCr_uint_(), lmmp_odd_nPr_uint_() , 以及 lmmp_primefac_().

这是这个函数的调用关系图:

◆ lmmp_prime_cache_next_()

void lmmp_prime_cache_next_ ( prime_cache_t * cache )

素数表缓存更新（从小到大遍历全局质数表）

参数

cache 缓存结构体

注解: 缓存只存储奇素数，当遍历到全局质数表末尾或者达到设置的范围时，is_end 置为 1

在文件 prime_table.c 第 236 行定义.

                                                  {
    uint size = 0;
    ulong idx = cache->start_idx;
 
    if (idx + PRIME_CACHE_BLOCK_NUM < cache->end_idx) {
        lmmp_bitset_t m0, m1, m2, m3;
        uintp begin = cache->pp;
        for (uint i = 0; i < PRIME_CACHE_BLOCK_NUM / 4; ++i) {
            m0 = G.map[idx + 0];
            m1 = G.map[idx + 1];
            m2 = G.map[idx + 2];
            m3 = G.map[idx + 3];
 
            while (m0) {
                uint cnt = lmmp_tailing_zeros_(m0);
                begin[size++] = ((idx + 0) * LMMP_BITSET_BITS + cnt) * 2 + 1;
                m0 &= (m0 - 1);
            }
            while (m1) {
                uint cnt = lmmp_tailing_zeros_(m1);
                begin[size++] = ((idx + 1) * LMMP_BITSET_BITS + cnt) * 2 + 1;
                m1 &= (m1 - 1);
            }
            while (m2) {
                uint cnt = lmmp_tailing_zeros_(m2);
                begin[size++] = ((idx + 2) * LMMP_BITSET_BITS + cnt) * 2 + 1;
                m2 &= (m2 - 1);
            }
            while (m3) {
                uint cnt = lmmp_tailing_zeros_(m3);
                begin[size++] = ((idx + 3) * LMMP_BITSET_BITS + cnt) * 2 + 1;
                m3 &= (m3 - 1);
            }
            idx += 4;
        }
        lmmp_debug_assert(idx - cache->start_idx == PRIME_CACHE_BLOCK_NUM);
        cache->start_idx = idx;
        cache->size = size;
        return;
    } else {
        uint max_bit_idx = (cache->end_num - 1) / 2;
        uint last_off = max_bit_idx % LMMP_BITSET_BITS;
        lmmp_bitset_t last_mask =
            (last_off == LMMP_BITSET_BITS - 1) ? (lmmp_bitset_t)-1 : ((1ULL << (last_off + 1)) - 1);
        lmmp_bitset_t m;
        for (uint i = idx; i < cache->end_idx; ++i) {
            m = G.map[i];
            while (m) {
                uint cnt = lmmp_tailing_zeros_(m);
                cache->pp[size++] = (i * LMMP_BITSET_BITS + cnt) * 2 + 1;
                m &= (m - 1);
            }
        }
        idx = cache->end_idx;
        m = G.map[idx] & last_mask;
        while (m) {
            uint cnt = lmmp_tailing_zeros_(m);
            cache->pp[size++] = (idx * LMMP_BITSET_BITS + cnt) * 2 + 1;
            m &= (m - 1);
        }
        cache->start_idx = G.map_size;
        cache->size = size;
        cache->is_end = 1;
        return;
    }
}

引用了 G, LMMP_BITSET_BITS, lmmp_debug_assert, lmmp_tailing_zeros_, n , 以及 PRIME_CACHE_BLOCK_NUM.

被这些函数引用 lmmp_odd_2factorial_uint_(), lmmp_odd_factorial_uint_(), lmmp_odd_multinomial_uint_(), lmmp_odd_nCr_uint_(), lmmp_odd_nPr_uint_() , 以及 lmmp_primefac_().

这是这个函数的调用关系图:

◆ lmmp_prime_cnt16_()

ushort lmmp_prime_cnt16_ ( ushort n )

计算小于等于 n 的素数数量

参数

n 范围

返回: 素数数量

在文件 prime_table.c 第 311 行定义.

                                   {
    if (n < 2)
        return 0;
    if (n >= prime_short_table[PRIME_SHORT_TABLE_SIZE - 1]) 
        return PRIME_SHORT_TABLE_SIZE;
 
    ushort lo = 0;
    ushort hi = PRIME_SHORT_TABLE_SIZE;  // [lo, hi)
 
    while (lo < hi) {
        ushort mid = lo + (hi - lo) / 2;
        if (prime_short_table[mid] <= n) {
            lo = mid + 1;
        } else {
            hi = mid;
        }
    }
    return lo; 
}

引用了 lo, n, prime_short_table , 以及 PRIME_SHORT_TABLE_SIZE.

被这些函数引用 lmmp_hyperfac_(), lmmp_is_prime_table_(), lmmp_next_prime_ulong_(), lmmp_odd_2factorial_ushort_(), lmmp_odd_multinomial_ushort_(), lmmp_odd_nCr_ushort_(), lmmp_odd_nPr_ushort_(), lmmp_prev_prime_ulong_(), lmmp_prime_int_table_init_(), lmmp_prime_size_(), lmmp_primefac_(), lmmp_superfac_() , 以及 lmmp_trialdiv_().

这是这个函数的调用关系图:

◆ lmmp_prime_int_table_free_()

void lmmp_prime_int_table_free_ ( void )

释放全局素数表

在文件 prime_table.c 第 331 行定义.

                                      {
    lmmp_free(G.map);
    G.map = NULL;
    G.max = 0;
    G.map_size = 0;
}

引用了 G, lmmp_free() , 以及 n.

被这些函数引用 lmmp_global_deinit().

函数调用图:

这是这个函数的调用关系图:

◆ lmmp_prime_int_table_init_()

void lmmp_prime_int_table_init_ ( uint n )

初始化全局素数表

参数

n 素数表大小（含n）

警告: 会自动扩容，可以重入；当 n < PRIME_SHORT_TABLE_N 时，将会直接返回

注解: 仅存储奇素数

在文件 prime_table.c 第 124 行定义.

                                        {
    if (n < PRIME_SHORT_TABLE_N || G.max >= n)
        return;
    if (G.map == NULL) {
        G.max = n;
        G.map_size = prime_table_size(n);
        lmmp_bitset_p restrict p = ALLOC_TYPE(G.map_size, lmmp_bitset_t);
 
        // 按 105 周期填充
        for (uint i = 0, s = 0; i < G.map_size; ++i) {
            p[i] = wheel_mask[s];
            // s = (s + 64) % 105;
            s += LMMP_BITSET_BITS;
            if (s >= 105)
                s -= 105;
        }
 
        set_not_prime(p, 0);
        set_prime(p, IDX(3));
        set_prime(p, IDX(5));
        set_prime(p, IDX(7));
 
        ushort sqrt_n = n > 4294836225 ? 0xffff : (ushort)sqrt(n);
        uint max_idx = lmmp_prime_cnt16_(sqrt_n);
        uint limit_idx = IDX(n);
 
        // 从质数 11 开始（下标 4）
        for (ushort i = 4; i < max_idx; ++i) {
            uint prime = prime_short_table[i];
            uint start_idx = IDX(prime * prime);
            for (uint idx = start_idx; idx <= limit_idx; idx += prime) {
                set_not_prime(p, idx);
            }
        }
        G.map = p;
    } else {
        // 扩展部分（重分配）
        uint old_N = G.max;
        uint new_size = prime_table_size(n);
        G.map = REALLOC_TYPE(G.map, new_size, lmmp_bitset_t);
 
        // 新块填充 wheel_mask
        for (uint i = G.map_size, s = (G.map_size * 64) % 105; i < new_size; ++i) {
            G.map[i] = wheel_mask[s];
            s += LMMP_BITSET_BITS;
            if (s >= 105)
                s -= 105;
        }
 
        G.map_size = new_size;
        G.max = n;
 
        lmmp_bitset_p restrict p = G.map;
        set_not_prime(p, 0);
        set_prime(p, IDX(3));
        set_prime(p, IDX(5));
        set_prime(p, IDX(7));
        uint limit_idx = IDX(n - 1);
        uint old_limit_idx = IDX(old_N - 1);
 
        ushort sqrt_n = n > 4294836225 ? 0xffff : (ushort)sqrt(n);
        uint max_idx = lmmp_prime_cnt16_(sqrt_n);
 
        // 从质数 11 开始
        for (ushort i = 4; i < max_idx; ++i) {
            uint prime = prime_short_table[i];
            uint start = prime * prime;
            uint start_idx = IDX(start);
 
            if (start_idx <= old_limit_idx) {
                uint k = (old_limit_idx + 1 - start_idx + prime - 1) / prime;
                start_idx += k * prime;
            }
 
            for (uint idx = start_idx; idx <= limit_idx; idx += prime) {
                set_not_prime(p, idx);
            }
        }
    }
}

引用了 ALLOC_TYPE, G, IDX, k, LMMP_BITSET_BITS, lmmp_prime_cnt16_(), n, prime_short_table, prime_table_size(), REALLOC_TYPE, s, set_not_prime, set_prime , 以及 wheel_mask.

被这些函数引用 lmmp_odd_2factorial_uint_(), lmmp_odd_factorial_uint_(), lmmp_odd_multinomial_uint_(), lmmp_odd_nCr_uint_(), lmmp_odd_nPr_uint_() , 以及 lmmp_primefac_().

函数调用图:

这是这个函数的调用关系图:

◆ prime_table_size()

static uint prime_table_size ( uint n )

inlinestatic

在文件 prime_table.c 第 37 行定义.

                                            {
    uint bits = n / 2 + 1;
    bits /= LMMP_BITSET_BITS;
    return bits + 1;
}

引用了 LMMP_BITSET_BITS , 以及 n.

被这些函数引用 lmmp_prime_int_table_init_().

这是这个函数的调用关系图:

变量说明

◆ global_prime_int_table

_Thread_local prime_int global_prime_int_table

static

初始值:

= {
    .map      = NULL,
    .map_size = 0,
    .max      = 0
}

在文件 prime_table.c 第 28 行定义.

                                                             {
    .map      = NULL,
    .map_size = 0,
    .max      = 0
};

◆ not_mask_64

const lmmp_bitset_t not_mask_64[(64)]

static

初始值:

= {
    (lmmp_bitset_t)0xfffffffffffffffe, (lmmp_bitset_t)0xfffffffffffffffd, (lmmp_bitset_t)0xfffffffffffffffb,
    (lmmp_bitset_t)0xfffffffffffffff7, (lmmp_bitset_t)0xffffffffffffffef, (lmmp_bitset_t)0xffffffffffffffdf,
    (lmmp_bitset_t)0xffffffffffffffbf, (lmmp_bitset_t)0xffffffffffffff7f, (lmmp_bitset_t)0xfffffffffffffeff,
    (lmmp_bitset_t)0xfffffffffffffdff, (lmmp_bitset_t)0xfffffffffffffbff, (lmmp_bitset_t)0xfffffffffffff7ff,
    (lmmp_bitset_t)0xffffffffffffefff, (lmmp_bitset_t)0xffffffffffffdfff, (lmmp_bitset_t)0xffffffffffffbfff,
    (lmmp_bitset_t)0xffffffffffff7fff, (lmmp_bitset_t)0xfffffffffffeffff, (lmmp_bitset_t)0xfffffffffffdffff,
    (lmmp_bitset_t)0xfffffffffffbffff, (lmmp_bitset_t)0xfffffffffff7ffff, (lmmp_bitset_t)0xffffffffffefffff,
    (lmmp_bitset_t)0xffffffffffdfffff, (lmmp_bitset_t)0xffffffffffbfffff, (lmmp_bitset_t)0xffffffffff7fffff,
    (lmmp_bitset_t)0xfffffffffeffffff, (lmmp_bitset_t)0xfffffffffdffffff, (lmmp_bitset_t)0xfffffffffbffffff,
    (lmmp_bitset_t)0xfffffffff7ffffff, (lmmp_bitset_t)0xffffffffefffffff, (lmmp_bitset_t)0xffffffffdfffffff,
    (lmmp_bitset_t)0xffffffffbfffffff, (lmmp_bitset_t)0xffffffff7fffffff, (lmmp_bitset_t)0xfffffffeffffffff,
    (lmmp_bitset_t)0xfffffffdffffffff, (lmmp_bitset_t)0xfffffffbffffffff, (lmmp_bitset_t)0xfffffff7ffffffff,
    (lmmp_bitset_t)0xffffffefffffffff, (lmmp_bitset_t)0xffffffdfffffffff, (lmmp_bitset_t)0xffffffbfffffffff,
    (lmmp_bitset_t)0xffffff7fffffffff, (lmmp_bitset_t)0xfffffeffffffffff, (lmmp_bitset_t)0xfffffdffffffffff,
    (lmmp_bitset_t)0xfffffbffffffffff, (lmmp_bitset_t)0xfffff7ffffffffff, (lmmp_bitset_t)0xffffefffffffffff,
    (lmmp_bitset_t)0xffffdfffffffffff, (lmmp_bitset_t)0xffffbfffffffffff, (lmmp_bitset_t)0xffff7fffffffffff,
    (lmmp_bitset_t)0xfffeffffffffffff, (lmmp_bitset_t)0xfffdffffffffffff, (lmmp_bitset_t)0xfffbffffffffffff,
    (lmmp_bitset_t)0xfff7ffffffffffff, (lmmp_bitset_t)0xffefffffffffffff, (lmmp_bitset_t)0xffdfffffffffffff,
    (lmmp_bitset_t)0xffbfffffffffffff, (lmmp_bitset_t)0xff7fffffffffffff, (lmmp_bitset_t)0xfeffffffffffffff,
    (lmmp_bitset_t)0xfdffffffffffffff, (lmmp_bitset_t)0xfbffffffffffffff, (lmmp_bitset_t)0xf7ffffffffffffff,
    (lmmp_bitset_t)0xefffffffffffffff, (lmmp_bitset_t)0xdfffffffffffffff, (lmmp_bitset_t)0xbfffffffffffffff,
    (lmmp_bitset_t)0x7fffffffffffffff}

在文件 prime_table.c 第 95 行定义.

                                                           {
    (lmmp_bitset_t)0xfffffffffffffffe, (lmmp_bitset_t)0xfffffffffffffffd, (lmmp_bitset_t)0xfffffffffffffffb,
    (lmmp_bitset_t)0xfffffffffffffff7, (lmmp_bitset_t)0xffffffffffffffef, (lmmp_bitset_t)0xffffffffffffffdf,
    (lmmp_bitset_t)0xffffffffffffffbf, (lmmp_bitset_t)0xffffffffffffff7f, (lmmp_bitset_t)0xfffffffffffffeff,
    (lmmp_bitset_t)0xfffffffffffffdff, (lmmp_bitset_t)0xfffffffffffffbff, (lmmp_bitset_t)0xfffffffffffff7ff,
    (lmmp_bitset_t)0xffffffffffffefff, (lmmp_bitset_t)0xffffffffffffdfff, (lmmp_bitset_t)0xffffffffffffbfff,
    (lmmp_bitset_t)0xffffffffffff7fff, (lmmp_bitset_t)0xfffffffffffeffff, (lmmp_bitset_t)0xfffffffffffdffff,
    (lmmp_bitset_t)0xfffffffffffbffff, (lmmp_bitset_t)0xfffffffffff7ffff, (lmmp_bitset_t)0xffffffffffefffff,
    (lmmp_bitset_t)0xffffffffffdfffff, (lmmp_bitset_t)0xffffffffffbfffff, (lmmp_bitset_t)0xffffffffff7fffff,
    (lmmp_bitset_t)0xfffffffffeffffff, (lmmp_bitset_t)0xfffffffffdffffff, (lmmp_bitset_t)0xfffffffffbffffff,
    (lmmp_bitset_t)0xfffffffff7ffffff, (lmmp_bitset_t)0xffffffffefffffff, (lmmp_bitset_t)0xffffffffdfffffff,
    (lmmp_bitset_t)0xffffffffbfffffff, (lmmp_bitset_t)0xffffffff7fffffff, (lmmp_bitset_t)0xfffffffeffffffff,
    (lmmp_bitset_t)0xfffffffdffffffff, (lmmp_bitset_t)0xfffffffbffffffff, (lmmp_bitset_t)0xfffffff7ffffffff,
    (lmmp_bitset_t)0xffffffefffffffff, (lmmp_bitset_t)0xffffffdfffffffff, (lmmp_bitset_t)0xffffffbfffffffff,
    (lmmp_bitset_t)0xffffff7fffffffff, (lmmp_bitset_t)0xfffffeffffffffff, (lmmp_bitset_t)0xfffffdffffffffff,
    (lmmp_bitset_t)0xfffffbffffffffff, (lmmp_bitset_t)0xfffff7ffffffffff, (lmmp_bitset_t)0xffffefffffffffff,
    (lmmp_bitset_t)0xffffdfffffffffff, (lmmp_bitset_t)0xffffbfffffffffff, (lmmp_bitset_t)0xffff7fffffffffff,
    (lmmp_bitset_t)0xfffeffffffffffff, (lmmp_bitset_t)0xfffdffffffffffff, (lmmp_bitset_t)0xfffbffffffffffff,
    (lmmp_bitset_t)0xfff7ffffffffffff, (lmmp_bitset_t)0xffefffffffffffff, (lmmp_bitset_t)0xffdfffffffffffff,
    (lmmp_bitset_t)0xffbfffffffffffff, (lmmp_bitset_t)0xff7fffffffffffff, (lmmp_bitset_t)0xfeffffffffffffff,
    (lmmp_bitset_t)0xfdffffffffffffff, (lmmp_bitset_t)0xfbffffffffffffff, (lmmp_bitset_t)0xf7ffffffffffffff,
    (lmmp_bitset_t)0xefffffffffffffff, (lmmp_bitset_t)0xdfffffffffffffff, (lmmp_bitset_t)0xbfffffffffffffff,
    (lmmp_bitset_t)0x7fffffffffffffff};

◆ prime_short_table

const ushort prime_short_table[6542]

在文件 prime_table.c 第 351 行定义.

                                       {
    2,     3,     5,     7,     11,    13,    17,    19,    23,    29,    31,    37,    41,    43,    47,    53,
    59,    61,    67,    71,    73,    79,    83,    89,    97,    101,   103,   107,   109,   113,   127,   131,
    137,   139,   149,   151,   157,   163,   167,   173,   179,   181,   191,   193,   197,   199,   211,   223,
    227,   229,   233,   239,   241,   251,   257,   263,   269,   271,   277,   281,   283,   293,   307,   311,
    313,   317,   331,   337,   347,   349,   353,   359,   367,   373,   379,   383,   389,   397,   401,   409,
    419,   421,   431,   433,   439,   443,   449,   457,   461,   463,   467,   479,   487,   491,   499,   503,
    509,   521,   523,   541,   547,   557,   563,   569,   571,   577,   587,   593,   599,   601,   607,   613,
    617,   619,   631,   641,   643,   647,   653,   659,   661,   673,   677,   683,   691,   701,   709,   719,
    727,   733,   739,   743,   751,   757,   761,   769,   773,   787,   797,   809,   811,   821,   823,   827,
    829,   839,   853,   857,   859,   863,   877,   881,   883,   887,   907,   911,   919,   929,   937,   941,
    947,   953,   967,   971,   977,   983,   991,   997,   1009,  1013,  1019,  1021,  1031,  1033,  1039,  1049,
    1051,  1061,  1063,  1069,  1087,  1091,  1093,  1097,  1103,  1109,  1117,  1123,  1129,  1151,  1153,  1163,
    1171,  1181,  1187,  1193,  1201,  1213,  1217,  1223,  1229,  1231,  1237,  1249,  1259,  1277,  1279,  1283,
    1289,  1291,  1297,  1301,  1303,  1307,  1319,  1321,  1327,  1361,  1367,  1373,  1381,  1399,  1409,  1423,
    1427,  1429,  1433,  1439,  1447,  1451,  1453,  1459,  1471,  1481,  1483,  1487,  1489,  1493,  1499,  1511,
    1523,  1531,  1543,  1549,  1553,  1559,  1567,  1571,  1579,  1583,  1597,  1601,  1607,  1609,  1613,  1619,
    1621,  1627,  1637,  1657,  1663,  1667,  1669,  1693,  1697,  1699,  1709,  1721,  1723,  1733,  1741,  1747,
    1753,  1759,  1777,  1783,  1787,  1789,  1801,  1811,  1823,  1831,  1847,  1861,  1867,  1871,  1873,  1877,
    1879,  1889,  1901,  1907,  1913,  1931,  1933,  1949,  1951,  1973,  1979,  1987,  1993,  1997,  1999,  2003,
    2011,  2017,  2027,  2029,  2039,  2053,  2063,  2069,  2081,  2083,  2087,  2089,  2099,  2111,  2113,  2129,
    2131,  2137,  2141,  2143,  2153,  2161,  2179,  2203,  2207,  2213,  2221,  2237,  2239,  2243,  2251,  2267,
    2269,  2273,  2281,  2287,  2293,  2297,  2309,  2311,  2333,  2339,  2341,  2347,  2351,  2357,  2371,  2377,
    2381,  2383,  2389,  2393,  2399,  2411,  2417,  2423,  2437,  2441,  2447,  2459,  2467,  2473,  2477,  2503,
    2521,  2531,  2539,  2543,  2549,  2551,  2557,  2579,  2591,  2593,  2609,  2617,  2621,  2633,  2647,  2657,
    2659,  2663,  2671,  2677,  2683,  2687,  2689,  2693,  2699,  2707,  2711,  2713,  2719,  2729,  2731,  2741,
    2749,  2753,  2767,  2777,  2789,  2791,  2797,  2801,  2803,  2819,  2833,  2837,  2843,  2851,  2857,  2861,
    2879,  2887,  2897,  2903,  2909,  2917,  2927,  2939,  2953,  2957,  2963,  2969,  2971,  2999,  3001,  3011,
    3019,  3023,  3037,  3041,  3049,  3061,  3067,  3079,  3083,  3089,  3109,  3119,  3121,  3137,  3163,  3167,
    3169,  3181,  3187,  3191,  3203,  3209,  3217,  3221,  3229,  3251,  3253,  3257,  3259,  3271,  3299,  3301,
    3307,  3313,  3319,  3323,  3329,  3331,  3343,  3347,  3359,  3361,  3371,  3373,  3389,  3391,  3407,  3413,
    3433,  3449,  3457,  3461,  3463,  3467,  3469,  3491,  3499,  3511,  3517,  3527,  3529,  3533,  3539,  3541,
    3547,  3557,  3559,  3571,  3581,  3583,  3593,  3607,  3613,  3617,  3623,  3631,  3637,  3643,  3659,  3671,
    3673,  3677,  3691,  3697,  3701,  3709,  3719,  3727,  3733,  3739,  3761,  3767,  3769,  3779,  3793,  3797,
    3803,  3821,  3823,  3833,  3847,  3851,  3853,  3863,  3877,  3881,  3889,  3907,  3911,  3917,  3919,  3923,
    3929,  3931,  3943,  3947,  3967,  3989,  4001,  4003,  4007,  4013,  4019,  4021,  4027,  4049,  4051,  4057,
    4073,  4079,  4091,  4093,  4099,  4111,  4127,  4129,  4133,  4139,  4153,  4157,  4159,  4177,  4201,  4211,
    4217,  4219,  4229,  4231,  4241,  4243,  4253,  4259,  4261,  4271,  4273,  4283,  4289,  4297,  4327,  4337,
    4339,  4349,  4357,  4363,  4373,  4391,  4397,  4409,  4421,  4423,  4441,  4447,  4451,  4457,  4463,  4481,
    4483,  4493,  4507,  4513,  4517,  4519,  4523,  4547,  4549,  4561,  4567,  4583,  4591,  4597,  4603,  4621,
    4637,  4639,  4643,  4649,  4651,  4657,  4663,  4673,  4679,  4691,  4703,  4721,  4723,  4729,  4733,  4751,
    4759,  4783,  4787,  4789,  4793,  4799,  4801,  4813,  4817,  4831,  4861,  4871,  4877,  4889,  4903,  4909,
    4919,  4931,  4933,  4937,  4943,  4951,  4957,  4967,  4969,  4973,  4987,  4993,  4999,  5003,  5009,  5011,
    5021,  5023,  5039,  5051,  5059,  5077,  5081,  5087,  5099,  5101,  5107,  5113,  5119,  5147,  5153,  5167,
    5171,  5179,  5189,  5197,  5209,  5227,  5231,  5233,  5237,  5261,  5273,  5279,  5281,  5297,  5303,  5309,
    5323,  5333,  5347,  5351,  5381,  5387,  5393,  5399,  5407,  5413,  5417,  5419,  5431,  5437,  5441,  5443,
    5449,  5471,  5477,  5479,  5483,  5501,  5503,  5507,  5519,  5521,  5527,  5531,  5557,  5563,  5569,  5573,
    5581,  5591,  5623,  5639,  5641,  5647,  5651,  5653,  5657,  5659,  5669,  5683,  5689,  5693,  5701,  5711,
    5717,  5737,  5741,  5743,  5749,  5779,  5783,  5791,  5801,  5807,  5813,  5821,  5827,  5839,  5843,  5849,
    5851,  5857,  5861,  5867,  5869,  5879,  5881,  5897,  5903,  5923,  5927,  5939,  5953,  5981,  5987,  6007,
    6011,  6029,  6037,  6043,  6047,  6053,  6067,  6073,  6079,  6089,  6091,  6101,  6113,  6121,  6131,  6133,
    6143,  6151,  6163,  6173,  6197,  6199,  6203,  6211,  6217,  6221,  6229,  6247,  6257,  6263,  6269,  6271,
    6277,  6287,  6299,  6301,  6311,  6317,  6323,  6329,  6337,  6343,  6353,  6359,  6361,  6367,  6373,  6379,
    6389,  6397,  6421,  6427,  6449,  6451,  6469,  6473,  6481,  6491,  6521,  6529,  6547,  6551,  6553,  6563,
    6569,  6571,  6577,  6581,  6599,  6607,  6619,  6637,  6653,  6659,  6661,  6673,  6679,  6689,  6691,  6701,
    6703,  6709,  6719,  6733,  6737,  6761,  6763,  6779,  6781,  6791,  6793,  6803,  6823,  6827,  6829,  6833,
    6841,  6857,  6863,  6869,  6871,  6883,  6899,  6907,  6911,  6917,  6947,  6949,  6959,  6961,  6967,  6971,
    6977,  6983,  6991,  6997,  7001,  7013,  7019,  7027,  7039,  7043,  7057,  7069,  7079,  7103,  7109,  7121,
    7127,  7129,  7151,  7159,  7177,  7187,  7193,  7207,  7211,  7213,  7219,  7229,  7237,  7243,  7247,  7253,
    7283,  7297,  7307,  7309,  7321,  7331,  7333,  7349,  7351,  7369,  7393,  7411,  7417,  7433,  7451,  7457,
    7459,  7477,  7481,  7487,  7489,  7499,  7507,  7517,  7523,  7529,  7537,  7541,  7547,  7549,  7559,  7561,
    7573,  7577,  7583,  7589,  7591,  7603,  7607,  7621,  7639,  7643,  7649,  7669,  7673,  7681,  7687,  7691,
    7699,  7703,  7717,  7723,  7727,  7741,  7753,  7757,  7759,  7789,  7793,  7817,  7823,  7829,  7841,  7853,
    7867,  7873,  7877,  7879,  7883,  7901,  7907,  7919,  7927,  7933,  7937,  7949,  7951,  7963,  7993,  8009,
    8011,  8017,  8039,  8053,  8059,  8069,  8081,  8087,  8089,  8093,  8101,  8111,  8117,  8123,  8147,  8161,
    8167,  8171,  8179,  8191,  8209,  8219,  8221,  8231,  8233,  8237,  8243,  8263,  8269,  8273,  8287,  8291,
    8293,  8297,  8311,  8317,  8329,  8353,  8363,  8369,  8377,  8387,  8389,  8419,  8423,  8429,  8431,  8443,
    8447,  8461,  8467,  8501,  8513,  8521,  8527,  8537,  8539,  8543,  8563,  8573,  8581,  8597,  8599,  8609,
    8623,  8627,  8629,  8641,  8647,  8663,  8669,  8677,  8681,  8689,  8693,  8699,  8707,  8713,  8719,  8731,
    8737,  8741,  8747,  8753,  8761,  8779,  8783,  8803,  8807,  8819,  8821,  8831,  8837,  8839,  8849,  8861,
    8863,  8867,  8887,  8893,  8923,  8929,  8933,  8941,  8951,  8963,  8969,  8971,  8999,  9001,  9007,  9011,
    9013,  9029,  9041,  9043,  9049,  9059,  9067,  9091,  9103,  9109,  9127,  9133,  9137,  9151,  9157,  9161,
    9173,  9181,  9187,  9199,  9203,  9209,  9221,  9227,  9239,  9241,  9257,  9277,  9281,  9283,  9293,  9311,
    9319,  9323,  9337,  9341,  9343,  9349,  9371,  9377,  9391,  9397,  9403,  9413,  9419,  9421,  9431,  9433,
    9437,  9439,  9461,  9463,  9467,  9473,  9479,  9491,  9497,  9511,  9521,  9533,  9539,  9547,  9551,  9587,
    9601,  9613,  9619,  9623,  9629,  9631,  9643,  9649,  9661,  9677,  9679,  9689,  9697,  9719,  9721,  9733,
    9739,  9743,  9749,  9767,  9769,  9781,  9787,  9791,  9803,  9811,  9817,  9829,  9833,  9839,  9851,  9857,
    9859,  9871,  9883,  9887,  9901,  9907,  9923,  9929,  9931,  9941,  9949,  9967,  9973,  10007, 10009, 10037,
    10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163,
    10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303,
    10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459,
    10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627,
    10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771,
    10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937,
    10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087,
    11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251,
    11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399,
    11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551,
    11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731,
    11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887,
    11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011,
    12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161,
    12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323,
    12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473,
    12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589,
    12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739,
    12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907,
    12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033,
    13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177,
    13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337,
    13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499,
    13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681,
    13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799,
    13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933,
    13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143,
    14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323,
    14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461,
    14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627,
    14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753,
    14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887,
    14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073,
    15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217,
    15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331,
    15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473,
    15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643,
    15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773,
    15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919,
    15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087,
    16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249,
    16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427,
    16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603,
    16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747,
    16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927,
    16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053,
    17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231,
    17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389,
    17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519,
    17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683,
    17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863,
    17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989,
    18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143,
    18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289,
    18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439,
    18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593,
    18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793,
    18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009,
    19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183,
    19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373,
    19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469,
    19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603,
    19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793,
    19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961,
    19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101,
    20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233,
    20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393,
    20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551,
    20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747,
    20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903,
    20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059,
    21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193,
    21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, 21383,
    21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523,
    21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661,
    21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821,
    21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997,
    22003, 22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123,
    22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279,
    22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453,
    22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637,
    22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769,
    22777, 22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943,
    22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063,
    23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 23209, 23227,
    23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417,
    23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561, 23563, 23567, 23581, 23593,
    23599, 23603, 23609, 23623, 23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743,
    23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879,
    23887, 23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023,
    24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137,
    24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359,
    24371, 24373, 24379, 24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517,
    24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709,
    24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 24889, 24907,
    24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073,
    25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237,
    25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391,
    25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579,
    25583, 25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717,
    25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889,
    25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, 26017, 26021, 26029,
    26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203,
    26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357,
    26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 26501, 26513,
    26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699,
    26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833, 26839,
    26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987,
    26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143,
    27179, 27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361,
    27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539,
    27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737,
    27739, 27743, 27749, 27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827,
    27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001,
    28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181,
    28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387,
    28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541,
    28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649,
    28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793,
    28807, 28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961,
    28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147,
    29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303,
    29311, 29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443,
    29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633,
    29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837,
    29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029,
    30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181,
    30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341,
    30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529,
    30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703,
    30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859,
    30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039,
    31051, 31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183,
    31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321,
    31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517,
    31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687,
    31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 31847, 31849, 31859, 31873,
    31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057, 32059, 32063,
    32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213,
    32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 32359, 32363,
    32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503,
    32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 32611, 32621, 32633, 32647,
    32653, 32687, 32693, 32707, 32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831,
    32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987,
    32993, 32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149,
    33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329,
    33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479,
    33487, 33493, 33503, 33521, 33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613,
    33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767,
    33769, 33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 33911, 33923,
    33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141,
    34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297,
    34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457,
    34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603,
    34607, 34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 34747, 34757,
    34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939,
    34949, 34961, 34963, 34981, 35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083, 35089, 35099, 35107, 35111,
    35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291,
    35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449,
    35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593, 35597, 35603,
    35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839,
    35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 35977, 35983, 35993, 35999,
    36007, 36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161,
    36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341,
    36343, 36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527,
    36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677,
    36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809,
    36821, 36833, 36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947,
    36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139,
    37159, 37171, 37181, 37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 37313, 37321,
    37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493,
    37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 37579, 37589, 37591, 37607,
    37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813,
    37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993,
    37997, 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197,
    38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333,
    38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, 38557, 38561, 38567, 38569,
    38593, 38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713,
    38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873,
    38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047,
    39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209,
    39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 39341, 39343, 39359, 39367,
    39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541,
    39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727,
    39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869,
    39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039,
    40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213,
    40231, 40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433,
    40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597,
    40609, 40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813,
    40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949,
    40961, 40973, 40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, 41131, 41141,
    41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257,
    41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411, 41413, 41443, 41453,
    41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 41609, 41611,
    41617, 41621, 41627, 41641, 41647, 41651, 41659, 41669, 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771,
    41777, 41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, 41897, 41903, 41911, 41927, 41941,
    41947, 41953, 41957, 41959, 41969, 41981, 41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073,
    42083, 42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 42193, 42197, 42209, 42221, 42223, 42227,
    42239, 42257, 42281, 42283, 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359, 42373, 42379, 42391, 42397,
    42403, 42407, 42409, 42433, 42437, 42443, 42451, 42457, 42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509,
    42533, 42557, 42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677, 42683, 42689, 42697, 42701,
    42703, 42709, 42719, 42727, 42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, 42839, 42841,
    42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961, 42967, 42979, 42989, 43003, 43013,
    43019, 43037, 43049, 43051, 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 43201, 43207,
    43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427,
    43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609,
    43613, 43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783,
    43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 43943, 43951, 43961, 43963, 43969, 43973,
    43987, 43991, 43997, 44017, 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101, 44111, 44119,
    44123, 44129, 44131, 44159, 44171, 44179, 44189, 44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269,
    44273, 44279, 44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 44453, 44483, 44491, 44497,
    44501, 44507, 44519, 44531, 44533, 44537, 44543, 44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641,
    44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797,
    44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 44959, 44963,
    44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161,
    45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 45317, 45319, 45329, 45337,
    45341, 45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533,
    45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697,
    45707, 45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869,
    45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091,
    46093, 46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261,
    46271, 46273, 46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447,
    46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601,
    46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757,
    46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933,
    46957, 46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, 47143,
    47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309, 47317,
    47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501,
    47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 47639, 47653,
    47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807,
    47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969,
    47977, 47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179,
    48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371,
    48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527,
    48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679,
    48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823, 48847, 48857,
    48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033,
    49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193,
    49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367,
    49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529,
    49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697,
    49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853,
    49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033,
    50047, 50051, 50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, 50147, 50153, 50159,
    50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, 50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359,
    50363, 50377, 50383, 50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 50513, 50527, 50539, 50543,
    50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723, 50741, 50753,
    50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891, 50893, 50909, 50923, 50929,
    50951, 50957, 50969, 50971, 50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061, 51071, 51109, 51131, 51133,
    51137, 51151, 51157, 51169, 51193, 51197, 51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287,
    51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, 51421, 51427, 51431, 51437, 51439,
    51449, 51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593,
    51599, 51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713, 51719, 51721, 51749, 51767,
    51769, 51787, 51797, 51803, 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871, 51893, 51899, 51907, 51913,
    51929, 51941, 51949, 51971, 51973, 51977, 51991, 52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103,
    52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237, 52249, 52253, 52259, 52267,
    52289, 52291, 52301, 52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, 52489, 52501,
    52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609, 52627, 52631, 52639, 52667,
    52673, 52691, 52697, 52709, 52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817, 52837,
    52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999,
    53003, 53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101, 53113, 53117, 53129, 53147, 53149, 53161,
    53171, 53173, 53189, 53197, 53201, 53231, 53233, 53239, 53267, 53269, 53279, 53281, 53299, 53309, 53323, 53327,
    53353, 53359, 53377, 53381, 53401, 53407, 53411, 53419, 53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549,
    53551, 53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, 53653, 53657, 53681, 53693,
    53699, 53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881,
    53887, 53891, 53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993, 54001, 54011, 54013, 54037,
    54049, 54059, 54083, 54091, 54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269,
    54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, 54409, 54413,
    54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521, 54539, 54541, 54547, 54559,
    54563, 54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, 54721,
    54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877, 54881, 54907, 54917, 54919,
    54941, 54949, 54959, 54973, 54979, 54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103,
    55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291,
    55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 55469, 55487,
    55501, 55511, 55529, 55541, 55547, 55579, 55589, 55603, 55609, 55619, 55621, 55631, 55633, 55639, 55661, 55663,
    55667, 55673, 55681, 55691, 55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793, 55799, 55807, 55813, 55817,
    55819, 55823, 55829, 55837, 55843, 55849, 55871, 55889, 55897, 55901, 55903, 55921, 55927, 55931, 55933, 55949,
    55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053, 56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131,
    56149, 56167, 56171, 56179, 56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267, 56269, 56299, 56311, 56333,
    56359, 56369, 56377, 56383, 56393, 56401, 56417, 56431, 56437, 56443, 56453, 56467, 56473, 56477, 56479, 56489,
    56501, 56503, 56509, 56519, 56527, 56531, 56533, 56543, 56569, 56591, 56597, 56599, 56611, 56629, 56633, 56659,
    56663, 56671, 56681, 56687, 56701, 56711, 56713, 56731, 56737, 56747, 56767, 56773, 56779, 56783, 56807, 56809,
    56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897, 56909, 56911, 56921, 56923, 56929, 56941, 56951,
    56957, 56963, 56983, 56989, 56993, 56999, 57037, 57041, 57047, 57059, 57073, 57077, 57089, 57097, 57107, 57119,
    57131, 57139, 57143, 57149, 57163, 57173, 57179, 57191, 57193, 57203, 57221, 57223, 57241, 57251, 57259, 57269,
    57271, 57283, 57287, 57301, 57329, 57331, 57347, 57349, 57367, 57373, 57383, 57389, 57397, 57413, 57427, 57457,
    57467, 57487, 57493, 57503, 57527, 57529, 57557, 57559, 57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653,
    57667, 57679, 57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737, 57751, 57773, 57781, 57787, 57791, 57793,
    57803, 57809, 57829, 57839, 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923, 57943, 57947, 57973, 57977,
    57991, 58013, 58027, 58031, 58043, 58049, 58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129, 58147, 58151,
    58153, 58169, 58171, 58189, 58193, 58199, 58207, 58211, 58217, 58229, 58231, 58237, 58243, 58271, 58309, 58313,
    58321, 58337, 58363, 58367, 58369, 58379, 58391, 58393, 58403, 58411, 58417, 58427, 58439, 58441, 58451, 58453,
    58477, 58481, 58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, 58603, 58613, 58631, 58657, 58661, 58679,
    58687, 58693, 58699, 58711, 58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831, 58889, 58897, 58901,
    58907, 58909, 58913, 58921, 58937, 58943, 58963, 58967, 58979, 58991, 58997, 59009, 59011, 59021, 59023, 59029,
    59051, 59053, 59063, 59069, 59077, 59083, 59093, 59107, 59113, 59119, 59123, 59141, 59149, 59159, 59167, 59183,
    59197, 59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 59273, 59281, 59333, 59341, 59351, 59357, 59359,
    59369, 59377, 59387, 59393, 59399, 59407, 59417, 59419, 59441, 59443, 59447, 59453, 59467, 59471, 59473, 59497,
    59509, 59513, 59539, 59557, 59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, 59659, 59663, 59669,
    59671, 59693, 59699, 59707, 59723, 59729, 59743, 59747, 59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863,
    59879, 59887, 59921, 59929, 59951, 59957, 59971, 59981, 59999, 60013, 60017, 60029, 60037, 60041, 60077, 60083,
    60089, 60091, 60101, 60103, 60107, 60127, 60133, 60139, 60149, 60161, 60167, 60169, 60209, 60217, 60223, 60251,
    60257, 60259, 60271, 60289, 60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383, 60397, 60413, 60427, 60443,
    60449, 60457, 60493, 60497, 60509, 60521, 60527, 60539, 60589, 60601, 60607, 60611, 60617, 60623, 60631, 60637,
    60647, 60649, 60659, 60661, 60679, 60689, 60703, 60719, 60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779,
    60793, 60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913, 60917, 60919, 60923, 60937, 60943, 60953,
    60961, 61001, 61007, 61027, 61031, 61043, 61051, 61057, 61091, 61099, 61121, 61129, 61141, 61151, 61153, 61169,
    61211, 61223, 61231, 61253, 61261, 61283, 61291, 61297, 61331, 61333, 61339, 61343, 61357, 61363, 61379, 61381,
    61403, 61409, 61417, 61441, 61463, 61469, 61471, 61483, 61487, 61493, 61507, 61511, 61519, 61543, 61547, 61553,
    61559, 61561, 61583, 61603, 61609, 61613, 61627, 61631, 61637, 61643, 61651, 61657, 61667, 61673, 61681, 61687,
    61703, 61717, 61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837, 61843, 61861, 61871, 61879, 61909, 61927,
    61933, 61949, 61961, 61967, 61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039, 62047, 62053, 62057, 62071,
    62081, 62099, 62119, 62129, 62131, 62137, 62141, 62143, 62171, 62189, 62191, 62201, 62207, 62213, 62219, 62233,
    62273, 62297, 62299, 62303, 62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417, 62423, 62459, 62467, 62473,
    62477, 62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 62581, 62591, 62597, 62603, 62617, 62627, 62633,
    62639, 62653, 62659, 62683, 62687, 62701, 62723, 62731, 62743, 62753, 62761, 62773, 62791, 62801, 62819, 62827,
    62851, 62861, 62869, 62873, 62897, 62903, 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983, 62987, 62989,
    63029, 63031, 63059, 63067, 63073, 63079, 63097, 63103, 63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211,
    63241, 63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353, 63361, 63367, 63377, 63389,
    63391, 63397, 63409, 63419, 63421, 63439, 63443, 63463, 63467, 63473, 63487, 63493, 63499, 63521, 63527, 63533,
    63541, 63559, 63577, 63587, 63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 63649, 63659, 63667, 63671,
    63689, 63691, 63697, 63703, 63709, 63719, 63727, 63737, 63743, 63761, 63773, 63781, 63793, 63799, 63803, 63809,
    63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907, 63913, 63929, 63949, 63977, 63997, 64007, 64013, 64019,
    64033, 64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, 64153, 64157, 64171, 64187, 64189, 64217, 64223,
    64231, 64237, 64271, 64279, 64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381, 64399, 64403, 64433, 64439,
    64451, 64453, 64483, 64489, 64499, 64513, 64553, 64567, 64577, 64579, 64591, 64601, 64609, 64613, 64621, 64627,
    64633, 64661, 64663, 64667, 64679, 64693, 64709, 64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849,
    64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927, 64937, 64951, 64969, 64997, 65003, 65011, 65027,
    65029, 65033, 65053, 65063, 65071, 65089, 65099, 65101, 65111, 65119, 65123, 65129, 65141, 65147, 65167, 65171,
    65173, 65179, 65183, 65203, 65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309, 65323, 65327, 65353, 65357,
    65371, 65381, 65393, 65407, 65413, 65419, 65423, 65437, 65447, 65449, 65479, 65497, 65519, 65521};

被这些函数引用 lmmp_hyperfac_(), lmmp_is_prime_table_(), lmmp_next_prime_ulong_(), lmmp_odd_2factorial_ushort_(), lmmp_odd_multinomial_ushort_(), lmmp_odd_nCr_ushort_(), lmmp_odd_nPr_ushort_(), lmmp_prev_prime_ulong_(), lmmp_prime_cnt16_(), lmmp_prime_int_table_init_(), lmmp_primefac_(), lmmp_superfac_(), lmmp_trialdiv_() , 以及 lmmp_trialdiv_short_().

◆ r35711_mask_map

const lmmp_bitset_t r35711_mask_map[19]

初始值:

= {
    (lmmp_bitset_t)(0x93cf359a5b74dee9), (lmmp_bitset_t)(0x6badd25dadb36966), (lmmp_bitset_t)(0x6ed3cd279e4bb4b6),
    (lmmp_bitset_t)(0xb66d6cd35ba6bb59), (lmmp_bitset_t)(0xc976b2cde59a4f3c), (lmmp_bitset_t)(0x34de792dd2f9a6b7),
    (lmmp_bitset_t)(0xb34d6e96ede59b4b), (lmmp_bitset_t)(0xcf3696793ef259ad), (lmmp_bitset_t)(0xf4b34b669add25fa),
    (lmmp_bitset_t)(0xfa4bb5966d2cd2f9), (lmmp_bitset_t)(0x59a4f7c9e696cf35), (lmmp_bitset_t)(0x2d9a7b76976b2cdb),
    (lmmp_bitset_t)(0xd659f4bb49e7b2cd), (lmmp_bitset_t)(0xcf259a7b34d6e93e), (lmmp_bitset_t)(0xadd65dacb36b66d3),
    (lmmp_bitset_t)(0xd2dd279e4b3cb769), (lmmp_bitset_t)(0x696cdb5ba4bb5d66), (lmmp_bitset_t)(0x77b2eda59acf3c96),
    (lmmp_bitset_t)(0x0000000000000001)}

在文件 prime_table.c 第 338 行定义.

                                          {
    (lmmp_bitset_t)(0x93cf359a5b74dee9), (lmmp_bitset_t)(0x6badd25dadb36966), (lmmp_bitset_t)(0x6ed3cd279e4bb4b6),
    (lmmp_bitset_t)(0xb66d6cd35ba6bb59), (lmmp_bitset_t)(0xc976b2cde59a4f3c), (lmmp_bitset_t)(0x34de792dd2f9a6b7),
    (lmmp_bitset_t)(0xb34d6e96ede59b4b), (lmmp_bitset_t)(0xcf3696793ef259ad), (lmmp_bitset_t)(0xf4b34b669add25fa),
    (lmmp_bitset_t)(0xfa4bb5966d2cd2f9), (lmmp_bitset_t)(0x59a4f7c9e696cf35), (lmmp_bitset_t)(0x2d9a7b76976b2cdb),
    (lmmp_bitset_t)(0xd659f4bb49e7b2cd), (lmmp_bitset_t)(0xcf259a7b34d6e93e), (lmmp_bitset_t)(0xadd65dacb36b66d3),
    (lmmp_bitset_t)(0xd2dd279e4b3cb769), (lmmp_bitset_t)(0x696cdb5ba4bb5d66), (lmmp_bitset_t)(0x77b2eda59acf3c96),
    (lmmp_bitset_t)(0x0000000000000001)};

被这些函数引用 trial_div35711().

◆ wheel_mask

const lmmp_bitset_t wheel_mask[105]

static

在文件 prime_table.c 第 58 行定义.

                                             {
    (lmmp_bitset_t)0x916d129a64b4cb61, (lmmp_bitset_t)0x48b6894d325a65b0, (lmmp_bitset_t)0xa45b44a6992d32d8,
    (lmmp_bitset_t)0x522da2534c96996c, (lmmp_bitset_t)0x2916d129a64b4cb6, (lmmp_bitset_t)0x948b6894d325a65b,
    (lmmp_bitset_t)0xca45b44a6992d32d, (lmmp_bitset_t)0x6522da2534c96996, (lmmp_bitset_t)0xb2916d129a64b4cb,
    (lmmp_bitset_t)0x5948b6894d325a65, (lmmp_bitset_t)0x2ca45b44a6992d32, (lmmp_bitset_t)0x96522da2534c9699,
    (lmmp_bitset_t)0xcb2916d129a64b4c, (lmmp_bitset_t)0x65948b6894d325a6, (lmmp_bitset_t)0x32ca45b44a6992d3,
    (lmmp_bitset_t)0x996522da2534c969, (lmmp_bitset_t)0x4cb2916d129a64b4, (lmmp_bitset_t)0x265948b6894d325a,
    (lmmp_bitset_t)0x932ca45b44a6992d, (lmmp_bitset_t)0x4996522da2534c96, (lmmp_bitset_t)0xa4cb2916d129a64b,
    (lmmp_bitset_t)0xd265948b6894d325, (lmmp_bitset_t)0x6932ca45b44a6992, (lmmp_bitset_t)0xb4996522da2534c9,
    (lmmp_bitset_t)0x5a4cb2916d129a64, (lmmp_bitset_t)0x2d265948b6894d32, (lmmp_bitset_t)0x96932ca45b44a699,
    (lmmp_bitset_t)0xcb4996522da2534c, (lmmp_bitset_t)0x65a4cb2916d129a6, (lmmp_bitset_t)0x32d265948b6894d3,
    (lmmp_bitset_t)0x996932ca45b44a69, (lmmp_bitset_t)0x4cb4996522da2534, (lmmp_bitset_t)0xa65a4cb2916d129a,
    (lmmp_bitset_t)0xd32d265948b6894d, (lmmp_bitset_t)0x6996932ca45b44a6, (lmmp_bitset_t)0xb4cb4996522da253,
    (lmmp_bitset_t)0xda65a4cb2916d129, (lmmp_bitset_t)0x6d32d265948b6894, (lmmp_bitset_t)0x36996932ca45b44a,
    (lmmp_bitset_t)0x1b4cb4996522da25, (lmmp_bitset_t)0xda65a4cb2916d12,  (lmmp_bitset_t)0x86d32d265948b689,
    (lmmp_bitset_t)0xc36996932ca45b44, (lmmp_bitset_t)0x61b4cb4996522da2, (lmmp_bitset_t)0x30da65a4cb2916d1,
    (lmmp_bitset_t)0x186d32d265948b68, (lmmp_bitset_t)0xc36996932ca45b4,  (lmmp_bitset_t)0x861b4cb4996522da,
    (lmmp_bitset_t)0xc30da65a4cb2916d, (lmmp_bitset_t)0x6186d32d265948b6, (lmmp_bitset_t)0xb0c36996932ca45b,
    (lmmp_bitset_t)0xd861b4cb4996522d, (lmmp_bitset_t)0x6c30da65a4cb2916, (lmmp_bitset_t)0xb6186d32d265948b,
    (lmmp_bitset_t)0x5b0c36996932ca45, (lmmp_bitset_t)0x2d861b4cb4996522, (lmmp_bitset_t)0x96c30da65a4cb291,
    (lmmp_bitset_t)0xcb6186d32d265948, (lmmp_bitset_t)0x65b0c36996932ca4, (lmmp_bitset_t)0x32d861b4cb499652,
    (lmmp_bitset_t)0x996c30da65a4cb29, (lmmp_bitset_t)0x4cb6186d32d26594, (lmmp_bitset_t)0xa65b0c36996932ca,
    (lmmp_bitset_t)0xd32d861b4cb49965, (lmmp_bitset_t)0x6996c30da65a4cb2, (lmmp_bitset_t)0xb4cb6186d32d2659,
    (lmmp_bitset_t)0x5a65b0c36996932c, (lmmp_bitset_t)0x2d32d861b4cb4996, (lmmp_bitset_t)0x96996c30da65a4cb,
    (lmmp_bitset_t)0x4b4cb6186d32d265, (lmmp_bitset_t)0x25a65b0c36996932, (lmmp_bitset_t)0x92d32d861b4cb499,
    (lmmp_bitset_t)0xc96996c30da65a4c, (lmmp_bitset_t)0x64b4cb6186d32d26, (lmmp_bitset_t)0x325a65b0c3699693,
    (lmmp_bitset_t)0x992d32d861b4cb49, (lmmp_bitset_t)0x4c96996c30da65a4, (lmmp_bitset_t)0xa64b4cb6186d32d2,
    (lmmp_bitset_t)0xd325a65b0c369969, (lmmp_bitset_t)0x6992d32d861b4cb4, (lmmp_bitset_t)0x34c96996c30da65a,
    (lmmp_bitset_t)0x9a64b4cb6186d32d, (lmmp_bitset_t)0x4d325a65b0c36996, (lmmp_bitset_t)0xa6992d32d861b4cb,
    (lmmp_bitset_t)0x534c96996c30da65, (lmmp_bitset_t)0x29a64b4cb6186d32, (lmmp_bitset_t)0x94d325a65b0c3699,
    (lmmp_bitset_t)0x4a6992d32d861b4c, (lmmp_bitset_t)0x2534c96996c30da6, (lmmp_bitset_t)0x129a64b4cb6186d3,
    (lmmp_bitset_t)0x894d325a65b0c369, (lmmp_bitset_t)0x44a6992d32d861b4, (lmmp_bitset_t)0xa2534c96996c30da,
    (lmmp_bitset_t)0xd129a64b4cb6186d, (lmmp_bitset_t)0x6894d325a65b0c36, (lmmp_bitset_t)0xb44a6992d32d861b,
    (lmmp_bitset_t)0xda2534c96996c30d, (lmmp_bitset_t)0x6d129a64b4cb6186, (lmmp_bitset_t)0xb6894d325a65b0c3,
    (lmmp_bitset_t)0x5b44a6992d32d861, (lmmp_bitset_t)0x2da2534c96996c30, (lmmp_bitset_t)0x16d129a64b4cb618,
    (lmmp_bitset_t)0x8b6894d325a65b0c, (lmmp_bitset_t)0x45b44a6992d32d86, (lmmp_bitset_t)0x22da2534c96996c3};

被这些函数引用 lmmp_prime_int_table_init_().