どの区間[n,n+600]にも必ず素数が2個含まれるというわけではない(出力例はgmp-5.1.3を使用)

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素数の新定理発見　極端な偏りなく分布　米英数学者「夢のような成果」 ― スポニチ Sponichi Annex 社会

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output_example.txt

YUKI.N>prime600 1024 10
# seed = 1393395669
# bits = 1024

60
1488
628
1170
1900
120
246
1842
162
1314

# max diff = 1900

prime600.c

#include <stdio.h>
#include <time.h>
#include <gmp.h>

int main(int argc,char* argv[]) {
	int bits=1024;
	int iteration=100;
	int i;
	unsigned long int seed=0;
	mpz_t now,next,diff,max;
	gmp_randstate_t rns;
	FILE* fp;
	if((fp=fopen("/dev/urandom","rb"))!=NULL) {
		if(fread((void*)&seed,sizeof(unsigned long int),1,fp)==0) {
			seed=(unsigned long int)time(NULL);
		}
	} else {
		seed=(unsigned long int)time(NULL);
	}
	if(argc>=2)sscanf(argv[1],"%d",&bits);
	if(argc>=3)sscanf(argv[2],"%d",&iteration);
	gmp_randinit_default(rns);
	gmp_randseed_ui(rns,seed);
	mpz_inits(now,next,diff,max,NULL);
	mpz_set_ui(max,0);
	printf("# seed = %lu\n",seed);
	printf("# bits = %d\n",bits);
	putchar('\n');
	for(i=0;i<iteration;i++) {
		mpz_urandomb(now,rns,bits);
		mpz_nextprime(now,now);
		mpz_nextprime(next,now);
		mpz_sub(diff,next,now);
		mpz_out_str(stdout,10,diff);
		putchar('\n');
		if(mpz_cmp(diff,max)>0) {
			mpz_set(max,diff);
		}
	}
	fputs("\n# max diff = ",stdout);
	mpz_out_str(stdout,10,max);
	putchar('\n');
	gmp_randclear(rns);
	mpz_clears(now,next,diff,max,NULL);
	return 0;
}