什么叫质数很多人对这个问题比较感兴趣，下面让我们一起来看浠涔川/h1> ョ棣椤/a>ㄦspan class="new-icon">璁よㄦ/a>瑙棰浣甯府/a>璁よ㈤浼浜img class="triangle_icon" src="https://iknow-zhidao.bdimg.com/static/common-new/widget/menu/img/triangle.47e7008.svg" alt="">浼涓濯浣垮朵缁缁娉寰虹棰惧害ラ> 绫/nav>浠涔川/span>，希望可以帮助到你。
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2锛?3锛?5锛?7锛?11锛?
13锛?17锛?19锛?23锛?
29锛?31锛?37锛?41锛?
43锛?47锛?53锛?59锛?
61锛?67锛?71锛?73锛?
79锛?83锛?89锛?97
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77/1=77
77/7=11
210梅2=105
210梅3=70
210梅5=42
210梅6=35
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姣?涓?骇??????绉?绛??板?ㄨ???舵?板??涓???姣?渚???4N/[(6N+1)(6N-1)].
??????绉?绛??板ぇ灏??板????浜??告???
???舵?板??涓????存?т?绛??版?板??锛??存?х??涓?绛??版?板??锛??虫?т?绛??版?板?????虫?т?绛??版?板????瀹?浠???绾у????????澶?锛?姣?涓?涓?骇?????板????绛??伴?芥??????澶???????涓?绉?绛??扮骇????????板???芥????告?????浜х??????锛?骞朵互涓ょ骇????绛??拌?绂荤??涔?绉???涓ユ?煎?伴?????????ㄨ?绠?涓?绉??ュ共??绾у????绛??版?剁?ㄨ?涔?寮?姝ｅソ??互琛ㄧず瀹???娓????????崇郴????绉?绛??版?板??涔??撮?芥??浜??告?????????锛???????涓?绾у???撮?充?涓??板??.涓?涓??板??娌℃??娓???.??绉??板??涔??寸??娓???????涓??ㄨ?绠?涔?瓒冲???互璇???浜???
浜???涓?绱??板??甯??烘????姝ョ??SN?洪??br />
?????舵?板??????12锛?24锛?36?︹?︿互12涓洪??澧???涓?涓?釜?洪?达?杩??风???洪?村??N?洪?淬??SN?洪?翠???绉?绛??版?板??????姝ョ??锛???
12锛?1+2+3+?︹??N锛?=6NN+6N
?ㄨ??风???洪?村??????绾у????浠ヤ?????????绉?绛??版?板????绛??帮?骞舵病??姣?N绾у??ぇ???板??绛??帮?涓???绉?绛??扮??绾у??????ㄥ??姝ョ??锛???浠ヤ?绱??扮????甯?涔?????姝ョ????
????姣?涓?ぇ浜?S8?洪?村???芥??8涓?互涓???瀹??ㄤ?绛???br />
?ㄦ?涓?涓?N?洪?村????瀛?????绾у??????绉??板??绛??帮?姣?涓?绾у????扮??姣?渚?????互纭??锛??变?涓?涓?绾у????娓?????灏卞??互?夸互涓?寮??ヨ?绠?S8?洪?寸??瀹??ㄤ?绛??扮???冲?涓??般??
12*8*11/35*95/143*251/323*479/575*779/899*1151/1295*1593/1763*2111/2303=8.2768
?朵?姣?涓?涓?N?洪?村???ㄨ?绉??规?璁＄?.
?????洪?寸??澧?澶у??ㄤ?绛??拌?绠????伴??涔?浼?瓒??ヨ?澶?.浠ュ???戒?瓒?杩?8涓?
涓???璇?樊????
?ㄦ??涓ユ?间????寸??璇?樊?????规?锛?灏?SN?洪?存??缁???1,2,4,8,16......2^(N-1)??LN?洪???ㄦ?涓?涓?ぇ浜?S8??SN?洪?磋?绠??藉ぇ浜?8涓???ㄤ?绛????ㄦ?涓?涓?N?洪?撮?芥??2^N-1绾у????版?板??, 姣?绾х骇????4绉?绛??版?板??,姣?涓?绾у???绉?绛??扮?涓?娆¤?宸??????? .姣?涓?涓?N?洪?磋?宸???????*(2^N-1).
8*2^(N-1)-4*(2^N-1)=4
??涓ユ?间????村??澶т?L4???洪?翠??惰???4涓???ㄤ?绛??般??
?????荤?
?规??互涓???璁鸿?锛??ㄥぇ浜?S8?洪?存?涓?涓?N?洪?撮?芥??8涓?互涓???瀹??ㄤ?绛???
涓ユ?肩??涓????村??锛?澶т?L4??姣?涓?涓?N?洪?撮?借???澶?浜?4涓???瀹??ㄤ?绛??颁互涓???????
LN?洪?存??????澶???锛?瀹??ㄤ?绛??颁?瀛???绱??板????涓?瀵瑰???锛???浠ュ???绱??颁???????澶?????
杩?涓??????寰?????濞???琛ㄦ????
?ц川
????
璐ㄦ?板?锋??璁稿????圭???ц川锛?
锛?1锛?璐ㄦ????绾︽?板????涓や釜锛?1??p??
锛?2锛???绛??板??烘?????锛?浠讳?澶т?1?????舵?帮?瑕?涔???韩??川?帮?瑕?涔???互??瑙ｄ负??涓?川?颁?绉??涓?杩?绉???瑙ｆ?????????
锛?3锛?璐ㄦ?扮??涓??版??????????
锛?4锛?璐ㄦ?扮??涓??板??? ??????芥?般??
锛?5锛???涓烘??存?帮?? ? 涔??磋?冲???涓?涓?川?般??
锛?6锛???涓哄ぇ浜???绛?浜?2??姝ｆ?存?帮???? 涔??磋?冲???涓?涓?川?般??
锛?7锛??ヨ川??涓轰?瓒?杩?n( )????澶ц川?帮??? ??
锛?8锛?????澶т?10??璐ㄦ?颁腑锛?涓???板????1,3,7,9??
缂?绋?
????
?烘???ゆ????璺??
?ㄤ??????锛?瀵规??存??锛?濡?????? 涔??寸???????存?板?婚?わ?????娉??撮?わ???n涓鸿川?般??
璐ㄦ?板ぇ浜?绛?浜?2 涓??借?瀹???韩??1浠ュ????版?撮??br />
Python 浠ｇ??锛?
from math import sqrt
def is_prime(n):
if n == 1:
return False
for i in range(2, int(sqrt(n))+1):
if n % i == 0:
return False
return True
Java浠ｇ??锛?
1.
public static boolean testIsPrime2(int n){
if (n <= 3) {
return n > 1;
}
for(int i=2;i<n;i++){
if(n%i == 0)
return false;
}
return true;
}
/*浼?????*/
public static boolean testIsPrime3(int n){
if (n <= 3) {
return n > 1;
}
for(int i=2;i<=Math.sqrt(n);i++){
if(n%i == 0)
return false;
}
return true;
}
2.
public class Prime {
public static void main(String[] args) {
int a = 17; //?ゆ??7?????川??br />int c = 0;
for (int b = 2; b < a; b++) {
if (a % b != 0) {
c++;
}
}
if (c == a - 2) {
System.out.println(a + "??川??quot;);
} else {
System.out.println(a + "涓???川??quot;);
}
}
}
Php浠ｇ??锛?
function isPrime($n) {//TurkHackTeam AVP production
if ($n <= 3) {
return $n > 1;
} else if ($n % 2 === 0 || $n % 3 === 0) {
return false;
} else {
for ($i = 5; $i * $i <= $n; $i += 6) {
if ($n % $i === 0 || $n % ($i + 2) === 0) {
return false;
}
}
return true;
}
}
C#浠ｇ??锛?
using System;
??namespace 璁＄?璐ㄦ??br />??{
?? class Program
?? {
?? static void Main(string[] args)
?? {
?? for (int i = 2,j=1; i < 2100000000&&j<=1000; i++)//杈???1浜垮????????璐ㄦ?帮?j?у?跺?????000涓???
?? {
?? if (st(i))
?? {
?? Console.WriteLine("{0,-10}{1}",j,i);
?? j++;
?? }
?? }
?? }
?? static bool st(int n)//?ゆ???涓??????︿负璐ㄦ??br />?? {
?? int m = (int)Math.Sqrt(n);
?? for(int i=2;i<=m;i++)
{
if(n%i==0 && i!=n)
return false;
?? }
return true;
?? }
?? }
??}
??
C/C++浠ｇ??锛?
#include<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
const long long size=100000;//淇???ize???板?间互?瑰????缁?杈??虹??澶у?
long long zhishu[size/2];
void work(){//涓昏?绋?搴?
zhishu[1]=2;
long long k=2;
for(long long i=3;i<=size;i++){//??涓炬?涓???br />bool ok=1;
for(long long j=1;j<k;j++){//??涓惧凡缁?寰??扮??璐ㄦ??br />if(i%zhishu[j]==0){
ok=!ok;
break;
}
}
if(ok){
zhishu[k]=i;
cout<<"count"<<k<<' '<<i<<endl;
k++;
}
}
}
int main(){
freopen("zhishu.out","w",stdout);
cout<<"count1 2"<<endl;
work();
return 0;
}
璐ㄦ?帮?prime number锛???绉扮??帮???????涓???璐ㄦ?板?涔?涓哄?ㄥぇ浜?1?????舵?颁腑锛??や?1??瀹???韩浠ュ?涓??????朵????扮???扮О涓鸿川?般??
涓?????
璐ㄦ??br />
澶?????
prime number
????
绱???br />
渚?瀛?
2??3??5??7??11??13??17??19
璁ㄨ?????br />
???舵?伴??
涓??
????
绱??颁袱?у???
6锛?x锛?+-1=锛?pP锛?6涔?浠ュ??ㄤ?绛??板????1???瀵瑰???绱??般??
?朵腑锛?6锛?X-1=锛?P 6涔?浠ラ?存?т?绛??板????绛?浜??存?х??帮?
6X锛?+1=P锛?6涔?浠ラ?虫?т?绛??板??涓?1绛?浜??虫?х??般??
锛?X=/=6NM+-锛?M-N锛??存?т?绛??颁?绛?浜??存?т?涓?涓ゅ?锛?
X锛?=/=6NM+-锛?N+M锛??虫?т?绛??颁?绛?浜??虫?т?涓?涓ゅ???
锛?x)=/=6NM+-(M+-N) 瀹??ㄤ?绛??颁?绛?浜??撮?充?涓???寮?浜х?????般??
锛?N锛?M涓や釜???舵?帮?N=??M锛?
绱??板??甯?瑙?寰?
浠?6N锛?N+1锛?涓哄??浣?锛?????N??澧?澶э?绱??扮??涓??颁互娉㈡氮褰㈠?娓?娓?澧?澶???
瀛???璐ㄦ?颁????稿??????甯?瑙?寰???
浠ヤ?15涓??洪?村??璐ㄦ?板??瀛???璐ㄦ?扮??缁?璁℃?般??
S1?洪??????72锛???绱???8涓??瀛???绱???瀵广??锛?2??3涓?璁＄??ㄥ??锛????????版???涓???涔?绠??ㄥ???㈠?洪?淬??锛?
S2?洪??3????216锛???绱???7涓??瀛???绱???瀵广??
S3?洪??17????432锛???绱???6涓??瀛???绱???瀵广??
S4?洪??33????720锛???绱???5涓??瀛???绱???瀵广??
S5?洪??21????1080锛???绱???2涓??瀛???绱???瀵广??
S6?洪??081????1512锛?绱???0涓??瀛???绱???瀵广??
S7?洪??513????2016锛?绱???5涓??瀛???绱???1瀵广??
S8?洪??017????2592锛?绱???2涓??瀛???绱???2瀵广??
S9?洪??593????3240锛?绱???0涓??瀛???绱???0瀵广??
S10?洪??241????3960锛?绱???1涓??瀛???绱???8瀵广??
S11?洪??961????4752绱???2涓??瀛???绱???7瀵广??
S12?洪??752????5616绱???8涓??瀛???绱???3瀵广??
S13?洪??617????6552绱???08涓??瀛???绱???4瀵广??
S14?洪??553????7560绱???13涓??瀛???绱???9瀵广??
S15?洪??561????8640绱???16涓??瀛???绱???4瀵广??锛?浠ヤ?娌℃???℃?锛????芥??璇?樊??锛?
绱??板??甯?瑙?寰??????帮?璁稿?绱??伴?????互瑙ｅ??br />
璐ㄦ?扮??涓??版????绌风????娆у????寰???????浣???????涓???涓?涓???哥??璇?????瀹?浣跨?ㄤ?璇???甯哥?ㄧ???规?锛???璇?娉????蜂?璇???濡?涓?锛???璁捐川?板??????????n涓??浠?灏??板ぇ渚?娆℃????涓?1锛?p2锛??︹?︼?pn锛?璁?=p1?p2??︹?γ?pn锛??ｄ?锛?pn??涓?????版????涓?????般??
濡???pn??涓?涓虹??帮???pn??涓?瑕?澶т?p1锛?p2锛??︹?︼?pn锛???浠ュ?涓??ㄩ?ｄ???璁剧??绱??伴????涓???
濡???pn??涓?涓哄???帮???涓轰换浣?涓?涓????伴?藉??互??瑙ｄ负??涓???扮??绉????N??N+1????澶у??害?版??锛???浠?n??涓?涓????借?p1锛?p2锛??︹?︼?pn?撮?わ???浠ヨ????板??瑙ｅ??扮??绱????拌???涓??ㄥ??璁剧??绱??伴????涓???
??姝ゆ??璁鸿??版????拌??????帮??芥???崇???ㄥ??璁剧??????涓???颁?澶?杩?瀛??ㄧ???朵?绱??般????浠ュ????????璁句???绔???涔?灏辨???锛?绱??版????绌峰?涓???
?朵??板?瀹剁??轰?涓?浜?涓?????璇?????娆ф???╃?ㄩ??煎?芥?拌???浜??ㄩ?ㄧ??扮?????颁????????ｇ??锛??╂???孤峰?榛???璇????翠负绠?娲?锛?????路寮????浼??煎???ㄦ????瀛﹀??浠ヨ?????
????
瀵逛?涓?瀹????村????绱??版?扮????璁＄?
灏界??翠釜绱??版????绌风??锛?浠??舵??浜轰?????100锛?000浠ヤ???澶?灏?涓???帮???锛???涓?涓????虹??100浣??板?澶у???芥????帮?????绱??板?????互??绛?姝ら?????
绱??板??甯?瑙?寰??????帮?璁稿?绱??伴?????互瑙ｅ?炽??
?ㄤ?涓?ぇ浜?1??????瀹???2??涔??达??冲?洪??a, 2a]涓??蹇?瀛??ㄨ?冲?涓?涓???般??
瀛??ㄤ换???垮害??绱??扮?宸??板????锛??兼?????跺?茶僵锛?2004骞?1]锛?
涓?涓??舵?板??互????涓や釜???颁???锛??朵腑姣?涓?涓????伴?芥??澶?????9涓?川???般??锛?????板?瀹跺???锛?1920骞达?
涓?涓??舵?板?瀹???互????涓?涓?川?板??涓?涓?涓??????帮??朵腑???扮????瀛?涓??版??涓?????锛???灏硷?1948骞达?
涓?涓??舵?板?瀹???互????涓?涓?川?板??涓?涓?涓???澶???涓???瀛???缁??????????般?????ワ???浜虹?绉拌?缁???涓 (1 + 5)(涓??芥??挎?锛?1968骞?
涓?涓?????澶у?舵?板?瀹???互????涓?涓???板??涓?涓?涓???澶???涓?川??瀛???缁??????????般??绠?绉颁负 (1 + 2)(涓??介????鼎)[2]
???
????
?ュ痉宸磋但???筹????︽?涓?ぇ浜?2???舵?伴?藉??????涓や釜绱??颁???锛?
瀛???绱??扮???筹?瀛???绱??板氨??樊涓???绱??板?锛?渚?濡?11??13?????﹀??ㄦ??绌峰???瀛???绱??帮?
??娉㈤?ｅ??板???????﹀??ㄦ??绌峰???绱??帮?
???︽????绌峰?涓???姊?妫???帮?
??2涓?锛?n+1锛?2涔??存???︽???n灏辨??涓?涓???帮?
???﹀??ㄦ??绌蜂釜褰㈠?濡?X2+1绱??帮?
榛??肩????br />
瀛???绱??版??????澶???璇???
?抽???:瀹??ㄤ?绛???SN?洪??LN?洪??
涓???绱??颁袱?у???
澶т?3??绱??板????甯???n-1??6n+1涓ゆ?板??涓???锛?n??0???舵?帮?涓???锛?
6n-1?板??涓??????板???存?у???帮??朵腑??绱??板???存?х??帮?6n+1?板??涓??????板???虫?у???帮??朵腑??绱??板???虫?х??般??
?存?у???板???
6[6NM+锛?M-N锛?]-1=锛?6N+1锛?锛?6M-1锛?锛?N M涓や釜??0???舵?帮?N=?? M锛?涓???锛?
6[6NM-锛?M-N锛?]-1=锛?6N-1锛?锛?6M+1锛?
??n-1?板??涓?????杩?涓ょ????帮?浣?涓?灏辨???存?х??颁?锛???浠ュ氨???存?х??板???
6NM+-锛?M-N锛?=/=x锛??存?т?绛??帮?
6x-1=q锛??存?х??帮?
?虫?у???板???
6[6NM+锛?N+M锛?]+1=锛?6N+1锛?锛?6M+1锛?
6[6NM-锛?N+M锛?]+1=锛?6N-1锛?锛?6M-1锛?
??n+1?板??涓?????杩?涓ょ????帮?浣?涓?灏辨???虫?х??颁?锛???浠ュ氨???虫?х??板???
6NM+-锛?N+M锛?=/=X锛??虫?т?绛??帮?
6X+1=P锛??虫?х??帮?
浜???涓?瀛???绱??扮?稿?搴???瀹??ㄤ?绛???br />
瀹??ㄤ?绛???X),瀹????绛?浜??存?т?涓?涓ゅ?锛?涔?涓?绛?浜??虫?т?涓?涓ゅ???
(X)=/=6NM+-(M+-N)
????6(X)+1=P 6(X)-1=q 锛?p??1?借?6?撮?ょ??绱??帮?q??1?借?6?撮?ょ??绱??帮?涓???锛?
涓?涓???ㄤ?绛??版??浜х?????存?х??????虫?х???灏辨???瀵瑰???绱???
骞朵?瀹??ㄤ?绛??颁?瀛???绱??版???涓?瀵瑰???.
涓????撮?冲??绉?绛??板?ㄨ???舵?板??涓?????甯?姒???br />
6NM+锛?M-N锛?=?存?т?绛???NM-锛?M-N锛?=?存?т?绛???br />
6NM+锛?N+M锛?=?虫?т?绛???NM-锛?N+M锛?=?虫?т?绛???br />
涓轰???娓?瀹?浠??ㄨ???舵?颁腑??甯????碉?????寮?涓???N??骇????瀛??帮?M????????瀛??般??
??绉?绛??扮??姣?涓?涓?骇??????灏?绛??伴?藉??NN+-锛?N+N锛????淬??
姣?涓?绾у????涓?绛??扮?搁?讳袱绛??拌?绂绘??n+1锛??ㄨ???舵?板??涓??渚???/锛?6n+1锛?锛?涓ょ?涓?绛??版?涓?骇????姣?渚???璁℃??/锛?6n+1锛?锛?锛?浣?瀹??????ュ?浜?杩?涓??渚???姣?涓?绾у????搴??ㄩ?芥病??杩?涓?骇????涓?绛??帮?涓?绛??颁?涓??风?????点??锛?
姣?涓?绾у????涓?绛??