Redraiment猜想

Description

redraiment在家极度无聊，于是找了张纸开始统计素数的个数。设函数f(n)返回从1->n之间素数的个数。 redraiment发现: f(1) = 0 f(10) = 4 f(100) = 25 ... 满足g(m) = 17 * m2 / 3 - 22 * m / 3 + 5 / 3 其中m为n的位数。他很激动，是不是自己发现了素数分布的规律了！请你设计一个程序，求出1->n范围内素数的个数，来验证redraiment是不是正确的，也许还可以得诺贝尔奖呢。^_^

Input

输入包括多组数据。每组数据仅有一个整数n (1≤n≤100000000)。输入以０结束

Output

对于每组数据输入，输出一行，为1->n(包括n)之间的素数的个数。

解题思路：

输入n 输出n以内的素数个数我们很容易想到我们用埃氏筛选法筛选出素数然后再统计一个前缀和就ok了

但是这个题 n的范围是1e8 数组没办法开这么大所以这个方法不行了

我们只好换一个方法想到了分块打表

把1e8 分成每10000 为一块我们统计出每隔一万个数字的素数个数

（就是把1到一万的素数个数存下来一万到两万存下来两万到三万存下来。。。。以此类推）

那么我们就把1e8分成了（1e8/10000）=1e4 块

我们做一个前缀和得到这一万个数的前缀和 每个数代表的就是 n*10000 以内的素数个数

那么每次询问我们就找到最近的10000的倍数然后暴力统计剩下的素数个数就好了

方法呢就是这个方法

但是如果你用最普通的方法打表可能需要好几十分钟甚至个把小时才能打出来表

即使你说你有时间硬要用朴素法杠这道题那么就算你花一个小时打出了表下边还是会错的

我用的是米勒拉宾素性检测算法来打表打表倒是很快打了三四分钟就出来了

但是这一万个数赋值给数组然后交题提示说 code is too long !

好吧看来分的块太小的 改成每块十万打表出来1000个数 这下就ok了

但是这下你每次暴力处理的数据就是十万了（那么如果你用朴素法判断素数还是会超时所以还是得米勒拉宾。。）

关于米勒拉宾算法米勒拉宾算法详解+代码

AC代码

#include<stdio.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
//分块打表得到的1000个数
int a[1007]={0,9592,17984,25997,33860,41538,49098,56543,63951,71274,78498,85714,92938,100021,107126,114155,121127,128141,135072,142029,148933,155805,162662,169511,176302,183072,189880,196645,203362,210109,216816,223492,230209,236900,243539,250150,256726,263397,269987,276611,283146,289774,296314,302824,309335,315948,322441,328964,335439,341992,348513,354971,361407,367900,374362,380800,387202,393606,399993,406429,412849,419246,425648,432073,438410,444757,451159,457497,463872,470283,476648,483015,489319,495666,501962,508261,514565,520910,527154,533506,539777,546024,552319,558597,564877,571119,577439,583714,590006,596222,602489,608672,614917,621177,627400,633578,639851,646054,652265,658445,664579,670820,676970,683178,689382,695609,701795,708007,714154,720341,726517,732707,738873,745001,751131,757288,763455,769639,775773,781906,788060,794149,800285,806435,812601,818703,824801,830940,837099,843192,849252,855281,861401,867482,873606,879640,885698,891833,897938,904057,910077,916147,922193,928293,934441,940455,946551,952566,958651,964695,970704,976761,982776,988851,994839,1000862,1006966,1013012,1019012,1025092,1031130,1037119,1043113,1049172,1055139,1061198,1067185,1073198,1079266,1085243,1091314,1097360,1103258,1109288,1115323,1121389,1127407,1133364,1139344,1145305,1151367,1157275,1163205,1169267,1175214,1181158,1187148,1193122,1199102,1205065,1211050,1216988,1222953,1228861,1234873,1240833,1246718,1252693,1258685,1264617,1270607,1276577,1282513,1288409,1294356,1300243,1306226,1312179,1318125,1324046,1329943,1335881,1341795,1347749,1353661,1359631,1365511,1371432,1377385,1383291,1389261,1395148,1401007,1406874,1412758,1418640,1424606,1430531,1436398,1442335,1448221,1454144,1460019,1465935,1471822,1477731,1483609,1489509,1495350,1501220,1507122,1512992,1518898,1524831,1530729,1536569,1542459,1548366,1554245,1560093,1565927,1571812,1577649,1583439,1589324,1595177,1601049,1606876,1612775,1618668,1624527,1630379,1636202,1642052,1647911,1653807,1659690,1665517,1671330,1677200,1683065,1688960,1694762,1700558,1706405,1712204,1718134,1723913,1729764,1735590,1741430,1747297,1753058,1758964,1764767,1770613,1776430,1782260,1788065,1793863,1799676,1805472,1811272,1817102,1822944,1828703,1834530,1840359,1846115,1852006,1857859,1863719,1869536,1875367,1881199,1886923,1892785,1898632,1904396,1910248,1915979,1921714,1927488,1933290,1939089,1944833,1950638,1956440,1962184,1968015,1973815,1979564,1985372,1991162,1996958,2002749,2008561,2014337,2020103,2025864,2031667,2037385,2043192,2048989,2054802,2060577,2066324,2072084,2077862,2083678,2089379,2095092,2100791,2106544,2112215,2118001,2123788,2129473,2135232,2141013,2146775,2152470,2158233,2163998,2169775,2175518,2181266,2187043,2192806,2198505,2204262,2210026,2215731,2221543,2227279,2233036,2238778,2244473,2250226,2255897,2261623,2267395,2273189,2278857,2284633,2290350,2296101,2301840,2307562,2313254,2318966,2324728,2330509,2336299,2342005,2347727,2353448,2359142,2364953,2370696,2376402,2382120,2387828,2393630,2399359,2405101,2410827,2416624,2422305,2427981,2433654,2439371,2445078,2450819,2456577,2462273,2467902,2473603,2479409,2485075,2490756,2496476,2502205,2507850,2513534,2519246,2524898,2530575,2536286,2542018,2547620,2553305,2559020,2564807,2570490,2576200,2581841,2587550,2593245,2598870,2604535,2610226,2615907,2621566,2627281,2632997,2638710,2644301,2649982,2655643,2661384,2667036,2672702,2678429,2684053,2689717,2695450,2701159,2706858,2712494,2718160,2723886,2729508,2735255,2740985,2746679,2752380,2758056,2763691,2769407,2775053,2780731,2786355,2791974,2797652,2803324,2808976,2814698,2820355,2826040,2831693,2837271,2842995,2848642,2854302,2859963,2865596,2871207,2876824,2882545,2888144,2893763,2899408,2905025,2910714,2916338,2921977,2927626,2933208,2938896,2944531,2950188,2955834,2961491,2967186,2972862,2978556,2984185,2989825,2995509,3001134,3006727,3012361,3018013,3023649,3029296,3034973,3040593,3046241,3051875,3057494,3063082,3068712,3074341,3080043,3085615,3091310,3096885,3102560,3108210,3113843,3119506,3125086,3130647,3136324,3141927,3147521,3153171,3158801,3164431,3170052,3175695,3181277,3186966,3192556,3198119,3203713,3209317,3214948,3220576,3226203,3231825,3237408,3242981,3248574,3254129,3259801,3265418,3271006,3276528,3282200,3287879,3293449,3299022,3304658,3310266,3315819,3321475,3327111,3332731,3338330,3343958,3349661,3355218,3360782,3366339,3371952,3377626,3383274,3388854,3394435,3400038,3405629,3411294,3416918,3422475,3428077,3433631,3439220,3444790,3450336,3455970,3461542,3467134,3472756,3478304,3483945,3489523,3495161,3500795,3506314,3511921,3517468,3523035,3528547,3534167,3539757,3545331,3550955,3556550,3562115,3567677,3573237,3578833,3584453,3590054,3595578,3601204,3606812,3612449,3618045,3623569,3629084,3634647,3640201,3645798,3651314,3656875,3662428,3668016,3673600,3679207,3684787,3690317,3695916,3701487,3707015,3712576,3718206,3723740,3729306,3734871,3740435,3746021,3751585,3757186,3762745,3768288,3773903,3779511,3785086,3790643,3796205,3801803,3807345,3812898,3818389,3823937,3829432,3835002,3840554,3846130,3851637,3857201,3862694,3868404,3873874,3879427,3884940,3890503,3896123,3901727,3907301,3912842,3918498,3924009,3929584,3935172,3940685,3946251,3951767,3957296,3962821,3968429,3973996,3979592,3985158,3990671,3996215,4001767,4007342,4012851,4018394,4023969,4029474,4035037,4040549,4046077,4051617,4057149,4062674,4068213,4073713,4079200,4084816,4090382,4095945,4101517,4107066,4112568,4118064,4123596,4129144,4134695,4140216,4145831,4151356,4156813,4162309,4167847,4173373,4178911,4184419,4189971,4195467,4201083,4206661,4212176,4217594,4223154,4228658,4234244,4239815,4245417,4250930,4256409,4261935,4267454,4272940,4278523,4284089,4289594,4295059,4300577,4306121,4311581,4317182,4322713,4328194,4333750,4339254,4344668,4350186,4355687,4361240,4366707,4372244,4377733,4383283,4388818,4394304,4399810,4405341,4410890,4416431,4421976,4427436,4432986,4438498,4444056,4449611,4455090,4460606,4466047,4471575,4477022,4482514,4487991,4493463,4498996,4504535,4510062,4515582,4521040,4526576,4532043,4537551,4543006,4548526,4554051,4559544,4565039,4570576,4576018,4581510,4586928,4592508,4597955,4603527,4608972,4614444,4619984,4625476,4630913,4636426,4641948,4647416,4652931,4658438,4663931,4669382,4674878,4680315,4685896,4691370,4696907,4702361,4707853,4713384,4718907,4724409,4730004,4735525,4740992,4746465,4752027,4757470,4762951,4768393,4773922,4779430,4784949,4790384,4795812,4801310,4806760,4812305,4817816,4823303,4828831,4834317,4839761,4845183,4850683,4856110,4861617,4867093,4872513,4878005,4883558,4889139,4894521,4899985,4905417,4910914,4916472,4921878,4927326,4932826,4938246,4943731,4949180,4954637,4960077,4965591,4971111,4976569,4982049,4987530,4993012,4998470,5003979,5009407,5014862,5020351,5025823,5031315,5036777,5042265,5047761,5053180,5058696,5064123,5069614,5075035,5080463,5085953,5091415,5096846,5102346,5107832,5113355,5118791,5124356,5129773,5135232,5140593,5146076,5151557,5157086,5162565,5167986,5173502,5178996,5184377,5189833,5195242,5200653,5206040,5211514,5216954,5222465,5227980,5233446,5238910,5244409,5249827,5255274,5260749,5266190,5271659,5277103,5282580,5288120,5293544,5298991,5304404,5309926,5315370,5320738,5326237,5331696,5337154,5342570,5348001,5353469,5358873,5364374,5369836,5375312,5380681,5386095,5391573,5396981,5402486,5407914,5413340,5418747,5424169,5429670,5435104,5440645,5446042,5451511,5456922,5462365,5467823,5473280,5478704,5484246,5489749,5495144,5500596,5506042,5511482,5516967,5522414,5527834,5533229,5538712,5544201,5549568,5555003,5560413,5565874,5571310,5576734,5582247,5587668,5593068,5598565,5604003,5609349,5614798,5620231,5625732,5631229,5636652,5642089,5647525,5652996,5658353,5663763,5669215,5674668,5680084,5685585,5691004,5696344,5701777,5707123,5712622,5718013,5723380,5728833,5734258,5739704,5745162,5750539,5756001,5761455};
ll mul(ll a,ll b,ll mod){//高精度a%=mod;b%=mod;ll c=(long double)a*b/mod;ll ans=a*b-c*mod;return (ans%mod+mod)%mod;
}
ll pow_mod(ll x,ll n,ll mod){//快速幂ll res=1;while(n){if(n&1)res=mul(res,x,mod);x=mul(x,x,mod);n>>=1;}return (res+mod)%mod;
}
bool Miller_Rabbin(ll a,ll n){ll s=n-1,r=0;while((s&1)==0){s>>=1;r++;}ll k=pow_mod(a,s,n);if(k==1)return true;for(int i=0;i<r;i++,k=k*k%n){if(k==n-1)return true;}return false;
}
bool isprime(ll n){if(n==1||n==0)return false;ll times=7;ll prime[100]={2,3,5,7,11,233,331};for(int i=0;i<times;i++){if(n==prime[i])return true;if(Miller_Rabbin(prime[i],n)==false)return false;}return true;
}
int main(){/* 分块打表代码ll cnt=0;//freopen("C:\\test.txt","w",stdout);printf("0,");for(ll i=1;i<=1e8;i+=100000){for(ll j=i;j<=i+100000-1;j++){if(isprime(j)){cnt++;}}printf("%lld,",cnt);}
*/ll n;while(scanf("%lld",&n)&&n!=0){ll f=n/100000;ll cnt=0;for(int i=100000*f+1;i<=n;i++){if(isprime(i)){cnt++;}}printf("%lld\n",cnt+a[f]);}return 0;
}