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看上去还挺好玩的，不过考虑到身份证检验码，很有可能会出现问题。果然，我的计算结果显示那天只有两个可能的情况：
身份证只有两位数看起来还挺容易做到的……那回文数呢？感觉上挺不容易的？毕竟要同时符合校验规则、省份、日期等等。不如用代码算一下？看看能有多少。网上找到的算法对前六位地区的验证做得似乎不够详细，于是我自己从民政部的网站上下载了[1990](http://www.mca.gov.cn/article/sj/tjbz/a/201713/201708041018.html)/[2000](http://www.mca.gov.cn/article/sj/tjbz/a/201713/201708220923.html)/[2010](http://www.mca.gov.cn/article/sj/tjbz/a/201713/201708220946.html)和最新[2019年11月](http://www.mca.gov.cn/article/sj/xzqh/2019/2019/201912251506.html)的数据，编码了前六位的各种可能情况放进代码里
using System;
using System.Numerics;
using System.Collections.Generic;
public class Program
{
//copied from https://blog.csdn.net/u013871100/article/details/51869315
private static bool CheckIDCard18(string Id)
{
long n = 0;
if (long.TryParse(Id.Remove(17), out n) == false || n < Math.Pow(10, 16) || long.TryParse(Id.Replace('x', '0').Replace('X', '0'), out n) == false)
{
return false;//数字验证
}
//string address = "11x22x35x44x53x12x23x36x45x54x13x31x37x46x61x14x32x41x50x62x15x33x42x51x63x21x34x43x52x64x65x71x81x82x91";
//if (Array.IndexOf(region, Id.Remove(6)) == -1)
//{
// return false;//省份验证
//}
string birth = Id.Substring(6, 8).Insert(6, "-").Insert(4, "-");
DateTime time = new DateTime();
if (DateTime.TryParse(birth, out time) == false)
{
return false;//生日验证
}
string[] arrVarifyCode = ("1,0,x,9,8,7,6,5,4,3,2").Split(',');
string[] Wi = ("7,9,10,5,8,4,2,1,6,3,7,9,10,5,8,4,2").Split(',');
char[] Ai = Id.Remove(17).ToCharArray();
int sum = 0;
for (int i = 0; i < 17; i++)
{
sum += int.Parse(Wi[i]) * int.Parse(Ai[i].ToString());
}
int y = -1;
Math.DivRem(sum, 11, out y);
if (arrVarifyCode[y] != Id.Substring(17, 1).ToLower())
{
return false;//校验码验证
}
return true;//符合GB11643-1999标准
}
//https://www.dotnetperls.com/reverse-string
public static string ReverseStringDirect(string s)
{
char[] array = new char[s.Length];
int forward = 0;
for (int i = s.Length - 1; i >= 0; i--)
{
array[forward++] = s[i];
}
return new string(array);
}
public static void Main()
{
//region列表因为太长，放在文章最后
//int[] year = new int[] { 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, };
List<int> year = new List<int>();
for (int i = 192; i < 999; i++)
{
year.Add(i);
}
foreach (var regionItem in region)
{
foreach (var yearItem in year)
{
string s = regionItem.ToString() + yearItem.ToString() + ReverseStringDirect(regionItem.ToString() + yearItem.ToString());
if (Program.CheckIDCard18(s))
{
using (System.IO.StreamWriter file = new System.IO.StreamWriter(@"C:\Users\C\Downloads\test.txt", true))
{
file.WriteLine(s);
}
}
}
Console.WriteLine(regionItem);
}
}
}
跑出来的结果也是令我挺惊讶的，2000/2011/2022的2月，能产生的回文数比我想象中多很多。单是2011年2月，顺序号小于200的就有
142131 2011 02 13 124 1
152131 2011 02 13 125 1
210121 2011 02 12 101 2
211002 2011 02 20 011 2
230121 2011 02 12 103 2
231002 2011 02 20 013 2
320122 2011 02 22 102 3
321121 2011 02 12 112 3
330122 2011 02 22 103 3
331121 2011 02 12 113 3
340122 2011 02 22 104 3
350122 2011 02 22 105 3
360122 2011 02 22 106 3
361121 2011 02 12 116 3
370122 2011 02 22 107 3
371121 2011 02 12 117 3
411122 2011 02 22 111 4
421122 2011 02 22 112 4
431122 2011 02 22 113 4
433002 2011 02 20 033 4
433030 2011 02 03 033 4
450110 2011 02 01 105 4
451122 2011 02 22 115 4
469022 2011 02 22 096 4
500111 2011 02 11 100 5
500152 2011 02 25 100 5
513031 2011 02 13 031 5
520111 2011 02 11 102 5
522122 2011 02 22 122 5
530111 2011 02 11 103 5
532122 2011 02 22 123 5
533121 2011 02 12 133 5
542122 2011 02 22 124 5
610112 2011 02 21 101 6
611021 2011 02 12 011 6
621021 2011 02 12 012 6
640181 2011 02 18 104 6
653122 2011 02 22 135 6
654121 2011 02 12 145 6
也就是说这些身份证号很可能是实际存在的，何况一些地区人口出生数量远远不止每天200人。那么完全平方数呢？一开始比较傻，想直接生成所有一个个验证：
public static void Main()
{
for (int i = 316227767; i < 999999999; i++)
{
BigInteger iSquare = BigInteger.Pow(i, 2);
string iSquareString = iSquare.ToString();
if (Program.CheckIDCard18(iSquareString))
{
Console.WriteLine(iSquareString);
}
if(iSquare%1000000==0){
Console.Write("Passed:");
Console.WriteLine(iSquareString);
}
}
}
但是后来发现这样效率实在太低了……因为其实很多结果是不会符合前六位的要求的。跑了一两小时也没跑出10%的结果。在开车撞了马路中间护栏以后茅塞顿开，可以根据地区列表生成要验证的底数。改良之后一两分钟就能得到结果：
public static void Main()
{
//region列表在文末
List<int> baseList = new List<int>();
foreach (var regionItem in region)
{
BigInteger startSquare = regionItem * BigInteger.Pow(10, 12);
BigInteger endSquare = (regionItem + 1) * BigInteger.Pow(10, 12);
//BigInteger start=BigInteger.
int start = (int)Math.Ceiling(Math.Sqrt((double)startSquare));
int end = (int)Math.Floor(Math.Sqrt((double)endSquare));
for (int i = start; i <= end; i++)
{
baseList.Add(i);
}
}
foreach (var i in baseList)
{
BigInteger iSquare = BigInteger.Pow(i, 2);
string iSquareString = iSquare.ToString();
if (Program.CheckIDCard18(iSquareString))
{
using (System.IO.StreamWriter file = new System.IO.StreamWriter(@"C:\Users\C\Downloads\test.txt", true))
{
file.WriteLine(iSquareString);
}
}
if (iSquare % 10000000 == 0)
{
Console.Write("Finised:");
Console.WriteLine(i);
}
}
}
结果也是出乎意料：差不多一年就有一个……假如一天能生那么多的话：
513401 1970 08 04 000 0
132128 1970 06 08 062 5
510681 1970 01 22 668 9
445302 1970 10 12 824 1
370123 1971 07 31 014 4
452624 1971 03 26 712 1
210727 1972 10 20 304 1
342523 1973 10 17 459 6
142631 1974 11 01 884 9
410325 1975 07 01 610 0
320122 1975 10 05 692 9
142634 1976 01 18 604 1
640422 1976 06 26 890 0
450902 1977 01 02 522 5
441423 1982 08 20 942 4
500115 1983 08 03 875 6
411282 1985 10 26 264 1
320107 1985 02 10 822 4
361126 1986 05 07 075 6
340321 1986 07 30 250 0
433101 1986 03 22 851 6
342423 1986 08 22 937 6
120111 1988 06 03 187 6
340203 1988 09 05 402 5
320506 1989 09 06 356 1
410621 1989 11 20 922 5
320202 1989 08 18 968 9
150502 1990 06 08 464 1
152921 1990 06 16 560 4
140926 1991 09 11 545 6
622822 1993 02 10 420 1
512535 1993 01 11 576 9
500229 1993 04 10 656 1
410181 1993 06 11 780 1
320724 1993 08 17 924 1
211281 1994 08 30 240 9
152525 1994 09 29 400 9
420922 1994 07 06 958 4
330182 1994 08 23 992 9
522523 1995 12 10 624 4
410521 1996 08 03 408 9
220284 1996 04 15 809 6
342922 1997 12 21 283 6
120112 1997 04 08 490 0
142133 1998 11 02 490 0
211421 1999 07 08 332 1
451026 2000 04 16 496 4
510229 2001 05 07 020 9
310118 2001 11 10 032 9
130922 2001 11 12 944 1
371424 2002 02 12 259 6
411023 2002 03 24 992 1
422725 2004 01 01 126 4
332602 2005 03 09 456 4
419004 2006 03 29 424 4
642221 2007 02 15 430 4
362428 2008 04 01 000 0
131127 2008 02 01 000 0
510115 2008 10 01 502 5
130123 2009 03 07 609 6
610429 2009 06 29 796 9
342522 2012 07 20 536 9
431127 2015 11 28 952 9
342426 2017 04 05 136 4
440511 2017 08 21 204 1
450502 2018 08 27 366 4
142729 2018 09 18 422 5
140303 2018 07 07 610 0
230225 2018 06 23 745 6
341282 2020 06 12 595 6
130433 2020 02 14 764 1
230719 2020 01 11 776 9
130323 2021 09 30 250 0
140211 2021 05 26 676 9
130222 2022 02 02 822 5
150603 2022 03 24 865 6
451221 2023 04 22 004 9
432322 2024 12 16 116 1
449001 2025 03 27 040 0
230811 2025 08 14 102 5
450303 2025 06 22 980 1
132336 2027 06 10 662 4
612732 2028 08 10 412 9
433001 2028 03 13 636 1
320324 2029 09 04 810 0
132436 2030 04 29 390 4
513423 2030 12 22 913 6
代码确实是个好东西。以前看似很难的东西，现在可以轻松得到结果。那么问题来了？素数呢？感觉很有挑战性……
//region below is not sorted
int[] region = new int[] {110101,110102,110103,110104,110105,110106,110107,110108,110109,110111,110221,110222,110223,110224,110226,110227,110228,110229,120101,120102,120103,120104,120105,120106,120107,120108,120109,120110,120111,120112,120113,120221,120222,120223,120224,120225,130102,130103,130104,130105,130106,130121,130122,130123,130124,130202,130203,130204,130205,130206,130221,130222,130223,130224,130225,130226,130227,130228,130229,130230,130302,130303,130304,130321,130322,130323,130324,130402,130403,130404,130406,130421,130502,130503,130521,130602,130603,130604,130621,130622,130702,130703,130705,130706,130721,130802,130803,130804,130821,130902,130903,130904,130921,130922,131002,131021,131022,131023,131024,131025,131026,131028,132121,132122,132123,132124,132125,132126,132127,132128,132129,132130,132132,132133,132135,132201,132202,132223,132224,132225,132226,132227,132228,132229,132231,132232,132233,132234,132235,132236,132237,132301,132302,132322,132323,132324,132326,132329,132330,132331,132332,132335,132336,132337,132401,132402,132421,132423,132424,132425,132426,132427,132428,132429,132432,132433,132434,132435,132436,132437,132438,132440,132441,132442,132521,132522,132523,132524,132525,132526,132527,132528,132529,132530,132532,132533,132622,132623,132624,132626,132627,132628,132629,132902,132903,132904,132905,132923,132924,132926,132927,132928,132929,132931,132934,133001,133022,133023,133024,133025,133026,133027,133028,133029,133030,133031,139001,139002,140102,140103,140104,140112,140113,140121,140122,140123,140202,140203,140211,140212,140302,140303,140311,140321,140322,140402,140411,140421,140422,140423,140424,140425,140426,140427,140428,140429,140430,140431,140502,140503,140521,140522,140523,140524,140602,140603,140621,142121,142122,142123,142124,142125,142126,142130,142131,142132,142133,142201,142222,142223,142224,142225,142226,142227,142228,142229,142230,142231,142232,142233,142234,142321,142322,142323,142324,142325,142326,142327,142328,142329,142330,142331,142332,142333,142401,142421,142422,142423,142424,142427,142429,142430,142431,142432,142433,142601,142602,142603,142621,142622,142623,142625,142627,142628,142629,142630,142631,142632,142633,142634,142635,142636,142701,142722,142723,142724,142725,142726,142727,142728,142729,142730,142731,142732,142733,149001,150102,150103,150104,150105,150121,150122,150202,150203,150204,150205,150206,150207,150221,150222,150302,150303,150304,150402,150403,150404,150421,150422,150423,150424,150425,150426,150428,150429,150430,152101,152102,152103,152104,152122,152123,152125,152126,152127,152128,152129,152130,152131,152201,152221,152222,152223,152224,152301,152302,152322,152323,152324,152325,152326,152327,152501,152502,152522,152523,152524,152525,152526,152527,152528,152529,152530,152531,152601,152602,152621,152622,152623,152624,152625,152626,152627,152629,152630,152631,152632,152633,152634,152701,152722,152723,152724,152725,152726,152727,152728,152801,152822,152823,152824,152825,152826,152827,152921,152922,152923,210102,210103,210104,210105,210106,210111,210112,210113,210114,210121,210122,210202,210203,210204,210211,210212,210213,210222,210224,210225,210302,210303,210304,210311,210321,210402,210403,210404,210411,210421,210422,210423,210502,210503,210504,210505,210521,210522,210602,210603,210604,210621,210622,210623,210624,210702,210703,210711,210724,210725,210726,210727,210802,210803,210804,210811,210821,210824,210902,210903,210904,210905,210911,210921,210922,211002,211003,211004,211005,211011,211021,211022,211102,211103,211121,211122,211202,211204,211221,211223,211224,211225,211226,211302,211303,211321,211322,211323,211324,211402,211404,211405,211421,211422,219001,219002,219004,219005,219006,219007,220102,220103,220104,220105,220111,220122,220124,220125,220202,220203,220204,220211,220221,220222,220223,220302,220303,220322,220323,220324,220402,220403,220421,220422,220502,220503,220521,220523,220524,220602,220603,220604,220621,220622,220623,222301,222302,222303,222304,222323,222324,222326,222327,222328,222401,222402,222403,222404,222405,222423,222424,222426,229001,229002,229003,229004,229005,229006,229007,230102,230103,230104,230105,230106,230107,230108,230121,230202,230203,230204,230205,230206,230207,230208,230221,230222,230223,230224,230225,230226,230227,230228,230229,230230,230231,230302,230303,230304,230305,230306,230307,230321,230402,230403,230404,230405,230406,230407,230421,230422,230502,230503,230505,230506,230521,230602,230603,230604,230605,230606,230702,230703,230704,230705,230706,230707,230708,230709,230710,230711,230712,230713,230714,230715,230716,230722,230802,230803,230804,230805,230811,230822,230823,230824,230826,230827,230828,230832,230833,230902,230903,230904,230921,231002,231003,231004,231005,231011,231021,231022,231023,231024,231025,231027,232101,232102,232122,232125,232126,232127,232128,232130,232131,232301,232302,232303,232304,232324,232325,232326,232328,232329,232330,232331,232332,232601,232602,232603,232622,232623,232625,232626,232721,232722,232723,239001,239002,239003,2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]]>