《数论探秘》电子版

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585505245847997855444218926825与585505245847997855444218966825之间有26对差大于200的素数对:
585505245847997855444218927427/448
585505245847997855444218927967/288
585505245847997855444218928269/302
585505245847997855444218929851/214
585505245847997855444218931591/324
585505245847997855444218935163/342
585505245847997855444218938071/250
585505245847997855444218939097/244
585505245847997855444218939999/218
585505245847997855444218942259/246
585505245847997855444218943317/266
585505245847997855444218944683/352
585505245847997855444218946419/206
585505245847997855444218948007/264
585505245847997855444218948319/298
585505245847997855444218950281/390
585505245847997855444218951309/288
585505245847997855444218952321/228
585505245847997855444218953713/240
585505245847997855444218954897/234
585505245847997855444218955939/318
585505245847997855444218957501/264
585505245847997855444218960853/246
585505245847997855444218962607/246
585505245847997855444218964881/410
585505245847997855444218965319/216
用时7494.01800000001秒

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585505245847997855444218985003与585505245847997855444219005003之间有6对差大于200的素数对:
585505245847997855444218986827/298
585505245847997855444218987267/350
585505245847997855444218988261/418
585505245847997855444218995979/282
585505245847997855444218996447/248
585505245847997855444219002919/276
用时14629.277秒

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产生差为2m的2生素数的充分条件（这个就是充分条件不是必要条件）：就是存在大于等于4的相邻素数，证明：
比如如下数列：
2n+1：        3，5，7，……
2n+2m+1：3+2m，5+2m，7+2m，……
对应项差为2m，对应项都是素数的话就是一对2生素数。设p1，p2为相邻素数，若p2-p1>=4，则在第二排数列的p2+2与3p2之间至少有一个素数与对应项构成2生素数，因为各素因子在每排数列中的一个周期内各占一个位置，2排数列就是占了二个位置，各素因子第一次出现的时候是以素数的身份出现的在p2的第一个周期是各素因子占位最多的情况，而在p2的第二个周期3和p2重复占位了，就产生了一个空缺，就必然产生一对2生素数，这是必然的。充分条件得证！

产生差为2,6n+4,和2的4生素数的充分条件（这个就是充分条件不是必要条件）：就是存在大于等于6的相邻素数，证明：
请看如下数列：
          2n1+1：3，5，7，……
          2n1+3：5，7，9，……
6n+4+2n1+3：6n+9，6n+11，……
6n+4+2n1+5：6n+11，6n+13，……
对应项差为2,6n+4,和2，对应项都是素数的话就是一组4生素数。设p1，p2为相邻素数，若p2-p1>=6，则在第四排数列的p2+2与3p2之间至少有一个素数与对应项构成4生素数，因为各素因子在每排数列中的一个周期内各占一个位置，4排数列就是4个位置，各素因子第一次出现的时候是以素数的身份出现的在p2的第一个周期是各素因子占位最多的情况，而在p2的第二个周期3和p2重复占位了，就产生了一个空缺，就产生了一组4生素数，这是必然的。充分条件得证！

有了这两个充分条件，就可以证明孪生素数是无穷多的，这样的4生素数是无穷多的，差为2m的2生素数是无穷多的.

因为素数是越来越稀的，差大于等于4的相邻素数，差大于等于6的相邻素数都是无穷多的

有了这两条定理，就可以证明:孪生素数猜想，哥德巴赫猜想，李明波孪中差猜想，李明波孪中和猜想都是远远成立的。

这两条定理又是如此简单明了 ，甚至小学生都能看懂。

还有多种方法证明这些猜想，上面的证明是最简单的一种，小学生能看懂的一种。

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585505245847997855444219002919与585505245847997855444219042919之间有23对差大于200的素数对:
585505245847997855444219011433/354
585505245847997855444219012927/246
585505245847997855444219014403/262
585505245847997855444219016559/252
585505245847997855444219017817/270
585505245847997855444219018683/266
585505245847997855444219020721/430
585505245847997855444219021233/210
585505245847997855444219021803/246
585505245847997855444219022667/276
585505245847997855444219026673/232
585505245847997855444219027099/250
585505245847997855444219029081/342
585505245847997855444219031347/210
585505245847997855444219033309/246
585505245847997855444219035577/204
585505245847997855444219036309/222
585505245847997855444219037041/210
585505245847997855444219037781/230
585505245847997855444219038463/394
585505245847997855444219039147/394
585505245847997855444219042483/346
585505245847997855444219043199/390
用时16707.914秒

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585505245847997855444219043199与585505245847997855444219083199之间有32对差大于200的素数对:
585505245847997855444219044231/252
585505245847997855444219045999/216
585505245847997855444219047169/262
585505245847997855444219051147/268
585505245847997855444219051437/218
585505245847997855444219051863/306
585505245847997855444219053543/360
585505245847997855444219054293/230
585505245847997855444219056591/318
585505245847997855444219057569/336
585505245847997855444219058331/264
585505245847997855444219058821/222
585505245847997855444219061323/264
585505245847997855444219061923/252
585505245847997855444219064337/380
585505245847997855444219064667/234
585505245847997855444219064989/216
585505245847997855444219065321/212
585505245847997855444219065553/204
585505245847997855444219066971/230
585505245847997855444219067281/244
585505245847997855444219068981/230
585505245847997855444219070343/206
585505245847997855444219071151/250
585505245847997855444219072063/262
585505245847997855444219076241/380
585505245847997855444219077543/224
585505245847997855444219078123/240
585505245847997855444219080169/240
585505245847997855444219080831/338
585505245847997855444219081449/206
585505245847997855444219083177/266
用时16313.373秒

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146376311462000229044089943070   -   27661941^2  =146,376,311,461,999,463,861,110,055,589，
146,376,311,461,999,463,861,110,055,589*4+1=585,505,245,847,997,855,444,440,222,357，
146,376,311,461,999,463,861,110,055,589-27661941=146,376,311,461,999,463,861,082,393,648，
146,376,311,461,999,463,861,082,393,648*4+1=585,505,245,847,997,855,444,329,574,593

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585505245847997855444329574593与585505245847997855444329594593之间有13对差大于200的素数对:
585505245847997855444329574977/230
585505245847997855444329575623/406
585505245847997855444329576679/268
585505245847997855444329578517/206
585505245847997855444329579499/258
585505245847997855444329579807/216
585505245847997855444329583387/228
585505245847997855444329583699/202
585505245847997855444329585241/244
585505245847997855444329588217/228
585505245847997855444329589789/232
585505245847997855444329591061/228
585505245847997855444329594783/236
用时3178.582秒

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585505245847997855444329594783与585505245847997855444329634783之间有35对差大于200的素数对:
585505245847997855444329595173/254
585505245847997855444329596011/334
585505245847997855444329598087/330
585505245847997855444329600897/290
585505245847997855444329602391/204
585505245847997855444329603021/282
585505245847997855444329603543/230
585505245847997855444329603967/324
585505245847997855444329604939/232
585505245847997855444329605601/308
585505245847997855444329606337/264
585505245847997855444329606681/234
585505245847997855444329608437/214
585505245847997855444329609243/596
585505245847997855444329610321/244
585505245847997855444329610971/204
585505245847997855444329612933/270
585505245847997855444329613743/254
585505245847997855444329614001/222
585505245847997855444329614221/220
585505245847997855444329614941/222
585505245847997855444329616017/300
585505245847997855444329617049/260
585505245847997855444329618541/208
585505245847997855444329619467/206
585505245847997855444329620193/242
585505245847997855444329622171/238
585505245847997855444329625137/264
585505245847997855444329627781/262
585505245847997855444329629311/238
585505245847997855444329630217/210
585505245847997855444329631683/224
585505245847997855444329632277/380
585505245847997855444329632811/524
585505245847997855444329633657/306
用时-79687.499秒

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585505245847997855444329653109与585505245847997855444329673109之间有16对差大于200的素数对:
585505245847997855444329653961/212
585505245847997855444329654769/306
585505245847997855444329655807/216
585505245847997855444329656221/232
585505245847997855444329657351/240
585505245847997855444329658021/204
585505245847997855444329658807/210
585505245847997855444329659367/254
585505245847997855444329660253/216
585505245847997855444329660727/204
585505245847997855444329661101/294
585505245847997855444329662169/246
585505245847997855444329664081/204
585505245847997855444329666441/212
585505245847997855444329670393/312
585505245847997855444329672697/240
用时3358.173秒

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585505245847997855444440222357与585505245847997855444440242357之间有19对差大于200的素数对:
585505245847997855444440223123/240
585505245847997855444440224551/210
585505245847997855444440224757/206
585505245847997855444440225903/282
585505245847997855444440226161/218
585505245847997855444440226839/218
585505245847997855444440228673/234
585505245847997855444440229309/216
585505245847997855444440231091/240
585505245847997855444440231729/210
585505245847997855444440233839/238
585505245847997855444440235809/216
585505245847997855444440237129/350
585505245847997855444440237777/246
585505245847997855444440239503/280
585505245847997855444440239769/216
585505245847997855444440240141/204
585505245847997855444440240637/294
585505245847997855444440241903/252
用时3354.832秒