《数论探秘》电子版

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1与500之间有24对孪生素数对:
3和 5  孪中4
5和 7  孪中6
11和 13  孪中12
17和 19  孪中18
29和 31  孪中30
41和 43  孪中42
59和 61  孪中60
71和 73  孪中72
101和 103  孪中102
107和 109  孪中108
137和 139  孪中138
149和 151  孪中150
179和 181  孪中180
191和 193  孪中192
197和 199  孪中198
227和 229  孪中228
239和 241  孪中240
269和 271  孪中270
281和 283  孪中282
311和 313  孪中312
347和 349  孪中348
419和 421  孪中420
431和 433  孪中432
461和 463  孪中462
用时5.59999999968568E-02秒

除了第一对的3和5，其他的孪生素数对中，第一个都是6n+5或者说3n+2型的，第二个都是6n+1或者说是3n+1型的。

有了这些规律，配合大整数的快速计算程序，就可以快速找到巨大的孪生素数对，破解世界纪录。

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585505245847997855444772203659与585505245847997855444772223659之间有15对差大于200的素数对:
585505245847997855444772206281/248
585505245847997855444772207011/298
585505245847997855444772208027/330
585505245847997855444772208337/238
585505245847997855444772210331/240
585505245847997855444772210577/224
585505245847997855444772212437/204
585505245847997855444772213041/310
585505245847997855444772214147/336
585505245847997855444772216757/218
585505245847997855444772218671/308
585505245847997855444772221203/204
585505245847997855444772221531/210
585505245847997855444772222799/248
585505245847997855444772223619/360
用时3142.772秒

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585505245847997855444661517881与585505245847997855444661537881之间有19对差大于200的素数对:
585505245847997855444661518767/234
585505245847997855444661521143/266
585505245847997855444661521443/240
585505245847997855444661524051/232
585505245847997855444661526031/334
585505245847997855444661526339/246
585505245847997855444661527933/292
585505245847997855444661528251/252
585505245847997855444661530149/212
585505245847997855444661530491/242
585505245847997855444661531317/238
585505245847997855444661532447/228
585505245847997855444661532889/220
585505245847997855444661533983/302
585505245847997855444661534703/224
585505245847997855444661535091/250
585505245847997855444661536377/236
585505245847997855444661537011/438
585505245847997855444661537989/358
用时15954.038秒

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585505245847997855444661537989与585505245847997855444661557989之间有7对差大于200的素数对:
585505245847997855444661541531/248
585505245847997855444661542557/306
585505245847997855444661545483/364
585505245847997855444661546463/356
585505245847997855444661548659/228
585505245847997855444661549539/256
585505245847997855444661554387/264
用时3804.288秒

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585505245847997855444661554387与585505245847997855444661574387之间有11对差大于200的素数对:
585505245847997855444661560507/438
585505245847997855444661561197/204
585505245847997855444661561409/212
585505245847997855444661563173/254
585505245847997855444661563503/216
585505245847997855444661564403/230
585505245847997855444661565271/252
585505245847997855444661566623/300
585505245847997855444661570221/504
585505245847997855444661571421/210
585505245847997855444661573841/314
用时3199.154秒

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Private Sub Command1_Click() '求由1个整数和孪生素数对组成的3生素数组的程序
Dim A, B
A = Val(Text1)
a1 = A
q = Val(Text2)
ts = Timer
m = Sqr(q)
t = Trim(Text4)
a12 = A \ 6
A = Val(a12) * 6 + 1
s = 0
a2 = A
Do While a2 <= m

b2 = a2
b3 = MPC1(Trim(b2), Trim(t))
b4 = MPC1(Trim(b3), 2)


c3 = fenjieyinzi0(Trim(b3))
D1 = fenjieyinzi0(Trim(b4))

If InStr(C1, "*") = 0 And InStr(D1, "*") = 0 And InStr(C2, "*") = 0 And InStr(c3, "*") = 0 Then
s = s + 1
Print B1, b2, b3, b4
Text3 = Text3 & "/" & B1 & "/" & b2 & "/" & b3 & "/" & b4 & vbCrLf
Else
s = s
End If
a2 = a2 + 6

Loop
a2 = a2
s1 = s
Do While a2 <= q


b2 = a2
b3 = MPC1(Trim(b2), Trim(t))
b4 = MPC1(Trim(b3), 2)


c3 = fenjieyinzi0(Trim(b3))
D1 = fenjieyinzi0(Trim(b4))

If InStr(C1, "*") = 0 And InStr(D1, "*") = 0 And InStr(C2, "*") = 0 And InStr(c3, "*") = 0 Then
s1 = s1 + 1
Print B1, b2, b3, b4
Text3 = Text3 & "/" & B1 & "/" & b2 & "/" & b3 & "/" & b4 & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 6

Loop
Combo1 = a1 & "与" & q & "之间的整数打头有" & s1 & "组差为" & t & "和2的整数加孪生素数对: (用时" & Timer - ts & "秒）" & vbCrLf & Text3

End Sub

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1与200之间的素数打头有6组差为22和2的整数加孪生素数对: (用时5.859375E-03秒）
//7/29/31
//19/41/43
//37/59/61
//79/101/103
//127/149/151
//157/179/181

另一种程序的结果：
1与200之间的整数打头有11组差为22和2的整数加孪生素数对: (用时1.171875E-02秒）
//7/29/31
//19/41/43
//37/59/61
//49/71/73
//79/101/103
//85/107/109
//115/137/139
//127/149/151
//157/179/181
//169/191/193
//175/197/199

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20000与21000之间的素数打头有1组差为1606938044258990275541962092341162602522202993782792835301376和2的整数加孪生素数对: (用时682.9688秒）
//20593/1606938044258990275541962092341162602522202993782792835321969/1606938044258990275541962092341162602522202993782792835321971

这是一对61位的孪生素数

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1与200之间的整数打头有13组差为10和2的整数加孪生素数对: (用时0.0234375秒）
//1/11/13
//7/17/19
//19/29/31
//31/41/43
//49/59/61
//61/71/73
//91/101/103
//97/107/109
//127/137/139
//139/149/151
//169/179/181
//181/191/193
//187/197/199
修改了一下代码，以上是修改代码后的程序结果

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其中1既不是素数也不是合数，而49=7*7,91=7*13,169=13*13,187=11*17都是合数。