基础理论中的两个重要定理的证明

ysr · 发表于 2026-4-1 13:57

在10000内的这样的素数组有77 组：
(3 31 37 )
(13 41 47 )
(19 47 53 )
(73 101 107 )
(79 107 113 )
(103 131 137 )
(139 167 173 )
(163 191 197 )
(199 227 233 )
(223 251 257 )
(229 257 263 )
(283 311 317 )
(433 461 467 )
(613 641 647 )
(619 647 653 )
(829 857 863 )
(853 881 887 )
(919 947 953 )
(1063 1091 1097 )
(1069 1097 1103 )
(1153 1181 1187 )
(1249 1277 1283 )
(1399 1427 1433 )
(1453 1481 1487 )
(1459 1487 1493 )
(1579 1607 1613 )
(1873 1901 1907 )
(1879 1907 1913 )
(2053 2081 2087 )
(2179 2207 2213 )
(2239 2267 2273 )
(2383 2411 2417 )
(2389 2417 2423 )
(2659 2687 2693 )
(3433 3461 3467 )
(3499 3527 3533 )
(3643 3671 3677 )
(3733 3761 3767 )
(3769 3797 3803 )
(3889 3917 3923 )
(4099 4127 4133 )
(4363 4391 4397 )
(4423 4451 4457 )
(4759 4787 4793 )
(4903 4931 4937 )
(4909 4937 4943 )
(5119 5147 5153 )
(5443 5471 5477 )
(5449 5477 5483 )
(5623 5651 5657 )
(5683 5711 5717 )
(5779 5807 5813 )
(5869 5897 5903 )
(5953 5981 5987 )
(6229 6257 6263 )
(6829 6857 6863 )
(6883 6911 6917 )
(6949 6977 6983 )
(7159 7187 7193 )
(7219 7247 7253 )
(7489 7517 7523 )
(7549 7577 7583 )
(7789 7817 7823 )
(7873 7901 7907 )
(8053 8081 8087 )
(8059 8087 8093 )
(8089 8117 8123 )
(8209 8237 8243 )
(8263 8291 8297 )
(8713 8741 8747 )
(8719 8747 8753 )
(8803 8831 8837 )
(9343 9371 9377 )
(9403 9431 9437 )
(9433 9461 9467 )
(9439 9467 9473 )
(9463 9491 9497 )
命题：项差依次为28，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

代码如下：
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b, k As String
a = Val(sa)

x = 3
If a <= 1 Or a > Int(a) Then
If a = 1 Then
fenjieyinzi = "它既不是质数，也不是合数"

Else
MsgBox "error"
End If

Else

Do While a / 2 = Int(a / 2) And a >= 4

If b = 0 Then
fenjieyinzi = fenjieyinzi & "2"
b = 1
Else
fenjieyinzi = fenjieyinzi & "*2"
End If
a = a / 2
k = a

Loop

Do While a > 1
Do While x <= Sqr(a)
Do While a / x = Int(a / x) And a >= x * x

If b = 0 Then
fenjieyinzi = fenjieyinzi & x
b = 1
Else
fenjieyinzi = fenjieyinzi & "*" & x
End If
a = a / x
Loop

x = x + 2
Loop

k = a
a = 1
Loop

If b = 1 Then
fenjieyinzi = fenjieyinzi & "*" & k
Else
fenjieyinzi = "这是一个质数"
End If





End If

End Function

Private Sub Command1_Click()
Dim a, b
a = Val(Text1)
p1 = 3
Do While p1 <= a
p1 = p1: p2 = p1 + 28: p3 = p2 + 6
p4 = p3 + 4: p5 = p4 + 210: p6 = p5 + 210: p7 = p6 + 210

p11 = fenjieyinzi(Val(p1)): p12 = fenjieyinzi(Val(p2)): p13 = fenjieyinzi(Val(p3))
p14 = fenjieyinzi(Val(p4)): p15 = fenjieyinzi(Val(p5)): p16 = fenjieyinzi(Val(p6)): p17 = fenjieyinzi(Val(p7))

If InStr(p11, "*") = 0 And InStr(p12, "*") = 0 And InStr(p13, "*") = 0 And InStr(p4, "*") = 0 And InStr(p5, "*") = 0 And InStr(p6, "*") = 0 And InStr(p7, "*") = 0 Then
s11 = s11 & "(" & p1 & " " & p2 & " " & p3 & " )  " & vbCrLf

s12 = s12 + 1
End If

p1 = p1 + 2
Loop
If s12 >= 1 Then
Text2 = "在" & Text1 & "内的这样的素数组有" & s12 & " 组： " & vbCrLf & s11
Else
Text2 = "wu  jie"
End If

Combo1 = Text2

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form21.Cls
End Sub

ysr · 发表于 2026-4-1 14:00

在10000内的这样的素数组有62 组：
(5 11 13 )
(11 17 19 )
(23 29 31 )
(53 59 61 )
(101 107 109 )
(131 137 139 )
(173 179 181 )
(191 197 199 )
(233 239 241 )
(263 269 271 )
(563 569 571 )
(593 599 601 )
(653 659 661 )
(821 827 829 )
(1013 1019 1021 )
(1223 1229 1231 )
(1283 1289 1291 )
(1481 1487 1489 )
(1601 1607 1609 )
(1613 1619 1621 )
(1871 1877 1879 )
(2081 2087 2089 )
(2333 2339 2341 )
(2543 2549 2551 )
(2963 2969 2971 )
(3251 3257 3259 )
(3323 3329 3331 )
(3461 3467 3469 )
(3533 3539 3541 )
(3761 3767 3769 )
(3911 3917 3919 )
(3923 3929 3931 )
(4013 4019 4021 )
(4211 4217 4219 )
(4253 4259 4261 )
(4643 4649 4651 )
(4793 4799 4801 )
(5003 5009 5011 )
(5273 5279 5281 )
(5471 5477 5479 )
(5651 5657 5659 )
(5843 5849 5851 )
(5861 5867 5869 )
(6263 6269 6271 )
(6353 6359 6361 )
(6563 6569 6571 )
(6653 6659 6661 )
(6863 6869 6871 )
(7121 7127 7129 )
(7451 7457 7459 )
(7481 7487 7489 )
(7541 7547 7549 )
(7583 7589 7591 )
(8081 8087 8089 )
(8423 8429 8431 )
(8831 8837 8839 )
(8963 8969 8971 )
(9413 9419 9421 )
(9431 9437 9439 )
(9623 9629 9631 )
(9851 9857 9859 )
(9923 9929 9931 )
命题：项差依次为6，2的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 14:01

在10000内的这样的素数组有85 组：
(7 13 17 )
(13 19 23 )
(31 37 41 )
(37 43 47 )
(61 67 71 )
(73 79 83 )
(97 103 107 )
(103 109 113 )
(157 163 167 )
(223 229 233 )
(271 277 281 )
(307 313 317 )
(373 379 383 )
(433 439 443 )
(457 463 467 )
(607 613 617 )
(733 739 743 )
(751 757 761 )
(853 859 863 )
(877 883 887 )
(1087 1093 1097 )
(1291 1297 1301 )
(1297 1303 1307 )
(1423 1429 1433 )
(1483 1489 1493 )
(1543 1549 1553 )
(1657 1663 1667 )
(1777 1783 1787 )
(1861 1867 1871 )
(1867 1873 1877 )
(1987 1993 1997 )
(1993 1999 2003 )
(2131 2137 2141 )
(2287 2293 2297 )
(2341 2347 2351 )
(2371 2377 2381 )
(2383 2389 2393 )
(2467 2473 2477 )
(2677 2683 2687 )
(2683 2689 2693 )
(2791 2797 2801 )
(2851 2857 2861 )
(3181 3187 3191 )
(3313 3319 3323 )
(3457 3463 3467 )
(3607 3613 3617 )
(3691 3697 3701 )
(4441 4447 4451 )
(4507 4513 4517 )
(4513 4519 4523 )
(4723 4729 4733 )
(4783 4789 4793 )
(4993 4999 5003 )
(5227 5233 5237 )
(5407 5413 5417 )
(5431 5437 5441 )
(5521 5527 5531 )
(5563 5569 5573 )
(5641 5647 5651 )
(5647 5653 5657 )
(5683 5689 5693 )
(5851 5857 5861 )
(6037 6043 6047 )
(6211 6217 6221 )
(6571 6577 6581 )
(6823 6829 6833 )
(6961 6967 6971 )
(6991 6997 7001 )
(7237 7243 7247 )
(7681 7687 7691 )
(7717 7723 7727 )
(7867 7873 7877 )
(7873 7879 7883 )
(7927 7933 7937 )
(8161 8167 8171 )
(8263 8269 8273 )
(8287 8293 8297 )
(8731 8737 8741 )
(8923 8929 8933 )
(9001 9007 9011 )
(9127 9133 9137 )
(9151 9157 9161 )
(9613 9619 9623 )
(9733 9739 9743 )
(9781 9787 9791 )
命题：项差依次为6，4的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 14:03

在10000内的这样的素数组有118 组：
(5 11 17 )
(7 13 19 )
(11 17 23 )
(17 23 29 )
(31 37 43 )
(41 47 53 )
(47 53 59 )
(61 67 73 )
(67 73 79 )
(97 103 109 )
(101 107 113 )
(151 157 163 )
(167 173 179 )
(227 233 239 )
(251 257 263 )
(257 263 269 )
(271 277 283 )
(347 353 359 )
(367 373 379 )
(557 563 569 )
(587 593 599 )
(601 607 613 )
(607 613 619 )
(641 647 653 )
(647 653 659 )
(727 733 739 )
(941 947 953 )
(971 977 983 )
(1091 1097 1103 )
(1097 1103 1109 )
(1117 1123 1129 )
(1181 1187 1193 )
(1217 1223 1229 )
(1277 1283 1289 )
(1291 1297 1303 )
(1361 1367 1373 )
(1427 1433 1439 )
(1447 1453 1459 )
(1481 1487 1493 )
(1487 1493 1499 )
(1601 1607 1613 )
(1607 1613 1619 )
(1657 1663 1669 )
(1741 1747 1753 )
(1747 1753 1759 )
(1777 1783 1789 )
(1861 1867 1873 )
(1867 1873 1879 )
(1901 1907 1913 )
(1987 1993 1999 )
(2131 2137 2143 )
(2281 2287 2293 )
(2371 2377 2383 )
(2377 2383 2389 )
(2411 2417 2423 )
(2671 2677 2683 )
(2677 2683 2689 )
(2687 2693 2699 )
(2707 2713 2719 )
(2791 2797 2803 )
(2897 2903 2909 )
(2957 2963 2969 )
(3301 3307 3313 )
(3307 3313 3319 )
(3457 3463 3469 )
(3527 3533 3539 )
(3631 3637 3643 )
(3727 3733 3739 )
(3911 3917 3923 )
(3917 3923 3929 )
(4001 4007 4013 )
(4007 4013 4019 )
(4127 4133 4139 )
(4451 4457 4463 )
(4507 4513 4519 )
(4591 4597 4603 )
(4637 4643 4649 )
(4651 4657 4663 )
(4787 4793 4799 )
(4931 4937 4943 )
(4987 4993 4999 )
(5101 5107 5113 )
(5107 5113 5119 )
(5297 5303 5309 )
(5381 5387 5393 )
(5387 5393 5399 )
(5407 5413 5419 )
(5431 5437 5443 )
(5437 5443 5449 )
(5471 5477 5483 )
(5557 5563 5569 )
(5641 5647 5653 )
(5647 5653 5659 )
(5737 5743 5749 )
(5801 5807 5813 )
(6067 6073 6079 )
(6257 6263 6269 )
(6311 6317 6323 )
(6317 6323 6329 )
(6361 6367 6373 )
(6367 6373 6379 )
(6857 6863 6869 )
(6971 6977 6983 )
(7207 7213 7219 )
(7517 7523 7529 )
(7577 7583 7589 )
(7817 7823 7829 )
(7867 7873 7879 )
(8081 8087 8093 )
(8111 8117 8123 )
(8231 8237 8243 )
(8707 8713 8719 )
(8741 8747 8753 )
(9001 9007 9013 )
(9337 9343 9349 )
(9391 9397 9403 )
(9461 9467 9473 )
(9467 9473 9479 )
命题：项差依次为6，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 14:04

在10000内的这样的素数组有76 组：
(5 11 19 )
(17 23 31 )
(23 29 37 )
(47 53 61 )
(53 59 67 )
(83 89 97 )
(167 173 181 )
(227 233 241 )
(257 263 271 )
(263 269 277 )
(353 359 367 )
(383 389 397 )
(443 449 457 )
(557 563 571 )
(563 569 577 )
(587 593 601 )
(593 599 607 )
(647 653 661 )
(677 683 691 )
(977 983 991 )
(1103 1109 1117 )
(1187 1193 1201 )
(1217 1223 1231 )
(1223 1229 1237 )
(1277 1283 1291 )
(1283 1289 1297 )
(1367 1373 1381 )
(1433 1439 1447 )
(1553 1559 1567 )
(1607 1613 1621 )
(1613 1619 1627 )
(1973 1979 1987 )
(1997 2003 2011 )
(2207 2213 2221 )
(2237 2243 2251 )
(2267 2273 2281 )
(2333 2339 2347 )
(2543 2549 2557 )
(2657 2663 2671 )
(2693 2699 2707 )
(2837 2843 2851 )
(2903 2909 2917 )
(2957 2963 2971 )
(3203 3209 3217 )
(3527 3533 3541 )
(3533 3539 3547 )
(3617 3623 3631 )
(3917 3923 3931 )
(4007 4013 4021 )
(4013 4019 4027 )
(4283 4289 4297 )
(4637 4643 4651 )
(4643 4649 4657 )
(4787 4793 4801 )
(4937 4943 4951 )
(5393 5399 5407 )
(5807 5813 5821 )
(5843 5849 5857 )
(6197 6203 6211 )
(6257 6263 6271 )
(6263 6269 6277 )
(6323 6329 6337 )
(6353 6359 6367 )
(6563 6569 6577 )
(6827 6833 6841 )
(6857 6863 6871 )
(6977 6983 6991 )
(7013 7019 7027 )
(7523 7529 7537 )
(7577 7583 7591 )
(8087 8093 8101 )
(8363 8369 8377 )
(8663 8669 8677 )
(8693 8699 8707 )
(8747 8753 8761 )
(9533 9539 9547 )
命题：项差依次为6，8的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 14:05

在10000内的这样的素数组有81 组：
(7 13 23 )
(13 19 29 )
(31 37 47 )
(37 43 53 )
(67 73 83 )
(73 79 89 )
(97 103 113 )
(151 157 167 )
(157 163 173 )
(223 229 239 )
(277 283 293 )
(331 337 347 )
(367 373 383 )
(373 379 389 )
(433 439 449 )
(541 547 557 )
(571 577 587 )
(601 607 617 )
(727 733 743 )
(823 829 839 )
(1033 1039 1049 )
(1087 1093 1103 )
(1291 1297 1307 )
(1423 1429 1439 )
(1483 1489 1499 )
(1543 1549 1559 )
(1621 1627 1637 )
(1693 1699 1709 )
(1861 1867 1877 )
(1873 1879 1889 )
(1987 1993 2003 )
(2011 2017 2027 )
(2083 2089 2099 )
(2137 2143 2153 )
(2281 2287 2297 )
(2341 2347 2357 )
(2377 2383 2393 )
(2383 2389 2399 )
(2671 2677 2687 )
(2677 2683 2693 )
(2683 2689 2699 )
(2713 2719 2729 )
(3307 3313 3323 )
(3313 3319 3329 )
(3511 3517 3527 )
(3541 3547 3557 )
(3607 3613 3623 )
(3847 3853 3863 )
(4357 4363 4373 )
(4441 4447 4457 )
(4507 4513 4523 )
(4657 4663 4673 )
(4783 4789 4799 )
(4903 4909 4919 )
(4951 4957 4967 )
(4987 4993 5003 )
(4993 4999 5009 )
(5557 5563 5573 )
(5641 5647 5657 )
(5653 5659 5669 )
(5851 5857 5867 )
(6037 6043 6053 )
(6073 6079 6089 )
(6271 6277 6287 )
(6337 6343 6353 )
(6373 6379 6389 )
(6547 6553 6563 )
(6673 6679 6689 )
(6703 6709 6719 )
(6961 6967 6977 )
(7213 7219 7229 )
(7237 7243 7253 )
(7867 7873 7883 )
(8053 8059 8069 )
(8521 8527 8537 )
(8731 8737 8747 )
(9043 9049 9059 )
(9277 9283 9293 )
(9397 9403 9413 )
(9613 9619 9629 )
(9733 9739 9749 )
命题：项差依次为6，10的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 14:08

其中这些命题都与无穷大有关，与无穷多有关，与无穷素数有关。
欢迎网友和爱好者惠阅和探讨！欢迎来证明或证伪！

ysr · 发表于 2026-4-1 15:01

在10000内的这样的素数组有125 组：
(5 11 23 )
(11 17 29 )
(13 19 31 )
(23 29 41 )
(41 47 59 )
(53 59 71 )
(61 67 79 )
(83 89 101 )
(131 137 149 )
(173 179 191 )
(193 199 211 )
(223 229 241 )
(233 239 251 )
(251 257 269 )
(263 269 281 )
(331 337 349 )
(383 389 401 )
(443 449 461 )
(461 467 479 )
(503 509 521 )
(601 607 619 )
(613 619 631 )
(641 647 659 )
(733 739 751 )
(751 757 769 )
(821 827 839 )
(991 997 1009 )
(1013 1019 1031 )
(1033 1039 1051 )
(1091 1097 1109 )
(1231 1237 1249 )
(1283 1289 1301 )
(1301 1307 1319 )
(1433 1439 1451 )
(1453 1459 1471 )
(1481 1487 1499 )
(1493 1499 1511 )
(1553 1559 1571 )
(1601 1607 1619 )
(1741 1747 1759 )
(1783 1789 1801 )
(1861 1867 1879 )
(1871 1877 1889 )
(1993 1999 2011 )
(2011 2017 2029 )
(2063 2069 2081 )
(2081 2087 2099 )
(2333 2339 2351 )
(2371 2377 2389 )
(2393 2399 2411 )
(2441 2447 2459 )
(2671 2677 2689 )
(2693 2699 2711 )
(2713 2719 2731 )
(3061 3067 3079 )
(3163 3169 3181 )
(3203 3209 3221 )
(3253 3259 3271 )
(3301 3307 3319 )
(3313 3319 3331 )
(3511 3517 3529 )
(3541 3547 3559 )
(3691 3697 3709 )
(3761 3767 3779 )
(3911 3917 3929 )
(4001 4007 4019 )
(4073 4079 4091 )
(4093 4099 4111 )
(4211 4217 4229 )
(4253 4259 4271 )
(4391 4397 4409 )
(4673 4679 4691 )
(4783 4789 4801 )
(4871 4877 4889 )
(4951 4957 4969 )
(4993 4999 5011 )
(5003 5009 5021 )
(5081 5087 5099 )
(5101 5107 5119 )
(5381 5387 5399 )
(5413 5419 5431 )
(5431 5437 5449 )
(5501 5507 5519 )
(5563 5569 5581 )
(5641 5647 5659 )
(5651 5657 5669 )
(5683 5689 5701 )
(5821 5827 5839 )
(5843 5849 5861 )
(5851 5857 5869 )
(5861 5867 5879 )
(6073 6079 6091 )
(6211 6217 6229 )
(6311 6317 6329 )
(6361 6367 6379 )
(6563 6569 6581 )
(6673 6679 6691 )
(6823 6829 6841 )
(7103 7109 7121 )
(7481 7487 7499 )
(7523 7529 7541 )
(7541 7547 7559 )
(7681 7687 7699 )
(7823 7829 7841 )
(7901 7907 7919 )
(8161 8167 8179 )
(8311 8317 8329 )
(8521 8527 8539 )
(8623 8629 8641 )
(8663 8669 8681 )
(8713 8719 8731 )
(8831 8837 8849 )
(8923 8929 8941 )
(9181 9187 9199 )
(9203 9209 9221 )
(9221 9227 9239 )
(9413 9419 9431 )
(9461 9467 9479 )
(9473 9479 9491 )
(9533 9539 9551 )
(9613 9619 9631 )
(9643 9649 9661 )
(9811 9817 9829 )
(9833 9839 9851 )
(9923 9929 9941 )

ysr · 发表于 2026-4-2 00:30

本帖最后由 ysr 于 2026-4-1 17:08 编辑

Private Function fenjieyinzi(sa As String) As String
Dim x, a, b, k As String
a = Val(sa)

x = 3
If a <= 1 Or a > Int(a) Then
If a = 1 Then
fenjieyinzi = "它既不是质数，也不是合数"

Else
MsgBox "error"
End If

Else

Do While a / 2 = Int(a / 2) And a >= 4

If b = 0 Then
fenjieyinzi = fenjieyinzi & "2"
b = 1
Else
fenjieyinzi = fenjieyinzi & "*2"
End If
a = a / 2
k = a

Loop

Do While a > 1
Do While x <= Sqr(a)
Do While a / x = Int(a / x) And a >= x * x

If b = 0 Then
fenjieyinzi = fenjieyinzi & x
b = 1
Else
fenjieyinzi = fenjieyinzi & "*" & x
End If
a = a / x
Loop

x = x + 2
Loop

k = a
a = 1
Loop

If b = 1 Then
fenjieyinzi = fenjieyinzi & "*" & k
Else
fenjieyinzi = "这是一个质数"
End If





End If

End Function

Private Sub Command1_Click()
Dim a, b
a = Val(Text1)
p1 = 3
Do While p1 <= a
p1 = p1: p2 = p1 + 210: p3 = p2 + 210
p4 = p3 + 210: p5 = p4 + 210: p6 = p5 + 210: p7 = p6 + 210
p8 = p7 + 210
p11 = fenjieyinzi(Val(p1)): p12 = fenjieyinzi(Val(p2)): p13 = fenjieyinzi(Val(p3))
p14 = fenjieyinzi(Val(p4)): p15 = fenjieyinzi(Val(p5)): p16 = fenjieyinzi(Val(p6)): p17 = fenjieyinzi(Val(p7))
p18 = fenjieyinzi(Val(p8))
If InStr(p11, "*") = 0 And InStr(p12, "*") = 0 And InStr(p13, "*") = 0 And InStr(p14, "*") = 0 And InStr(p15, "*") = 0 And InStr(p16, "*") = 0 And InStr(p17, "*") = 0 And InStr(p18, "*") = 0 Then
s11 = s11 & "(" & p1 & " " & p2 & " " & p3 & " " & p4 & " " & p5 & " " & p6 & " " & p7 & " " & p8 & " )  " & vbCrLf

s12 = s12 + 1
End If

p1 = p1 + 2
Loop
If s12 >= 1 Then
Text2 = "在" & Text1 & "内的这样的素数组有" & s12 & " 组： " & vbCrLf & s11
Else
Text2 = "wu  jie"
End If

Combo1 = Text2

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form21.Cls
End Sub

ysr · 发表于 2026-4-2 01:10

在10000内的这样的素数组有6 组：
(199 409 619 829 1039 1249 1459 1669 )
(409 619 829 1039 1249 1459 1669 1879 )
(619 829 1039 1249 1459 1669 1879 2089 )
(881 1091 1301 1511 1721 1931 2141 2351 )
(3499 3709 3919 4129 4339 4549 4759 4969 )
(3709 3919 4129 4339 4549 4759 4969 5179 )
命题：公差为210的8生素数组有无穷多，其中有的组中间可能还有其他素数。

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