数论问题巅峰对决

ysr · 发表于 2021-7-23 11:42

本帖最后由 ysr 于 2021-7-23 03:46 编辑

若m=105，则105*105=11025，其中11027是素数，而11021，11023，11029都不是素数。
若m=15，则15*105=1575，其中1571，1579都是素数，而1573，1577都不是素数。

ysr · 发表于 2021-7-23 14:42

蔡家雄发表于 2021-7-22 14:25
定义：若 m±2 和 m±4 是四生素数，则称 m 为双中数。

奇数双中比猜想：一奇数均可表为两个双中数之 ...

1与1000之间的k*105有11组4生素数对: (用时0.1054688秒）
/3251/3253/3257/3259m=31k=1
/3461/3463/3467/3469m=33k=1
/15641/15643/15647/15649m=149k=1
/16061/16063/16067/16069m=153k=1
/19421/19423/19427/19429m=185k=1
/25301/25303/25307/25309m=241k=1
/43781/43783/43787/43789m=417k=1
/51341/51343/51347/51349m=489k=1
/55331/55333/55337/55339m=527k=1
/79691/79693/79697/79699m=759k=1
/101111/101113/101117/101119m=963k=1
这里的m不一定是孪中，而m*k*105是孪中。

ysr · 发表于 2021-7-23 14:45

1与10000之间的k*105有51组4生素数对: (用时2.089844秒）
/3251/3253/3257/3259m=31k=1
/3461/3463/3467/3469m=33k=1
/15641/15643/15647/15649m=149k=1
/16061/16063/16067/16069m=153k=1
/19421/19423/19427/19429m=185k=1
/25301/25303/25307/25309m=241k=1
/43781/43783/43787/43789m=417k=1
/51341/51343/51347/51349m=489k=1
/55331/55333/55337/55339m=527k=1
/79691/79693/79697/79699m=759k=1
/101111/101113/101117/101119m=963k=1
/144161/144163/144167/144169m=1373k=1
/166841/166843/166847/166849m=1589k=1
/187631/187633/187637/187639m=1787k=1
/201491/201493/201497/201499m=1919k=1
/243701/243703/243707/243709m=2321k=1
/276041/276043/276047/276049m=2629k=1
/285281/285283/285287/285289m=2717k=1
/294311/294313/294317/294319m=2803k=1
/334421/334423/334427/334429m=3185k=1
/340931/340933/340937/340939m=3247k=1
/346391/346393/346397/346399m=3299k=1
/419051/419053/419057/419059m=3991k=1
/427241/427243/427247/427249m=4069k=1
/442571/442573/442577/442579m=4215k=1
/470081/470083/470087/470089m=4477k=1
/477011/477013/477017/477019m=4543k=1
/510611/510613/510617/510619m=4863k=1
/518801/518803/518807/518809m=4941k=1
/536441/536443/536447/536449m=5109k=1
/570041/570043/570047/570049m=5429k=1
/594821/594823/594827/594829m=5665k=1
/633461/633463/633467/633469m=6033k=1
/666431/666433/666437/666439m=6347k=1
/680291/680293/680297/680299m=6479k=1
/715151/715153/715157/715159m=6811k=1
/734471/734473/734477/734479m=6995k=1
/736361/736363/736367/736369m=7013k=1
/795791/795793/795797/795799m=7579k=1
/814061/814063/814067/814069m=7753k=1
/823721/823723/823727/823729m=7845k=1
/845981/845983/845987/845989m=8057k=1
/857951/857953/857957/857959m=8171k=1
/876011/876013/876017/876019m=8343k=1
/881471/881473/881477/881479m=8395k=1
/889871/889873/889877/889879m=8475k=1
/954971/954973/954977/954979m=9095k=1
/958541/958543/958547/958549m=9129k=1
/978071/978073/978077/978079m=9315k=1
/1022381/1022383/1022387/1022389m=9737k=1
/1043591/1043593/1043597/1043599m=9939k=1

ysr · 发表于 2021-7-23 14:46

程序代码如下：（仅发主程序）

Private Sub Command1_Click() '求由2个孪生素数对组成的4生素数组的程序
Dim A, B
A = Val(Text1)
a1 = A
q = Val(Text2)
ts = Timer
m = Sqr(q)
t = Val(Text4)

s = 0
k = q
k2 = Val(k * 105)
k1 = k
a2 = A
Do While a2 <= m
B1 = a2 * k2 - 2
b2 = a2 * k2 + 2
B3 = MPC1(Trim(B1), Trim(2))
b4 = MPC1(Trim(b2), 2)

C1 = fenjieyinzi0(Val(B1))
C2 = fenjieyinzi0(Val(b2))
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 & "/" & B3 & "/" & B1 & "/" & b2 & "/" & b4 & "m=" & a2 & "k=" & k & vbCrLf
Else
s = s
End If
a2 = a2 + 1

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

B1 = a2 * k2 - 2
b2 = a2 * k2 + 2
B3 = MPC(Trim(B1), Trim(2))
b4 = MPC1(Trim(b2), 2)

C1 = fenjieyinzi0(Val(B1))
C2 = fenjieyinzi0(Val(b2))
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 & "/" & B3 & "/" & B1 & "/" & b2 & "/" & b4 & "m=" & a2 & "k=" & k & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 1

Loop
Combo1 = k1 & "与" & t & "之间的k*105有" & s1 & "组4生素数对: (用时" & Timer - ts & "秒）" & vbCrLf & Text3

End Sub

ysr · 发表于 2021-7-23 14:57

1与1000之间的k*105有5组4生素数对: (用时1.953125E-02秒）
/3251/3253/3257/3259m=31k=17
/3461/3463/3467/3469m=33k=19
/15641/15643/15647/15649m=149k=135
/16061/16063/16067/16069m=153k=139
/19421/19423/19427/19429m=185k=171
改了一下程序，仍然是只有m*k*105是孪中

ysr · 发表于 2021-7-23 15:00

1与10000之间的k*105有15组4生素数对: (用时0.265625秒）
/3251/3253/3257/3259m=31k=17
/3461/3463/3467/3469m=33k=19
/15641/15643/15647/15649m=149k=135
/16061/16063/16067/16069m=153k=139
/19421/19423/19427/19429m=185k=171
/25301/25303/25307/25309m=241k=227
/43781/43783/43787/43789m=417k=403
/51341/51343/51347/51349m=489k=475
/55331/55333/55337/55339m=527k=513
/79691/79693/79697/79699m=759k=745
/101111/101113/101117/101119m=963k=949
/144161/144163/144167/144169m=1373k=1359
/166841/166843/166847/166849m=1589k=1575
/187631/187633/187637/187639m=1787k=1773
/201491/201493/201497/201499m=1919k=1905

ysr · 发表于 2021-7-23 15:03

1919*1905=3655695，而3655691~3655699之间的素数有1个：
3655693

ysr · 发表于 2021-7-24 00:27

201491~201499之间的素数有4个：
201491 201493 201497 201499

ysr · 发表于 2021-7-24 00:40

本帖最后由 ysr 于 2021-7-23 16:42 编辑

1与10000之间的k*105有1组4生素数对: (用时3.355957秒）
/55331/55333/55337/55339m=31k=17
改了下程序，没有找到解，再修改一下试试。

31*17=527，523~531之间的素数有1个：
523 .
所以，不是双孪中数。

ysr · 发表于 2021-7-24 00:53

本帖最后由 ysr 于 2021-7-23 16:55 编辑

1与10000之间的k*105有51组4生素数对: (用时2.064941秒）
/3251/3253/3257/3259m=31k=1
/3461/3463/3467/3469m=33k=1
/15641/15643/15647/15649m=149k=1
/16061/16063/16067/16069m=153k=1
/19421/19423/19427/19429m=185k=1
/25301/25303/25307/25309m=241k=1
/43781/43783/43787/43789m=417k=1
/51341/51343/51347/51349m=489k=1
/55331/55333/55337/55339m=527k=1
/79691/79693/79697/79699m=759k=1
/101111/101113/101117/101119m=963k=1
/144161/144163/144167/144169m=1373k=1
/166841/166843/166847/166849m=1589k=1
/187631/187633/187637/187639m=1787k=1
/201491/201493/201497/201499m=1919k=1
/243701/243703/243707/243709m=2321k=1
/276041/276043/276047/276049m=2629k=1
/285281/285283/285287/285289m=2717k=1
/294311/294313/294317/294319m=2803k=1
/334421/334423/334427/334429m=3185k=1
/340931/340933/340937/340939m=3247k=1
/346391/346393/346397/346399m=3299k=1
/419051/419053/419057/419059m=3991k=1
/427241/427243/427247/427249m=4069k=1
/442571/442573/442577/442579m=4215k=1
/470081/470083/470087/470089m=4477k=1
/477011/477013/477017/477019m=4543k=1
/510611/510613/510617/510619m=4863k=1
/518801/518803/518807/518809m=4941k=1
/536441/536443/536447/536449m=5109k=1
/570041/570043/570047/570049m=5429k=1
/594821/594823/594827/594829m=5665k=1
/633461/633463/633467/633469m=6033k=1
/666431/666433/666437/666439m=6347k=1
/680291/680293/680297/680299m=6479k=1
/715151/715153/715157/715159m=6811k=1
/734471/734473/734477/734479m=6995k=1
/736361/736363/736367/736369m=7013k=1
/795791/795793/795797/795799m=7579k=1
/814061/814063/814067/814069m=7753k=1
/823721/823723/823727/823729m=7845k=1
/845981/845983/845987/845989m=8057k=1
/857951/857953/857957/857959m=8171k=1
/876011/876013/876017/876019m=8343k=1
/881471/881473/881477/881479m=8395k=1
/889871/889873/889877/889879m=8475k=1
/954971/954973/954977/954979m=9095k=1
/958541/958543/958547/958549m=9129k=1
/978071/978073/978077/978079m=9315k=1
/1022381/1022383/1022387/1022389m=9737k=1
/1043591/1043593/1043597/1043599m=9939k=1
而9315/15=621，而9311~9319之间的素数有2个：
9311 9319 .
所以，9315不是双孪中数。（休息了，程序需要改进，明天再说吧）

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