数论问题巅峰对决

ysr

1000000与2000000之间有18组p, p+30, p+210, p+2310, p+30030, p+510510, p+9699690, p+223092870素数对:
/1020989/1021019/1021199/1023299/1051019/1531499/10720679/224113859
/1115239/1115269/1115449/1117549/1145269/1625749/10814929/224208109
/1128509/1128539/1128719/1130819/1158539/1639019/10828199/224221379
/1141031/1141061/1141241/1143341/1171061/1651541/10840721/224233901
/1199689/1199719/1199899/1201999/1229719/1710199/10899379/224292559
/1226651/1226681/1226861/1228961/1256681/1737161/10926341/224319521
/1249481/1249511/1249691/1251791/1279511/1759991/10949171/224342351
/1304209/1304239/1304419/1306519/1334239/1814719/11003899/224397079
/1362997/1363027/1363207/1365307/1393027/1873507/11062687/224455867
/1372097/1372127/1372307/1374407/1402127/1882607/11071787/224464967
/1448177/1448207/1448387/1450487/1478207/1958687/11147867/224541047
/1478021/1478051/1478231/1480331/1508051/1988531/11177711/224570891
/1529419/1529449/1529629/1531729/1559449/2039929/11229109/224622289
/1557623/1557653/1557833/1559933/1587653/2068133/11257313/224650493
/1571747/1571777/1571957/1574057/1601777/2082257/11271437/224664617
/1708979/1709009/1709189/1711289/1739009/2219489/11408669/224801849
/1729681/1729711/1729891/1731991/1759711/2240191/11429371/224822551
/1870117/1870147/1870327/1872427/1900147/2380627/11569807/224962987

蔡家雄

然后，发到我的贴子中，

ysr

2000000与3000000之间有15组p, p+30, p+210, p+2310, p+30030, p+510510, p+9699690, p+223092870素数对:
/2030459/2030489/2030669/2032769/2060489/2540969/11730149/225123329
/2053979/2054009/2054189/2056289/2084009/2564489/11753669/225146849
/2229103/2229133/2229313/2231413/2259133/2739613/11928793/225321973
/2316173/2316203/2316383/2318483/2346203/2826683/12015863/225409043
/2350741/2350771/2350951/2353051/2380771/2861251/12050431/225443611
/2359963/2359993/2360173/2362273/2389993/2870473/12059653/225452833
/2360509/2360539/2360719/2362819/2390539/2871019/12060199/225453379
/2399113/2399143/2399323/2401423/2429143/2909623/12098803/225491983
/2426609/2426639/2426819/2428919/2456639/2937119/12126299/225519479
/2440049/2440079/2440259/2442359/2470079/2950559/12139739/225532919
/2477747/2477777/2477957/2480057/2507777/2988257/12177437/225570617
/2501071/2501101/2501281/2503381/2531101/3011581/12200761/225593941
/2572667/2572697/2572877/2574977/2602697/3083177/12272357/225665537
/2641337/2641367/2641547/2643647/2671367/3151847/12341027/225734207
/2759411/2759441/2759621/2761721/2789441/3269921/12459101/225852281

蔡家雄

估计需要300分钟左右，，

ysr

4000000与5000000之间有9组p, p+30, p+210, p+2310, p+30030, p+510510, p+9699690, p+223092870素数对:
/4053113/4053143/4053323/4055423/4083143/4563623/13752803/227145983
/4162727/4162757/4162937/4165037/4192757/4673237/13862417/227255597
/4292059/4292089/4292269/4294369/4322089/4802569/13991749/227384929
/4312123/4312153/4312333/4314433/4342153/4822633/14011813/227404993
/4808827/4808857/4809037/4811137/4838857/5319337/14508517/227901697
/4857341/4857371/4857551/4859651/4887371/5367851/14557031/227950211
/4863263/4863293/4863473/4865573/4893293/5373773/14562953/227956133
/4891253/4891283/4891463/4893563/4921283/5401763/14590943/227984123
/4930421/4930451/4930631/4932731/4960451/5440931/14630111/228023291

蔡家雄

只计算这一个就行了，

4000000与5000000之间有9组p, p+30, p+210, p+2310, p+30030, p+510510, p+9699690, p+223092870素数对，

4000000与5000000之间的4生素数 p, p+30, p+210, p+2310, 有多少组？

我想大概了解一下这种4生素数（的数量）大约是这种8生素数（的数量）的多少倍？

ysr

上班呢，下班再说吧，下午再弄吧！这个容易验证。

ysr

4000000与4500000之间有606组p, p+30, p+210, p+2310素数对:
/4000987/4001017/4001197/4003297////
/4001531/4001561/4001741/4003841////
/4003667/4003697/4003877/4005977////
/4004207/4004237/4004417/4006517////
/4004909/4004939/4005119/4007219////
/4006319/4006349/4006529/4008629////
/4006939/4006969/4007149/4009249////
/4008643/4008673/4008853/4010953////
/4011701/4011731/4011911/4014011////
/4012037/4012067/4012247/4014347////
/4013153/4013183/4013363/4015463////
/4013951/4013981/4014161/4016261////
/4014653/4014683/4014863/4016963////
/4015279/4015309/4015489/4017589////
/4015463/4015493/4015673/4017773////
/4018151/4018181/4018361/4020461////
/4018769/4018799/4018979/4021079////
/4018867/4018897/4019077/4021177////
/4019101/4019131/4019311/4021411////
/4020197/4020227/4020407/4022507////
/4020431/4020461/4020641/4022741////
/4020563/4020593/4020773/4022873////
/4021417/4021447/4021627/4023727////
/4021739/4021769/4021949/4024049////
/4022719/4022749/4022929/4025029////
/4022773/4022803/4022983/4025083////
/4023191/4023221/4023401/4025501////
/4023323/4023353/4023533/4025633////
/4023599/4023629/4023809/4025909////
/4023631/4023661/4023841/4025941////
/4023973/4024003/4024183/4026283////
/4024819/4024849/4025029/4027129////
/4025863/4025893/4026073/4028173////
/4027883/4027913/4028093/4030193////
/4028231/4028261/4028441/4030541////
/4029131/4029161/4029341/4031441////
/4029587/4029617/4029797/4031897////
/4029841/4029871/4030051/4032151////
/4030657/4030687/4030867/4032967////
/4032191/4032221/4032401/4034501////
/4032517/4032547/4032727/4034827////
/4032571/4032601/4032781/4034881////
/4032703/4032733/4032913/4035013////
/4032881/4032911/4033091/4035191////
/4033619/4033649/4033829/4035929////
/4036183/4036213/4036393/4038493////
/4036547/4036577/4036757/4038857////
/4036733/4036763/4036943/4039043////
/4037981/4038011/4038191/4040291////
/4038581/4038611/4038791/4040891////
/4039037/4039067/4039247/4041347////
/4039097/4039127/4039307/4041407////
/4039801/4039831/4040011/4042111////
/4039843/4039873/4040053/4042153////
/4041173/4041203/4041383/4043483////
/4041731/4041761/4041941/4044041////
/4043519/4043549/4043729/4045829////
/4043747/4043777/4043957/4046057////
/4044541/4044571/4044751/4046851////
/4044631/4044661/4044841/4046941////
/4044683/4044713/4044893/4046993////
/4044767/4044797/4044977/4047077////
/4045387/4045417/4045597/4047697////
/4049399/4049429/4049609/4051709////
/4050493/4050523/4050703/4052803////
/4052021/4052051/4052231/4054331////
/4052911/4052941/4053121/4055221////
/4053113/4053143/4053323/4055423////
/4055927/4055957/4056137/4058237////
/4056509/4056539/4056719/4058819////
/4057897/4057927/4058107/4060207////
/4057939/4057969/4058149/4060249////
/4058333/4058363/4058543/4060643////
/4060181/4060211/4060391/4062491////
/4060867/4060897/4061077/4063177////
/4061017/4061047/4061227/4063327////
/4061803/4061833/4062013/4064113////
/4061873/4061903/4062083/4064183////
/4062221/4062251/4062431/4064531////
/4063417/4063447/4063627/4065727////
/4064197/4064227/4064407/4066507////
/4064299/4064329/4064509/4066609////
/4066537/4066567/4066747/4068847////
/4067213/4067243/4067423/4069523////
/4068011/4068041/4068221/4070321////
/4069187/4069217/4069397/4071497////
/4070167/4070197/4070377/4072477////
/4071241/4071271/4071451/4073551////
/4072249/4072279/4072459/4074559////
/4073521/4073551/4073731/4075831////
/4074559/4074589/4074769/4076869////
/4074793/4074823/4075003/4077103////
/4075297/4075327/4075507/4077607////
/4075469/4075499/4075679/4077779////
/4075507/4075537/4075717/4077817////
/4077319/4077349/4077529/4079629////
/4077443/4077473/4077653/4079753////
/4078201/4078231/4078411/4080511////
/4078409/4078439/4078619/4080719////

ysr

4500000与6000000之间有1773组p, p+30, p+210, p+2310素数对:
/4500229/4500259/4500439/4502539
/4500233/4500263/4500443/4502543
/4500547/4500577/4500757/4502857
/4501459/4501489/4501669/4503769
/4502341/4502371/4502551/4504651
/4502857/4502887/4503067/4505167
/4503127/4503157/4503337/4505437
/4504039/4504069/4504249/4506349
/4505227/4505257/4505437/4507537
/4505899/4505929/4506109/4508209
/4506301/4506331/4506511/4508611
/4507309/4507339/4507519/4509619
/4508291/4508321/4508501/4510601
/4508953/4508983/4509163/4511263
/4509077/4509107/4509287/4511387
/4511021/4511051/4511231/4513331
/4511333/4511363/4511543/4513643
/4512007/4512037/4512217/4514317
/4514219/4514249/4514429/4516529
/4516189/4516219/4516399/4518499
/4516439/4516469/4516649/4518749
/4517113/4517143/4517323/4519423
/4517143/4517173/4517353/4519453
/4519517/4519547/4519727/4521827
/4520069/4520099/4520279/4522379
/4520543/4520573/4520753/4522853
/4521607/4521637/4521817/4523917
/4522339/4522369/4522549/4524649
/4524313/4524343/4524523/4526623
/4526003/4526033/4526213/4528313
/4527331/4527361/4527541/4529641
/4528399/4528429/4528609/4530709
/4530271/4530301/4530481/4532581
/4530497/4530527/4530707/4532807
/4531799/4531829/4532009/4534109
/4532609/4532639/4532819/4534919
/4535819/4535849/4536029/4538129
/4535863/4535893/4536073/4538173
/4538113/4538143/4538323/4540423
/4538197/4538227/4538407/4540507
/4538923/4538953/4539133/4541233
/4539541/4539571/4539751/4541851
/4541681/4541711/4541891/4543991
/4541981/4542011/4542191/4544291
/4543961/4543991/4544171/4546271
/4545059/4545089/4545269/4547369
/4545193/4545223/4545403/4547503
/4545703/4545733/4545913/4548013
/4546573/4546603/4546783/4548883
/4547129/4547159/4547339/4549439
/4547237/4547267/4547447/4549547
/4548329/4548359/4548539/4550639
/4549087/4549117/4549297/4551397
/4551619/4551649/4551829/4553929
/4552363/4552393/4552573/4554673
/4552901/4552931/4553111/4555211
/4553191/4553221/4553401/4555501
/4553821/4553851/4554031/4556131
/4553873/4553903/4554083/4556183
/4555043/4555073/4555253/4557353
/4556471/4556501/4556681/4558781
/4557199/4557229/4557409/4559509
/4558217/4558247/4558427/4560527
/4559831/4559861/4560041/4562141
/4560761/4560791/4560971/4563071
/4561211/4561241/4561421/4563521
/4561591/4561621/4561801/4563901
/4562287/4562317/4562497/4564597
/4562291/4562321/4562501/4564601
/4562893/4562923/4563103/4565203
/4563619/4563649/4563829/4565929
/4564121/4564151/4564331/4566431
/4564457/4564487/4564667/4566767
/4564667/4564697/4564877/4566977
/4564841/4564871/4565051/4567151
/4565101/4565131/4565311/4567411
/4566271/4566301/4566481/4568581
/4566907/4566937/4567117/4569217
/4567349/4567379/4567559/4569659
/4569533/4569563/4569743/4571843
/4570519/4570549/4570729/4572829
/4570847/4570877/4571057/4573157
/4570897/4570927/4571107/4573207
/4571023/4571053/4571233/4573333
/4571573/4571603/4571783/4573883
/4571813/4571843/4572023/4574123
/4572277/4572307/4572487/4574587
/4573421/4573451/4573631/4575731
/4576067/4576097/4576277/4578377
/4576457/4576487/4576667/4578767
/4576639/4576669/4576849/4578949
/4578811/4578841/4579021/4581121
/4580911/4580941/4581121/4583221
/4581221/4581251/4581431/4583531
/4581403/4581433/4581613/4583713
/4583741/4583771/4583951/4586051
/4584379/4584409/4584589/4586689
/4586707/4586737/4586917/4589017
/4587181/4587211/4587391/4589491

ysr

4500000与5000000之间有578组p, p+30, p+210, p+2310素数对:
/4500229/4500259/4500439/4502539
/4500233/4500263/4500443/4502543
/4500547/4500577/4500757/4502857
/4501459/4501489/4501669/4503769
/4502341/4502371/4502551/4504651
/4502857/4502887/4503067/4505167
/4503127/4503157/4503337/4505437
/4504039/4504069/4504249/4506349
/4505227/4505257/4505437/4507537
/4505899/4505929/4506109/4508209
/4506301/4506331/4506511/4508611
/4507309/4507339/4507519/4509619
/4508291/4508321/4508501/4510601
/4508953/4508983/4509163/4511263
/4509077/4509107/4509287/4511387
/4511021/4511051/4511231/4513331
/4511333/4511363/4511543/4513643
/4512007/4512037/4512217/4514317
/4514219/4514249/4514429/4516529
/4516189/4516219/4516399/4518499
/4516439/4516469/4516649/4518749
/4517113/4517143/4517323/4519423
/4517143/4517173/4517353/4519453
/4519517/4519547/4519727/4521827
/4520069/4520099/4520279/4522379
/4520543/4520573/4520753/4522853
/4521607/4521637/4521817/4523917
/4522339/4522369/4522549/4524649
/4524313/4524343/4524523/4526623
/4526003/4526033/4526213/4528313
/4527331/4527361/4527541/4529641
/4528399/4528429/4528609/4530709
/4530271/4530301/4530481/4532581
/4530497/4530527/4530707/4532807
/4531799/4531829/4532009/4534109
/4532609/4532639/4532819/4534919
/4535819/4535849/4536029/4538129
/4535863/4535893/4536073/4538173
/4538113/4538143/4538323/4540423
/4538197/4538227/4538407/4540507
/4538923/4538953/4539133/4541233
/4539541/4539571/4539751/4541851
/4541681/4541711/4541891/4543991
/4541981/4542011/4542191/4544291
/4543961/4543991/4544171/4546271
/4545059/4545089/4545269/4547369
/4545193/4545223/4545403/4547503
/4545703/4545733/4545913/4548013
/4546573/4546603/4546783/4548883
/4547129/4547159/4547339/4549439
/4547237/4547267/4547447/4549547
/4548329/4548359/4548539/4550639
/4549087/4549117/4549297/4551397
/4551619/4551649/4551829/4553929
/4552363/4552393/4552573/4554673
/4552901/4552931/4553111/4555211
/4553191/4553221/4553401/4555501
/4553821/4553851/4554031/4556131
/4553873/4553903/4554083/4556183
/4555043/4555073/4555253/4557353
/4556471/4556501/4556681/4558781
/4557199/4557229/4557409/4559509
/4558217/4558247/4558427/4560527
/4559831/4559861/4560041/4562141
/4560761/4560791/4560971/4563071
/4561211/4561241/4561421/4563521
/4561591/4561621/4561801/4563901
/4562287/4562317/4562497/4564597
/4562291/4562321/4562501/4564601
/4562893/4562923/4563103/4565203
/4563619/4563649/4563829/4565929
/4564121/4564151/4564331/4566431
/4564457/4564487/4564667/4566767
/4564667/4564697/4564877/4566977
/4564841/4564871/4565051/4567151
/4565101/4565131/4565311/4567411
/4566271/4566301/4566481/4568581
/4566907/4566937/4567117/4569217
/4567349/4567379/4567559/4569659
/4569533/4569563/4569743/4571843
/4570519/4570549/4570729/4572829
/4570847/4570877/4571057/4573157
/4570897/4570927/4571107/4573207
/4571023/4571053/4571233/4573333
/4571573/4571603/4571783/4573883
/4571813/4571843/4572023/4574123
/4572277/4572307/4572487/4574587
/4573421/4573451/4573631/4575731
/4576067/4576097/4576277/4578377
/4576457/4576487/4576667/4578767
/4576639/4576669/4576849/4578949
/4578811/4578841/4579021/4581121
/4580911/4580941/4581121/4583221
/4581221/4581251/4581431/4583531
/4581403/4581433/4581613/4583713
/4583741/4583771/4583951/4586051
/4584379/4584409/4584589/4586689
/4586707/4586737/4586917/4589017
/4587181/4587211/4587391/4589491

578+606=1184，故4000000~5000000之间有1184组4生素数。