急求最小的八生素数（三组）排列形式如下

素数粉

假设素数的个位数如下：
第一个素数为p,其个位数必为1；最后一个素数为p+26，其个位数必为7
1，3，7，9
   3，   9
1，   7   
我只能提供最小的第一组八生素数：
11，13，17，19
    23，    29
31，    37   
请各位高人提供另外两组八生素数，万分感激，先谢谢了！
可能通过寻找素数的程序才能找到。

tprime

我的程序瞬间能找到很多

tprime

最小8生素数有三组形式
n, n+6, n+8, n+14, n+18, n+20, n+24, n+26
n, n+2, n+6, n+12, n+14, n+20, n+24, n+26
n, n+2, n+6, n+8 , n+12, n+18, n+20, n+26
计算其中一组10^16 以内8生素数需要20小时

下面是计算1分钟的部分结果, 针对第一组数据的n值
n = 10302503086853
n = 50382178302083
n = 336308783307173
n = 294954801534293
n = 351782802123653
n = 478805412608423
n = 694368452060183
n = 269899390140623
n = 652005272719043
n = 975385526755883
n = 39578906083883
n = 103011347996723
n = 474743189027273
n = 38708472056693
n = 186526461325643
n = 367218523546313
n = 424664491385573
n = 949698167522543
n = 66374962399373
n = 295315765800683
n = 20952510546413
n = 132013272368423
n = 162400529098253
n = 547639304850083
n = 946600299942743
n = 45362142556253
n = 411107732606093
n = 454635828657533
n = 547311730155713
n = 18347232011813
n = 138760939315703
n = 232123074482003
n = 409470528395633
n = 663202303882823
n = 903704002900403
n = 126706190327393
n = 175780821312773
n = 329456560069313
n = 459179263559693
n = 487138600585313
n = 659778348756203
n = 992758288989143
n = 7280264031563
n = 34116997735343
n = 36372020465303
n = 331172962390793
n = 355576199068613
n = 590782565723873
n = 598141060947953
n = 336730577608283
n = 725346756319043
n = 304710801619313
n = 567519333615323
n = 683456905575533
n = 140199516389063
n = 225710567274323
n = 359765734300103
n = 383462435858633
n = 616702015771973
n = 906713599964303
n = 999420288278543
n = 64334926995323
n = 77977279088693
n = 414018722776643
n = 706139203869083
n = 909770567354633
n = 156401487505163
n = 219476311547393
n = 354210127083713
n = 539216136131573
n = 929764745282273
n = 982742832214043
n = 2104286376323
n = 40456627843763
n = 172872731553653
n = 463349241287063
n = 560003781028823
n = 287257651347833
n = 489810583899803
n = 40500800234333
n = 63058835784383
n = 218484291920333
n = 238764995453423
n = 980291785217183
n = 77202700663793
n = 81386807440643
n = 287936448758663
n = 598432271378303
n = 706230076883693
n = 739945209955313
n = 751984193591993
n = 50318150714963
n = 168899373184673
n = 593432834686823
n = 711146448985103
n = 713993560192043
n = 942737818774883
n = 89946657777653
n = 221159175453893
n = 366479863136063
n = 597096540176813
n = 659662043196833
n = 806226250536383
n = 838429483228013
n = 56716082423243
n = 138221500827653
n = 618560305203083
n = 792015457813823
n = 154845117152633
n = 163374849944213
n = 315608739481943
n = 363942702138923
n = 560921659333943
n = 79564733612453
n = 181166803932203
n = 537234848374313
n = 926092190477543
n = 943019585081663
n = 66803449635053
n = 674203905747503
n = 693110357201393
n = 617024087705933
n = 803365753766483
n = 903795024868643
n = 120149044747793
n = 238679848228883
n = 383477606223773
n = 415890100027463
n = 428157753855893
n = 519499336898603
n = 6303042944903
n = 287301229003493
n = 525787730126363
n = 724847251427003
n = 970505072856023
n = 119066747016383
n = 153662204553023
n = 996633561070313
n = 125028680878463
n = 254831920894913
n = 738672018993893
n = 21010217322953
n = 242606580350993
n = 355422413781293
n = 470449766831903
n = 31295765372933
n = 65914201475183
n = 168810656626673
n = 561090689541443
n = 161285287945913
n = 204336411441293
n = 581906815972613
n = 687062978804333
n = 181523196293
n = 34783896611903
n = 42926340181163
n = 88922512653413
n = 412398696624353
n = 829636128906023
n = 76584510368273
n = 142801820577323
n = 790010299133963
n = 899754366837233
n = 988103605214633
n = 120325808842223
n = 619798396306073
n = 629943098383583
n = 709698799408583
n = 833877421986593
n = 970652760376283
n = 35525383137683
n = 122599199577293
n = 458590001183753
n = 589943736646703
n = 820860250504733
n = 932641825389713
n = 34897599813053
n = 90279958604813
n = 237563417357243
n = 491733347241113
n = 922902706161413
n = 46328924003
n = 75787027567613
n = 627284426129723
n = 710514798604973
n = 884193713364323
n = 933387029756543
n = 963903011072363
n = 292265714685803
n = 682877905304453
n = 38962798097123
n = 389457090275153
n = 545640169797623
n = 648869479511153
n = 842173874044403
n = 928615891476173
n = 389371598243
n = 119521187271113
n = 144684947542763
n = 251631430656233
n = 465772699247483
n = 24702329826263
n = 72961779464663
n = 139311383745623
n = 713174957989583
n = 768119385477533
n = 936943130107073
n = 390174482548373
n = 428052082388453
n = 561104000777843
n = 10148123019893
n = 11408151549653
n = 95126651224463
n = 419815344943853
n = 66948237009743
n = 98749233256763
n = 268117101396233
n = 369654697876553
n = 471724593944693
n = 721007228325473
n = 4584484096253
n = 41834969878763
n = 498287443756163
n = 696028486195103
n = 773174446826843
n = 18784717328543
n = 31383887161793
n = 172992309487163
n = 338190125700593
n = 497098953908723
n = 18040405074053
n = 640719227735753
n = 75528314372873
n = 675254450197493
n = 178910442702353
n = 302581529001113
n = 162848722882823
n = 230755961582123
n = 489013845215873
n = 701443545308483
n = 34057729338533
n = 79025220587213
n = 124302141646583
n = 232308092799683
n = 334796287999073
n = 498786279414323
n = 833387435533553
n = 242916307749743
n = 536088225538493
n = 618107873008253
n = 675449656477223
n = 805876664158193
n = 927379287760553
n = 947367293448203
n = 8550480581543
n = 96894364730063
n = 523138502359373
n = 636498236206733
n = 76477425901553
n = 136297548063353
n = 232543381667273
n = 330455719010093
n = 608857550247623
n = 655852509498863
n = 744583013591093
n = 62029485469313
n = 323619930395123
n = 502773321091403
n = 747238711130273
n = 956319787244183
n = 12626312784713
n = 121760667674273
n = 388575501429743
n = 913931546763863
n = 38962946808413
n = 86513853491693
n = 191876377228163
n = 4494057399893
n = 66359718086723
n = 101510007591053
n = 850852632962393
n = 861199457180123
n = 885506094645233
n = 476635760456483
n = 526277939703143
n = 562489705082933
n = 645175730955383
n = 678120078161153
n = 800436321460403
n = 861223551213653
n = 6517137664553
n = 178801052707793
n = 149263854324443
n = 42634683753023
n = 124673294116733
n = 141538222717253
n = 197819868867983
n = 306175629641243
n = 412909505249603
n = 421350893264663
n = 627689042541923
n = 938195276329673
n = 27049862063663
n = 98400762304283
n = 421620612567593
n = 475161785903243
n = 145285810866173
n = 339648334881833
n = 435601693733183
n = 746010659029613
n = 883589131751303
n = 54209634252863
n = 56572857024773
n = 266762927795453
n = 563696860651013
n = 281084076984233
n = 662883608903
n = 9218495173403
n = 16254621200333
n = 140518688347553
n = 257305797956723
n = 375310771543223
n = 516295203111203
n = 961429283322023
n = 342852394682243
n = 423071013412493
n = 512797404076403
n = 994959472414073
n = 199853062839953
n = 260703650968283
n = 393076251568523
n = 801690921331823
n = 27763759290713
n = 216082251272333
n = 228546896104973
n = 400556630010983
n = 956628101686703
n = 53131203362753
n = 897168274520033
n = 910924403977103
n = 922090871399213
n = 119337879163403
n = 138426151306343
n = 179515619195813
n = 888361088247533
n = 906957663704993
n = 940083162321203
n = 127823514101183
n = 572419494309563
n = 903034873213373
n = 414878746109273
n = 421350893360843
n = 512972457955403
n = 604672997425943
n = 739211383608143
n = 42733960181813
n = 82918340297693
n = 932994312353003
n = 951946944030983
n = 101638583232863
n = 150300492408743
n = 331265397209423
n = 408422512484663
n = 664452590718593
n = 971921638174163
n = 87474045268853
n = 185389729004723
n = 277376719720343
n = 716927677766543
n = 535350234478043
n = 654261411302483
n = 857675259239783
n = 439813613116043
n = 287159267546513
n = 536554563826643
n = 730865553389333
n = 574761998333
n = 25227862690553
n = 661918181705303
n = 881709946507913
n = 377887196638313
n = 395258099867993
n = 465562025269703
n = 485109422539103
n = 793487796532793
n = 60642294164513
n = 590376537072383
n = 148657785615323
n = 297879029036573
n = 315989782232213
n = 329013274704203
n = 387504209546543
n = 433217500259633
n = 509859940283783
n = 905901318986753
n = 973226731481093
n = 178251445433
n = 104710869705503
n = 352557232189223
n = 811759771875113
n = 5532554868083
n = 18243271136333
n = 874471252174763
n = 56329909011353
n = 462926034486893
n = 652730101889843
n = 213769521573053
n = 276979539894503
n = 307177167684833
n = 410553495599693
n = 867053934444143
n = 94380182745833
n = 150512579766533
n = 183710583565493
n = 262008372685043
n = 304830602895803
n = 415422423505073
n = 650466378550973
n = 707131967530973
n = 719639000008913
n = 60062401266383
n = 75076105231643
n = 442806998731613
n = 53667741819053
n = 79129554165023
n = 155738307165803
n = 229915124790713
n = 291262540740533
n = 455348685182753
n = 730639263255263
n = 957529173902663
n = 995544198950663
n = 197129693686553
n = 199316673091163
n = 242913258653693
n = 256635924180263
n = 289734874744943
n = 429984884584883
n = 469737579997313
n = 649771518251483
n = 704411870157623
n = 889003149560153
n = 3308765188433
n = 388867233022973
n = 445389819473303
n = 458178172060313
n = 545401014537083
n = 702094530546113
n = 175198177456433
n = 310629381304373
n = 327674568943853
n = 334216544263733
n = 6382761847523
n = 14289396253193
n = 240165795992183
n = 428853952859393
n = 640264118536103
n = 312436582105163
n = 80284282876313
n = 103922311010033
n = 231196570252163
n = 330167037077393
n = 348627748977023
n = 511864355770283
n = 821525736859343
n = 5196353988803
n = 30742049253893
n = 28197154291283
n = 164043310877423
n = 272138722271393
n = 410256633552743
n = 780858509196743
n = 221502292699133
n = 789842310574763
n = 971792616582233
n = 3916544140493
n = 37815282644123
n = 141009789869933
n = 174564965353763
n = 312940325807093
n = 246661591114643
n = 337284815115953
n = 896035632160373
n = 38406553311803
n = 93367489672133
n = 268160307131393
n = 372381264652073
n = 446915700147593
n = 710429205612803
n = 757423272492563
n = 982974402827093
n = 20506771481873
n = 21562670035583
n = 36860594317223
n = 57107610826943
n = 162828421712633
n = 462067573193903
n = 549619923839663
n = 586824452490953
n = 677094966664793
n = 748786975903643
n = 912781875362033
n = 938688534890783
n = 39135546250043
n = 63372355646843
n = 272094921518663
n = 294664334805083
n = 321178476218843
n = 682110837598433
n = 20642411954603
n = 601743788179973
n = 607502261340413
n = 640682640802643
n = 735311497284803
n = 826678289821823
n = 12447466966373
n = 313234659872573
n = 494149814963243
n = 514511055022403
n = 679289902825973
n = 732649032379703
n = 14466308941943
n = 19920483427703
n = 268375666353653
n = 624105725097713
n = 656080287597593
n = 703668450790163
n = 744147313494443
n = 898569520994003
n = 323606172845933
n = 534997152535823
n = 651776007708803
n = 767808617231633
n = 850974515867453
n = 66094907124923
n = 336312799519373
n = 398929390806623
n = 453968186578583
n = 905822270219543
n = 179590045493
n = 38185022100083
n = 65651770068743
n = 550650984498473
n = 687635807093093
n = 36447649458743
n = 244342317689993
n = 249612440558003
n = 564581647210103
n = 670802409217463
n = 917736098770013
n = 84911898357263
n = 362771390827823
n = 641741439605243
n = 795290238518753
n = 108429084070823
n = 229924122515603
n = 320366864385083
n = 503134805761103
n = 545689993806473
n = 786754109949323
n = 972437205857633
n = 845428353215423
n = 8121993959063
n = 198408611239823
n = 671066997379763
n = 2441305562603
n = 340148806803713
n = 358184526785993
n = 476647733127473
n = 649631267411033
n = 920351341855853
n = 219129477010883
n = 652726755635393
n = 89080239462653
n = 339159984667943
n = 527816685440483
n = 763797407447513
n = 50795867418203
n = 333780695484143
n = 738917347404143
n = 747622431191543
n = 17645084658563
n = 42010618641353
n = 226553040705353
n = 471045648074363
n = 484636019529023
n = 551972140481123
n = 699826047702143
n = 882177697782743
n = 52842521408843
n = 58455984203783
n = 127381864947503
n = 241533355390493
n = 346403959348613
n = 774739369541303
n = 954657745688813
n = 983969025506633
n = 17616677323103
n = 133186592233553
n = 561024505326143
n = 634665676970183
n = 862973342806433
n = 912800242949453
n = 953262596781353
n = 112094649135173
n = 662072115973973
n = 251781721018343
n = 268519709775833
n = 361165716829433
n = 372054879814133
n = 37510017748103
n = 398744446873673
n = 410477123999843
n = 608366746290203
n = 635412518013173
n = 758135905800173
n = 838966022087093
n = 995861883329213
n = 482296816247153
n = 497520673695953
n = 528607326573233
n = 646900089962033
n = 163790844447473
n = 545104524244523
n = 114468059541743
n = 146047078383113
n = 173469877056383
n = 289181679032153
n = 338296243641263
n = 625104660406133
n = 356415698100593
n = 667635829072343
n = 776856520902593
n = 876408813932783
n = 10880983524773
n = 77784304309073
n = 181209117261233
n = 276007524324593
n = 364037739897893
n = 511399281154823
n = 486695612934053
n = 899356964266283
n = 109878444597983
n = 159683481639743
n = 248381860358693
n = 534497573762213
n = 988048501772393
n = 152299776928283
n = 294736766172833
n = 392065269474863
n = 639402980214983
n = 871133113769903
n = 873357572776673
n = 319310296582793
n = 495768948502343
n = 623568145267583
n = 691292670906353
n = 879579037514693
n = 8100354013883
n = 68899853874983
n = 112495993251773
n = 630517637391773
n = 881463206025533
n = 894123503305163
n = 764985775643
n = 410148879754703
n = 548574882289523
n = 757633426023563
n = 868162111350623
n = 877099657908563
n = 209261187077003
n = 390927495860963
n = 765913815679073
n = 88606390249823
n = 152100628887653
n = 407556689167073
n = 475602245445773
n = 744658047080393
n = 787117082098793
n = 169388913887093
n = 333030880425143
n = 532875688628183
n = 602971245289313
n = 628381746275183
n = 239115623342573
n = 361642243218233
n = 440501557091573
n = 916493619987923
n = 58349568983333
n = 198879560375123
n = 356118538451303
n = 657109415147813
n = 20060808992663
n = 73669133282183
n = 96854729075543
n = 121159581797693
n = 564180526343873
n = 738266585590973
n = 817391156886743
n = 912395701761983
n = 275038855109723
n = 338689928035163
n = 366540841925963
n = 386746809347603
n = 514427097613133
n = 537366398878013
n = 899855502304463
n = 111476384167853
n = 261482022120023
n = 152906143384853
n = 214891604942873
n = 269464359709403
n = 395469666706973
n = 35249194682063
n = 117127847457983
n = 357141419276003
n = 710898667770653
n = 837460814571743
n = 908182369826093
n = 237259862326163
n = 259498651979243
n = 368169642977813
n = 836140847919053
n = 312623831654573
n = 537437863146623
n = 572394508039793
n = 460984910363
n = 94554195411653
n = 674862030298433
n = 710134128509783
n = 49468911133703
n = 122472929541023
n = 245719916293913
n = 715240278124433
n = 987698915305163
n = 73276117512113
n = 287903728559963
n = 289812288062813
n = 451577597378423
n = 682789709289203
n = 708439812017453
n = 928208375161583
n = 131735745511613
n = 309738200091563
n = 327791544410573
n = 741655812497843
n = 905543627378633
n = 872442148100423
n = 941690398041293
n = 27502517896943
n = 272419447904693
n = 992765354404913
n = 16928435874593
n = 104974044855923
n = 315827593821983
n = 899702609873513
n = 176080286811413
n = 248693000324753
n = 119290732888493
n = 295159304166893
n = 938012786808263
n = 7060741341743
n = 199898202498083
n = 366095697861983
n = 626334869274203
n = 707028229631813
n = 10341395817653
n = 267897875468123
n = 325023705038933
n = 783918153471353
n = 337505379501533
n = 901681592051483
n = 502665344633513
n = 907259657786543
n = 16689652712633
n = 327498177339233
n = 627654686701943
n = 894073530613163
n = 938758363195553
n = 69169870189943
n = 83066325062243
n = 339167793014573
n = 418562306683043
n = 579049070760683
n = 931877360544653
n = 306200541803063
n = 308858247163373
n = 331073388972233
n = 562005742424033
n = 656316691566443
n = 109482008698193
n = 184338813390863
n = 466773494439383
n = 507216885377333
n = 766171711136963
n = 773225684593493
n = 891981365687543
n = 1512867877043
n = 462003991980053
n = 603788434579853
n = 762030438199553
n = 865365270840593
n = 976191785149103
n = 6295458106103
n = 72582596383463
n = 104244605772473
n = 117230395549433
n = 210468714172883
n = 470755181273543
n = 7250444125013
n = 78034242290093
n = 101074158439343
n = 228284390027783
n = 445126643996123
n = 936259573793633
n = 306171391359923
n = 399391193275163
n = 855476233195673
n = 6772728484583
n = 76931197335053
n = 326288121641543
n = 361296524080553
n = 474065954193893
n = 533679492358073
n = 190114390001513
n = 433520312000753
n = 730548390047453
n = 925625926711463
n = 199097076053783
n = 616750576538003
n = 112652678407253
n = 270380899147343
n = 327071697621653
n = 606332659501553
n = 876552113546093
n = 609702180422963
n = 118999373680703
n = 189537100410173
n = 279820777063343
n = 311538113484113
n = 543426196790993
n = 814619005027343
n = 105837488880023
n = 250144442560913
n = 790717652557733
n = 993329704720253
n = 328761179927423
n = 424415817425843
n = 877345431793073
n = 991060106396603
n = 95600501110973
n = 165667055699003
n = 444754451326043
n = 554956974877163
n = 723762872077103

[ 本帖最后由 tprime 于 2008-7-16 12:19 编辑 ]

无心人

老大
能用附件形式贴么？
有点长了阿
呵呵

素数粉

形式为p, p+2, p+6, p+8 , p+12, p+18, p+20, p+26
另外请问有无形式为p, p+6, p+10, p+12 , p+16, p+18, p+22, p+26的八生素数
有的话也请给出三个这种形式的八生素数。
谢谢了，我等你的好消息！

无心人

另外请问有无形式为p, p+6, p+10, p+12 , p+16, p+18, p+22, p+26的八生素数
＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝
我想这个序列的数字可能也是能被小素数整除吧
我觉得是至少一个能被3或者7整除

无心人

证明很简单，设小素数为q
设序列为p + k
对所有k取q的剩余
则，如果序列的剩余组成q的完全剩余系0..q-1
则序列至少有一项能被q整除

tprime

最小K生素数有一定模式 很多网站都有
http://primes.utm.edu/glossary/page.php?sort=PrimeConstellation
http://www.opertech.com/primes/k-tuples.html
http://mathworld.wolfram.com/

tprime

你要的两种8生素数数据

无心人

tprime帮我算下
a * b# + C
a是正整数
b#代表不大于b的所有素数的乘积
C代表大于b#中最大的素数p且小于p * p的四生素数

这么考虑下的3000位十进制数字计算多少个能找到一个四生素数阿