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