PRP Records

Probable Primes Top 10000

(202622 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
350110^96377-2000196377Robert Price11/2016
35022^320124-279044996367Enzo Doria03/2016
35032^320043-10877596343Enzo Doria04/2014
350410^96338+42493996339Patrick De Geest03/2016
350510^96338-928196338Robert Price09/2015
3506(3*2^320008+1)/796332Lelio R Paula09/2013
35072^319838+425796281Lelio R Paula03/2016
35082^319830-1699596279Lelio R Paula03/2016
35096^123713+14396268Lelio R Paula05/2016
3510(28*10^96265-97)/396266Robert Price07/2016
3511103^47825-10296264Norbert Schneider10/2016
35122^319713-8196244Lelio R Paula11/2012
3513(55459*2^319706+1)/2016796242Lelio R Paula07/2014
351412^89153-4396213Lelio R Paula06/2016
3515(2*10^96195-59)/396195Robert Price05/2017
35162^319545+14796193Lelio R Paula11/2012
3517(50^56597+1)/5196155Robert Price03/2014
3518(41*10^96137-59)/996138Robert Price10/2017
35192^319353-11034396135Enzo Doria05/2014
352011^92309-4296130Lelio R Paula05/2016
352114^83869-13^8386996125Jean-Louis Charton01/2009
3522(7*10^96112+143)/396113Robert Price04/2016
35232^319237+6583596100Lelio R Paula03/2016
35242^319194-184196087Yves Minet03/2013
352520^73847-3196078Lelio R Paula05/2016
35262^319107-10955596061Enzo Doria04/2014
3527(3*2^319114-1)/262796060Lelio R Paula02/2014
35282^319098-11215796059Enzo Doria06/2014
352915^81673+9496055Lelio R Paula07/2016
35302^319074+187174996051Enzo Doria05/2016
35312^319007-11211196031Enzo Doria06/2014
35322^318946-142196013Yves Minet01/2013
35332^318834-11041195979Enzo Doria05/2014
35342^318831-196595978Lelio R Paula03/2016
3535(5*10^95976+7)/395977Erik Branger03/2014
35365*3^201089-895945Lelio R Paula08/2014
35372^318711-13995942Lelio R Paula11/2012
35382^318635-116795919Lelio R Paula03/2016
353915^81555+1695917Lelio R Paula07/2016
3540(37*10^95895+377)/995896Robert Price10/2017
3541(22699*2^318527+1)/2195890Lelio R Paula07/2014
35422^318496-9730595877Lelio R Paula03/2016
35432^318466+1501595868Lelio R Paula03/2016
35446^123187-17312995859Mike Oakes04/2011
35452^318423-48795855Yves Minet03/2012
3546(10223*2^318350+1)/156395834Lelio R Paula07/2014
354745369!2+102495787Robert Price02/2015
35483^200758-8695786Lelio R Paula05/2016
35493*10^95776-5995777Robert Price10/2017
3550193^41901-295768Lelio R Paula10/2017
35514*10^95752-7195753Robert Price11/2017
3552(509203*2^317881-1)/5280595693Lelio R Paula04/2015
35534*10^95672+9195673Robert Price11/2017
3554(11*10^95641-113)/395642Robert Price01/2017
3555(13*10^95588+11)/395589Robert Price05/2015
3556Phi(191188,10)/19118995587Maksym Voznyy11/2015
35573^200325+7095580Lelio R Paula05/2016
3558(25*10^95574-7)/995575Robert Price12/2014
3559(2^317485-3)/2131395569Lelio R Paula06/2013
35602^317464+3195567Lelio R Paula11/2012
35617^113073+8295558Lelio R Paula04/2016
35622^317251+46595503Lelio R Paula03/2016
356319^74684+5895503Lelio R Paula06/2016
3564(2^317250-7)/33995500Lelio R Paula07/2013
35656^122718-7995494Lelio R Paula05/2016
35662^317141-11049195469Enzo Doria05/2014
35672^317094+7630995455Enzo Doria05/2016
35682^317085+9595453Lelio R Paula11/2012
3569(17*10^95451-377)/995452Robert Price11/2017
35702^317057-10955195444Enzo Doria04/2014
35713^200026+2895437Lelio R Paula05/2016
35722^317024+9395434Donovan Johnson06/2008
35732^316999+160595427Lelio R Paula03/2016
35742^316995-11042795426Enzo Doria05/2014
35762^316937+17795408Lelio R Paula11/2012
35754*10^95407+9195408Robert Price11/2017
35772^316908+191595399Lelio R Paula03/2016
35782^316894+9995395Lelio R Paula11/2012
35796^122547+1195361Lelio R Paula05/2016
35802^316771+8287595358Lelio R Paula03/2016
3582(23*10^95326+1)/395327Serge Batalov05/2009
35811*10^95326+5795327Robert Price03/2011
358310^95326-39368795326Patrick De Geest09/2013
3584(3^199803+4)/47953995325Lelio R Paula04/2013
35852^316654-10948195323Enzo Doria04/2014
35868*10^95316+5195317Robert Price05/2017
3587(50^56099+43^56099)/9395309Serge Batalov12/2016
3588(23*2^316559+1)/392595292Lelio R Paula09/2013
3589(71*10^95277-539)/995278Robert Price11/2017
359019^74503-5695271Lelio R Paula06/2016
359111^91475-438095262Enzo Doria01/2013
3592(62*10^95251-611)/995252Robert Price05/2017
3593(2^316321-509203)/6937795218Lelio R Paula06/2013
3594(79*10^95214-43)/995215Erik Branger11/2013
3595(9*2^316233-1)/175195194Lelio R Paula02/2014
35965*2^316213+995191Lelio R Paula08/2014
35972^316205-184816395188Enzo Doria07/2015
35982^316185-278791395182Enzo Doria04/2016
3599(9787*2^316142-1)/395172Lelio R Paula04/2015
36002^316140-595168Henri Lifchitz02/2006
3601(15185*2^316117-1)/395165Lelio R Paula04/2015
3602(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
36032^316069+7681795147Enzo Doria05/2016
3604(199*10^95134-7)/395136Robert Price02/2017
36052^316027-9730595134Lelio R Paula03/2016
36062^316006-279805195128Enzo Doria04/2016
36072^315921-279760395102Enzo Doria04/2016
36082*10^95095+6395096Robert Price10/2017
36092^315857+129995083Lelio R Paula03/2016
361014^82955-4395078Lelio R Paula06/2016
3611(2*10^95072-17)/395072Robert Price08/2014
36122^315727+6595044Lelio R Paula11/2012
36132^315725+188575795043Enzo Doria03/2017
36141*10^94983+2194984Robert Price03/2011
361510^94983-71794983Patrick De Geest08/2013
361617^77187-8294975Lelio R Paula07/2016
36173*10^94964+3794965Robert Price10/2017
3618(2^315481-1017)/2062728594962Lelio R Paula06/2013
36192^315423-11032994952Enzo Doria05/2014
362011^91169-723094943Enzo Doria02/2013
36217*10^94938+6194939Robert Price02/2017
36222^315351+102594931Lelio R Paula03/2016
36232^315350-11225394930Enzo Doria06/2014
3626((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
36242^315268+794906Lelio R Paula10/2012
362511^91133+6294906Lelio R Paula05/2016
362730^64244+4194897Lelio R Paula08/2012
3628(151*10^94885-7)/994887Robert Price07/2017
36294^157583+2214794875Mike Oakes01/2011
36302^315098+12394854Lelio R Paula11/2012
36313^198791-3494848Robert Price11/2013
36323*2^315067+794846Lelio R Paula08/2014
3633(9*2^315057+1)/7394841Lelio R Paula09/2013
3634(16*10^94822+53)/394823Robert Price12/2016
36358*6^121849-794818Lelio R Paula10/2014
3636(85*10^94802+473)/994803Robert Price03/2017
36372^314870-10876194786Enzo Doria03/2014
36385*2^314841-394778Lelio R Paula08/2014
36396^121772+11394758Lelio R Paula05/2016
36406^121756-1625394745Enzo Doria02/2013
36412^314718-11279394740Enzo Doria06/2014
36422^314697-184729394734Enzo Doria07/2015
36432^314548-24994689Yves Minet02/2012
36445^135469+4294689Lelio R Paula04/2016
3645gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
3646(2*10^94604+547)/994604Robert Price10/2017
36473*2^314152+594570Lelio R Paula08/2014
36482*6^121530-594570Lelio R Paula10/2014
36497*10^94563+8794564Robert Price11/2016
36502^314114-10967794558Enzo Doria04/2014
3651(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
36522^314059+7658394542Enzo Doria05/2016
36532^314041-403594536Lelio R Paula03/2016
3654(7*2^314003-11)/1594524Renaud Lifchitz03/2011
365511^90760-471094517Enzo Doria01/2013
3656(7*2^313926-1)/14882194497Lelio R Paula02/2014
365794*10^94493-394495Robert Price11/2016
3658(1000547^15749+1)/100054894492Faysal YAtim12/2008
3659(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
36607^111792-3294476Lelio R Paula04/2016
366111^90680-585094434Enzo Doria01/2013
36622^313675-11012594426Enzo Doria04/2014
3663(2999*29^64556-2427)/494410Curtis Bright05/2015
36642^313609-11222594406Enzo Doria06/2014
36652^313584+7290194399Enzo Doria04/2016
36662^313510-11286594376Enzo Doria06/2014
36677*10^94373+8794374Robert Price11/2016
3668(9^98897+8^98897)/1794371Robert Price12/2012
36692^313453-11470394359Enzo Doria04/2015
36708*10^94357-5194358Robert Price10/2017
3671(379*10^94337-1)/994339Robert Price08/2017
36722^313344-313344+194326Robert Price10/2014
367320^72481-4994300Lelio R Paula05/2016
367444725!2+12894289Robert Price03/2015
36754*10^94286+994287Robert Price05/2015
367617^76621+2494279Lelio R Paula07/2016
36772^313156-11285994270Enzo Doria06/2014
36786^121130-5994258Lelio R Paula05/2016
36793^197542+2894252Robert Price11/2013
3680(3^197521+2)/5165594237Lelio R Paula04/2013
36812^313045-595594236Lelio R Paula03/2016
3682(67*10^94212+23)/994213Ray Chandler02/2011
36832^312909-186520394195Enzo Doria03/2016
36842^312848-14994177Lelio R Paula11/2012
36854^156403-7759794164Mike Oakes04/2011
368618^75004-8594151Lelio R Paula06/2016
368719^73622-4894145Lelio R Paula06/2016
3688(11^90397-3^90397)/894138Robert Price04/2011
3689(3^197287+5)/1694129Lelio R Paula04/2013
369012^87212-3794118Lelio R Paula06/2016
369111^90376+7694117Lelio R Paula05/2016
3692(6^120946-11)/594114Paul Bourdelais11/2011
3693(10^94096+191)/394096Robert Price11/2017
36942^312562-11268594091Enzo Doria06/2014
3695137^44026-294072Lelio R Paula10/2017
36962^312404-86968810594043Lelio R Paula09/2016
36972^312387+279353394038Enzo Doria03/2016
369910^94016+9194017Robert Price04/2011
3698(15*2^312325-1)/720194017Lelio R Paula02/2014
370110^94016-18896394016Patrick De Geest08/2013
3700(17*2^312315-1)/4594016Lelio R Paula02/2014
37026^120802+766194003Mike Oakes04/2011
3703(67607*2^312254+1)/17794001Lelio R Paula06/2014
3704(11*2^312207+1)/1993984Lelio R Paula09/2013
37052^312201+5193982Lelio R Paula11/2012
3706(4*6^120749+1)/593961Serge Batalov10/2014
37073^196892+5893942Lelio R Paula05/2016
37082^312060+1891593940Lelio R Paula03/2016
37092^311992-1620993919Enzo Doria04/2013
3710(85^48677+1)/8693917Paul Bourdelais08/2017
37112^311965-3993911Lelio R Paula11/2012
37122^311920-11168993898Enzo Doria05/2014
37137*10^93887-4793888Robert Price02/2017
371412^86965-1393851Lelio R Paula06/2016
37152^311705+1609593833Lelio R Paula03/2016
37162^311665-8193821Lelio R Paula11/2012
3717730^32761+32761^73093806Norbert Schneider09/2017
371811^90073+9293802Lelio R Paula05/2016
37196*10^93792+4193793Robert Price01/2017
3720(2^311580+7)/59132993790Lelio R Paula06/2013
372112^86900-7793781Lelio R Paula06/2016
37222^311508-10976993774Enzo Doria04/2014
37232^311486-185962193767Enzo Doria03/2016
3724Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
37252^311471+31146993763Renaud Lifchitz01/2003
3726(88*10^93760-1)/393762Robert Price10/2017
37272^311426+7945993749Enzo Doria06/2016
37282^311294+577593709Lelio R Paula03/2016
37292^311252-101793697Lelio R Paula03/2016
37302^311247-11204193695Enzo Doria06/2014
37317*10^93692-8393693Robert Price09/2017
37322^311205-10964593683Enzo Doria04/2014
37335^134027-8493681Lelio R Paula04/2016
3734(2^311148-1017)/55793663Lelio R Paula06/2013
3735(2^311027-2^155514+1)/59362811/2006
37363^196192-2893608Robert Price12/2013
3737216091#+26143393606Makoto Morimoto12/2015
37385^133917+6893604Lelio R Paula04/2016
37392^310924-170993598Yves Minet03/2013
3740(266*10^93577-11)/393579Robert Price09/2016
3741(16*10^93577+161)/393578Robert Price05/2016
37423^196113-5693570Lelio R Paula04/2016
37432^310806-11034593562Enzo Doria05/2014
37443^196093+8693561Lelio R Paula04/2016
37452^310780-232793555Yves Minet10/2013
374630^63332+4193550Lelio R Paula08/2012
3747(21181*2^310707+1)/2193536Lelio R Paula06/2014
37488*5^133807+793528Lelio R Paula10/2014
37492^310686+819393526Lelio R Paula03/2016
37502^310646+6393514Lelio R Paula11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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