PRP Records

Probable Primes Top 10000

(224926 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 ?
37512^322413+7797056Lelio R Paula12/2012
37522^322406+17797054Lelio R Paula12/2012
3753(14*10^97044+31)/997045Robert Price02/2015
37542^322302+25525597023Lelio R Paula07/2016
37552^322196-11309396991Enzo Doria07/2014
37562^322000-186146996932Enzo Doria03/2016
37572^321971-11274796923Enzo Doria06/2014
375811^93062-9296915Lelio R Paula06/2016
3759(11*2^321841-7)/1596884Renaud Lifchitz03/2011
37603^203051+3496880Lelio R Paula05/2016
37612*10^96867-5196868Robert Price11/2017
3762(64*10^96863-1)/2796864Serge Batalov05/2010
37632^321716-278693996847Enzo Doria03/2016
37642^321701-11305396842Enzo Doria07/2014
37652^321700-2863596842Lelio R Paula06/2016
3766(5*2^321691-1)/2796838Lelio R Paula02/2014
37676^124433-12443396828Robert Price01/2014
37682^321631+6996821Lelio R Paula12/2012
3769(13*2^321606+1)/11996813Lelio R Paula11/2013
3770(46*10^96798-1)/996799Serge Batalov10/2014
3771(59*10^96798+31)/996799Robert Price09/2015
3772223319#+23122396790Makoto Morimoto02/2016
37732^321519-2863596787Lelio R Paula06/2016
37742^321487-186723796778Enzo Doria03/2016
37752^321461-6396770Lelio R Paula12/2012
37762^321439+12396763Lelio R Paula12/2012
37772^321434+70996762Lelio R Paula02/2013
377814^84413+8996749Lelio R Paula07/2016
3779(28*10^96743+71)/996744Serge Batalov12/2008
378013^86847+9696743Lelio R Paula06/2016
37819*2^321336-796733Lelio R Paula08/2014
3782(209*10^96722-17)/396724Robert Price05/2017
37832^321187-115996687Yves Minet11/2012
37842^321182-185008196686Enzo Doria08/2015
37852^321116-11282996666Enzo Doria06/2014
37862^321108-10949996664Enzo Doria04/2014
37872^321098+279385996661Enzo Doria03/2016
37882^321057+409796648Lelio R Paula06/2016
3789(4435*29^66081-4)/796640Curtis Bright05/2015
3790p(19849)#/2-6496581Robert Price04/2017
37912^320817+18996576Lelio R Paula12/2012
3792(361*10^96567-163)/996569Robert Price10/2017
37932^320788-11032796567Enzo Doria05/2014
37942^320764+79396560Lelio R Paula02/2013
3795(9179*2^320652-1)/22196528Lelio R Paula05/2015
37962^320616-7879596516Lelio R Paula03/2016
37972^320612-46193996514Enzo Doria07/2015
37985*2^320431+796461Lelio R Paula08/2014
379919^75431-9096458Lelio R Paula06/2016
3800(2^320370+3)/6796440Lelio R Paula10/2013
38012^320309+187147796423Enzo Doria05/2016
3802tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
3803(21*2^320252-1)/189596404Lelio R Paula02/2014
38042^320232-17396400Lelio R Paula12/2012
3805175^42975-296395Lelio R Paula10/2017
380610^96377+19991196378Patrick De Geest12/2016
380710^96377-2000196377Robert Price11/2016
38082^320124-279044996367Enzo Doria03/2016
38092^320043-10877596343Enzo Doria04/2014
381010^96338+42493996339Patrick De Geest03/2016
381110^96338-928196338Robert Price09/2015
3812(3*2^320008+1)/796332Lelio R Paula09/2013
38132^319838+425796281Lelio R Paula03/2016
38142^319830-1699596279Lelio R Paula03/2016
38156^123713+14396268Lelio R Paula05/2016
3816(28*10^96265-97)/396266Robert Price07/2016
3817103^47825-10296264Norbert Schneider10/2016
38182^319713-8196244Lelio R Paula11/2012
3819(55459*2^319706+1)/2016796242Lelio R Paula07/2014
382012^89153-4396213Lelio R Paula06/2016
3821(2*10^96195-59)/396195Robert Price05/2017
38222^319545+14796193Lelio R Paula11/2012
3823(50^56597+1)/5196155Robert Price03/2014
3824(41*10^96137-59)/996138Robert Price10/2017
38252^319353-11034396135Enzo Doria05/2014
382611^92309-4296130Lelio R Paula05/2016
382714^83869-13^8386996125Jean-Louis Charton01/2009
3828(7*10^96112+143)/396113Robert Price04/2016
38292^319237+6583596100Lelio R Paula03/2016
38302^319194-184196087Yves Minet03/2013
383120^73847-3196078Lelio R Paula05/2016
383250^56543-4996065Norbert Schneider09/2018
38332^319107-10955596061Enzo Doria04/2014
3834(3*2^319114-1)/262796060Lelio R Paula02/2014
38352^319098-11215796059Enzo Doria06/2014
383615^81673+9496055Lelio R Paula07/2016
38372^319074+187174996051Enzo Doria05/2016
38382^319007-11211196031Enzo Doria06/2014
38392^318946-142196013Yves Minet01/2013
38402^318834-11041195979Enzo Doria05/2014
38412^318831-196595978Lelio R Paula03/2016
3842(5*10^95976+7)/395977Erik Branger03/2014
38435*3^201089-895945Lelio R Paula08/2014
38442^318711-13995942Lelio R Paula11/2012
38452^318635-116795919Lelio R Paula03/2016
384615^81555+1695917Lelio R Paula07/2016
3847(37*10^95895+377)/995896Robert Price10/2017
3848(22699*2^318527+1)/2195890Lelio R Paula07/2014
38492^318496-9730595877Lelio R Paula03/2016
38502^318466+1501595868Lelio R Paula03/2016
38516^123187-17312995859Mike Oakes04/2011
38522^318423-48795855Yves Minet03/2012
3853(10223*2^318350+1)/156395834Lelio R Paula07/2014
385445369!2+102495787Robert Price02/2015
38553^200758-8695786Lelio R Paula05/2016
38563*10^95776-5995777Robert Price10/2017
3857193^41901-295768Lelio R Paula10/2017
38584*10^95752-7195753Robert Price11/2017
3859(509203*2^317881-1)/5280595693Lelio R Paula04/2015
38604*10^95672+9195673Robert Price11/2017
3861(11*10^95641-113)/395642Robert Price01/2017
3862(13*10^95588+11)/395589Robert Price05/2015
3863Phi(191188,10)/19118995587Maksym Voznyy11/2015
38643^200325+7095580Lelio R Paula05/2016
3865(25*10^95574-7)/995575Robert Price12/2014
3866(2^317485-3)/2131395569Lelio R Paula06/2013
38672^317464+3195567Lelio R Paula11/2012
38687^113073+8295558Lelio R Paula04/2016
38692^317251+46595503Lelio R Paula03/2016
387019^74684+5895503Lelio R Paula06/2016
3871(2^317250-7)/33995500Lelio R Paula07/2013
38726^122718-7995494Lelio R Paula05/2016
38732^317141-11049195469Enzo Doria05/2014
38742^317094+7630995455Enzo Doria05/2016
38752^317085+9595453Lelio R Paula11/2012
3876(17*10^95451-377)/995452Robert Price11/2017
38772^317057-10955195444Enzo Doria04/2014
38783^200026+2895437Lelio R Paula05/2016
38792^317024+9395434Donovan Johnson06/2008
38802^316999+160595427Lelio R Paula03/2016
38812^316995-11042795426Enzo Doria05/2014
38832^316937+17795408Lelio R Paula11/2012
38824*10^95407+9195408Robert Price11/2017
38842^316908+191595399Lelio R Paula03/2016
38852^316894+9995395Lelio R Paula11/2012
38866^122547+1195361Lelio R Paula05/2016
38872^316771+8287595358Lelio R Paula03/2016
3889(23*10^95326+1)/395327Serge Batalov05/2009
38881*10^95326+5795327Robert Price03/2011
389010^95326-39368795326Patrick De Geest09/2013
3891(3^199803+4)/47953995325Lelio R Paula04/2013
38922^316654-10948195323Enzo Doria04/2014
38938*10^95316+5195317Robert Price05/2017
3894(50^56099+43^56099)/9395309Serge Batalov12/2016
3895(23*2^316559+1)/392595292Lelio R Paula09/2013
3896(71*10^95277-539)/995278Robert Price11/2017
389719^74503-5695271Lelio R Paula06/2016
389811^91475-438095262Enzo Doria01/2013
3899(62*10^95251-611)/995252Robert Price05/2017
3900(2^316321-509203)/6937795218Lelio R Paula06/2013
3901(79*10^95214-43)/995215Erik Branger11/2013
3902(9*2^316233-1)/175195194Lelio R Paula02/2014
39035*2^316213+995191Lelio R Paula08/2014
39042^316205-184816395188Enzo Doria07/2015
39052^316185-278791395182Enzo Doria04/2016
3906(9787*2^316142-1)/395172Lelio R Paula04/2015
39072^316140-595168Henri Lifchitz02/2006
3908(15185*2^316117-1)/395165Lelio R Paula04/2015
3909(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
39102^316069+7681795147Enzo Doria05/2016
3911(199*10^95134-7)/395136Robert Price02/2017
39122^316027-9730595134Lelio R Paula03/2016
39132^316006-279805195128Enzo Doria04/2016
39142^315921-279760395102Enzo Doria04/2016
39152*10^95095+6395096Robert Price10/2017
39162^315857+129995083Lelio R Paula03/2016
391714^82955-4395078Lelio R Paula06/2016
3918(2*10^95072-17)/395072Robert Price08/2014
39192^315727+6595044Lelio R Paula11/2012
39202^315725+188575795043Enzo Doria03/2017
39211*10^94983+2194984Robert Price03/2011
392210^94983-71794983Patrick De Geest08/2013
392317^77187-8294975Lelio R Paula07/2016
39243*10^94964+3794965Robert Price10/2017
3925(2^315481-1017)/2062728594962Lelio R Paula06/2013
39262^315423-11032994952Enzo Doria05/2014
392711^91169-723094943Enzo Doria02/2013
39287*10^94938+6194939Robert Price02/2017
39292^315351+102594931Lelio R Paula03/2016
39302^315350-11225394930Enzo Doria06/2014
3933((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
39312^315268+794906Lelio R Paula10/2012
393211^91133+6294906Lelio R Paula05/2016
393430^64244+4194897Lelio R Paula08/2012
3935(151*10^94885-7)/994887Robert Price07/2017
39364^157583+2214794875Mike Oakes01/2011
39372^315098+12394854Lelio R Paula11/2012
39383^198791-3494848Robert Price11/2013
39393*2^315067+794846Lelio R Paula08/2014
3940(9*2^315057+1)/7394841Lelio R Paula09/2013
3941(16*10^94822+53)/394823Robert Price12/2016
39428*6^121849-794818Lelio R Paula10/2014
3943(85*10^94802+473)/994803Robert Price03/2017
39442^314870-10876194786Enzo Doria03/2014
39455*2^314841-394778Lelio R Paula08/2014
39466^121772+11394758Lelio R Paula05/2016
39476^121756-1625394745Enzo Doria02/2013
39482^314718-11279394740Enzo Doria06/2014
39492^314697-184729394734Enzo Doria07/2015
39512^314548-24994689Yves Minet02/2012
39505^135469+4294689Lelio R Paula04/2016
3952gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
3953(2*10^94604+547)/994604Robert Price10/2017
39543*2^314152+594570Lelio R Paula08/2014
39552*6^121530-594570Lelio R Paula10/2014
39567*10^94563+8794564Robert Price11/2016
39572^314114-10967794558Enzo Doria04/2014
3958(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
39592^314059+7658394542Enzo Doria05/2016
39602^314041-403594536Lelio R Paula03/2016
3961(7*2^314003-11)/1594524Renaud Lifchitz03/2011
396211^90760-471094517Enzo Doria01/2013
3963(7*2^313926-1)/14882194497Lelio R Paula02/2014
396494*10^94493-394495Robert Price11/2016
3965(1000547^15749+1)/100054894492Faysal YAtim12/2008
3966(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
39677^111792-3294476Lelio R Paula04/2016
396811^90680-585094434Enzo Doria01/2013
39692^313675-11012594426Enzo Doria04/2014
3970(2999*29^64556-2427)/494410Curtis Bright05/2015
39712^313609-11222594406Enzo Doria06/2014
39722^313584+7290194399Enzo Doria04/2016
39732^313510-11286594376Enzo Doria06/2014
39747*10^94373+8794374Robert Price11/2016
3975(9^98897+8^98897)/1794371Robert Price12/2012
39762^313453-11470394359Enzo Doria04/2015
39778*10^94357-5194358Robert Price10/2017
3978(379*10^94337-1)/994339Robert Price08/2017
39792^313344-313344+194326Robert Price10/2014
398020^72481-4994300Lelio R Paula05/2016
398144725!2+12894289Robert Price03/2015
39824*10^94286+994287Robert Price05/2015
398317^76621+2494279Lelio R Paula07/2016
39842^313156-11285994270Enzo Doria06/2014
39856^121130-5994258Lelio R Paula05/2016
39863^197542+2894252Robert Price11/2013
3987(3^197521+2)/5165594237Lelio R Paula04/2013
39882^313045-595594236Lelio R Paula03/2016
3989(67*10^94212+23)/994213Ray Chandler02/2011
39902^312909-186520394195Enzo Doria03/2016
39912^312848-14994177Lelio R Paula11/2012
39924^156403-7759794164Mike Oakes04/2011
399318^75004-8594151Lelio R Paula06/2016
399419^73622-4894145Lelio R Paula06/2016
3995(11^90397-3^90397)/894138Robert Price04/2011
3996(3^197287+5)/1694129Lelio R Paula04/2013
399712^87212-3794118Lelio R Paula06/2016
399811^90376+7694117Lelio R Paula05/2016
3999(6^120946-11)/594114Paul Bourdelais11/2011
4000(10^94096+191)/394096Robert Price11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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