PRP Records

Probable Primes Top 10000

(290751 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 (> 50000) Who ? When ?
77519*10^97247-2997248Robert Price05/2017
775224382^9735+9735^2438297244Hans Havermann02/2020
7753(31*10^97242+41)/997243Robert Price04/2015
7754GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
775512^90098-4197233Lelio R Paula07/2016
77562^322928-21692997212Enzo Doria05/2014
7757(16731^23017-1)/1673097209Serge Batalov06/2022
77583*10^97205-6197206Robert Price04/2021
7759(7*2^322896-1)/5797201Lelio R Paula02/2014
7760(35*10^97194-341)/997195Robert Price08/2021
7761(4872^26357-1)/487197194Serge Batalov06/2022
7762(2^322897+5)/314610748997193Lelio R Paula10/2013
7763(2^322789+2214)/297169Stefano Morozzi09/2020
77642^322725+7576197150Enzo Doria04/2016
7765(13*2^322686+1)/11997138Lelio R Paula11/2013
7766(2175^29101-1)/217497121Serge Batalov06/2022
776722402^21639+21639^2240297118Hans Havermann07/2020
776823399^14128+14128^2339997108Hans Havermann06/2020
7769(2892^28057-1)/289197108Serge Batalov06/2022
7770(9578^24391-1)/957797104Serge Batalov06/2022
7771(2^322525+2606)/297090Stefano Morozzi09/2020
7772(9563^24391-1)/956297087Serge Batalov06/2022
7773(41*10^97085+373)/997086Robert Price04/2017
7774(2^322473+854)/297074Stefano Morozzi02/2021
77752^322413+7797056Lelio R Paula12/2012
77762^322406+17797054Lelio R Paula12/2012
7777(349^38167-1)/34897050Serge Batalov06/2022
7778(14*10^97044+31)/997045Robert Price02/2015
77792^322302+25525597023Lelio R Paula07/2016
7780(1302^31147-1)/130197008Serge Batalov06/2022
77812^322196-11309396991Enzo Doria07/2014
7782(2^322169+2690)/296983Stefano Morozzi09/2020
7783(49*10^96980+221)/996981Robert Price02/2022
77849*10^96968-4796969Robert Price11/2021
7785(5895^25717-1)/589496962Serge Batalov06/2022
7786(27473^21841-1)/2747296946Serge Batalov06/2022
778723109^15668+15668^2310996943Hans Havermann07/2020
77882^322000-186146996932Enzo Doria03/2016
77892^321971-11274796923Enzo Doria06/2014
779023754^12023+12023^2375496917Hans Havermann07/2020
779111^93062-9296915Lelio R Paula06/2016
7792(37871^21169-1)/3787096914Serge Batalov06/2022
7793(2^321922+2214)/296908Stefano Morozzi09/2020
7794(2^321900+2086)/296902Stefano Morozzi09/2020
7795(11*2^321841-7)/1596884Renaud Lifchitz03/2011
77963^203051+3496880Lelio R Paula05/2016
77972*10^96867-5196868Robert Price11/2017
7798(2^321779+2618)/296865Stefano Morozzi09/2020
7799(64*10^96863-1)/2796864Serge Batalov05/2010
78002^321716-278693996847Enzo Doria03/2016
780122496^20181+20181^2249696844Hans Havermann03/2020
78022^321701-11305396842Enzo Doria07/2014
78032^321700-2863596842Lelio R Paula06/2016
7804(5*2^321691-1)/2796838Lelio R Paula02/2014
78056*10^96835+1396836Robert Price10/2021
78066^124433-12443396828Robert Price01/2014
78072^321631+6996821Lelio R Paula12/2012
7808(27109^21841-1)/2710896820Serge Batalov06/2022
7809(13*2^321606+1)/11996813Lelio R Paula11/2013
7810(5052^26141-1)/505196809Serge Batalov06/2022
7811(46*10^96798-1)/996799Serge Batalov10/2014
7812(59*10^96798+31)/996799Robert Price09/2015
7813(2^321536+2062)/296792Stefano Morozzi09/2020
7814223319#+23122396790Makoto Morimoto02/2016
78152^321519-2863596787Lelio R Paula06/2016
78162^321487-186723796778Enzo Doria03/2016
78172^321461-6396770Lelio R Paula12/2012
7818(16053^23011-1)/1605296770Serge Batalov06/2022
78192^321439+12396763Lelio R Paula12/2012
78202^321434+70996762Lelio R Paula02/2013
7821(2^321415+554)/296756Stefano Morozzi09/2020
782214^84413+8996749Lelio R Paula07/2016
7823(28*10^96743+71)/996744Serge Batalov12/2008
782413^86847+9696743Lelio R Paula06/2016
78259*2^321336-796733Lelio R Paula08/2014
7826(209*10^96722-17)/396724Robert Price05/2017
7827(54163^20431-1)/5416296710Serge Batalov06/2022
78282^321237-461596702Yves Minet05/2019
7829(27273^21799-1)/2727296691Serge Batalov06/2022
78302^321187-115996687Yves Minet11/2012
78312^321182-185008196686Enzo Doria08/2015
783323359^13768+13768^2335996680Hans Havermann06/2020
7832(65630^20071-1)/6562996680Serge Batalov06/2022
78342^321116-11282996666Enzo Doria06/2014
78352^321108-10949996664Enzo Doria04/2014
78362^321098+279385996661Enzo Doria03/2016
7837(2^321100+1170)/296661Stefano Morozzi09/2020
78382^321057+409796648Lelio R Paula06/2016
7839(4435*29^66081-4)/796640Curtis Bright05/2015
784022743^17750+17750^2274396640Hans Havermann04/2020
784122882^16679+16679^2288296612Hans Havermann02/2020
784223452^13163+13163^2345296608Hans Havermann02/2020
7843(1042^32009-1)/104196596Serge Batalov06/2022
7844(85*10^96594-373)/996595Robert Price05/2021
7845(2^320863+666)/296590Stefano Morozzi09/2020
7846p(19849)#/2-6496581Robert Price04/2017
78472^320817+18996576Lelio R Paula12/2012
78482^320816-468596576Yves Minet05/2019
7850(361*10^96567-163)/996569Robert Price10/2017
7849(19*10^96568+137)/396569Robert Price03/2022
78512^320788-11032796567Enzo Doria05/2014
7852(3065^27697-1)/306496561Serge Batalov06/2022
78532^320764+79396560Lelio R Paula02/2013
7854(2^320752+1842)/296556Stefano Morozzi02/2021
7855(48331^20611-1)/4833096542Serge Batalov06/2022
7856(50595^20521-1)/5059496529Serge Batalov06/2022
7857(9179*2^320652-1)/22196528Lelio R Paula05/2015
785823288^13947+13947^2328896517Hans Havermann07/2020
78592^320616-7879596516Lelio R Paula03/2016
78602^320612-46193996514Enzo Doria07/2015
7861(21245^22303-1)/2124496507Serge Batalov06/2022
786210^96504+98765432196505Robert Price12/2019
786310^96504+7188796505Patrick De Geest02/2020
786422654^18195+18195^2265496505Hans Havermann07/2020
786510^96504-13927796504Patrick De Geest02/2020
7866(218^41263-1)/21796490Serge Batalov06/2022
7867(47220^20641-1)/4721996474Serge Batalov06/2022
78685*2^320431+796461Lelio R Paula08/2014
786919^75431-9096458Lelio R Paula06/2016
7870(11853^23677-1)/1185296452Serge Batalov06/2022
7871(2^320386+2814)/296446Stefano Morozzi02/2021
7872(2^320370+3)/6796440Lelio R Paula10/2013
78733*10^96431-1796432Robert Price03/2021
78742^320309+187147796423Enzo Doria05/2016
7875(10412^24001-1)/1041196421Serge Batalov06/2022
7876tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
7877(29*10^96407-23)/396408Robert Price03/2022
7878(21*2^320252-1)/189596404Lelio R Paula02/2014
78792^320232-17396400Lelio R Paula12/2012
7880175^42975-296395Lelio R Paula10/2017
7881(2^320170+2718)/296381Stefano Morozzi09/2020
788210^96377+19991196378Patrick De Geest12/2016
788310^96377-2000196377Robert Price11/2016
7884(18079^22639-1)/1807896374Serge Batalov06/2022
78862^320124-279044996367Enzo Doria03/2016
788510^96366+1919796367Patrick De Geest08/2021
788810^96366-1000000000196366Robert Price04/2021
788710^96366-28736796366Patrick De Geest08/2021
7889(26351^21799-1)/2635096365Serge Batalov06/2022
789022488^19255+19255^2248896351Hans Havermann11/2019
789123248^13939+13939^2324896346Hans Havermann11/2019
7892(5928^25537-1)/592796345Serge Batalov06/2022
78942^320043-10877596343Enzo Doria04/2014
789324989^7168+7168^2498996343Hans Havermann11/2019
789510^96338+42493996339Patrick De Geest03/2016
789610^96338-928196338Robert Price09/2015
7897(8527^24509-1)/852696336Serge Batalov06/2022
7898(3*2^320008+1)/796332Lelio R Paula09/2013
7899(2444^28433-1)/244396331Serge Batalov06/2022
7900(48690^20551-1)/4868996327Serge Batalov06/2022
7901(61935^20101-1)/6193496318Serge Batalov06/2022
790225699^5596+5596^2569996317Hans Havermann07/2020
7903(11*10^96298+529)/996299Robert Price09/2021
790526502^4297+4297^2650296287Hans Havermann07/2020
7904(54180^20341-1)/5417996287Serge Batalov06/2022
79062^319838+425796281Lelio R Paula03/2016
79072^319830-1699596279Lelio R Paula03/2016
79086^123713+14396268Lelio R Paula05/2016
7909(28*10^96265-97)/396266Robert Price07/2016
7910(3799^26893-1)/379896265Serge Batalov06/2022
7912103^47825-10296264Norbert Schneider10/2016
7911(54041^20341-1)/5404096264Serge Batalov06/2022
7913(2^319777+2082)/296263Stefano Morozzi09/2020
7914(2^319771+3686)/296261Stefano Morozzi09/2020
79152^319713-8196244Lelio R Paula11/2012
7916(55459*2^319706+1)/2016796242Lelio R Paula07/2014
791722834^16393+16393^2283496238Hans Havermann05/2020
79188*10^96236+2796237Robert Price09/2021
791912^89153-4396213Lelio R Paula06/2016
7920(25048^21871-1)/2504796202Serge Batalov06/2022
7922(2*10^96195-59)/396195Robert Price05/2017
79219*10^96194-7796195Robert Price08/2020
79232^319545+14796193Lelio R Paula11/2012
792423357^13128+13128^2335796189Hans Havermann02/2020
7925(19838^22381-1)/1983796179Serge Batalov06/2022
7926(221^41023-1)/22096172Serge Batalov06/2022
792725952^5073+5073^2595296160Hans Havermann12/2019
7928(50891^20431-1)/5089096157Serge Batalov06/2022
7929(50^56597+1)/5196155Robert Price03/2014
793022313^20374+20374^2231396149Hans Havermann12/2019
793122279^20668+20668^2227996141Hans Havermann11/2019
7932(41*10^96137-59)/996138Robert Price10/2017
79332^319353-11034396135Enzo Doria05/2014
793411^92309-4296130Lelio R Paula05/2016
7935(21675^22171-1)/2167496129Serge Batalov06/2022
793614^83869-13^8386996125Jean-Louis Charton01/2009
7937(7*10^96112+143)/396113Robert Price04/2016
793826731^3940+3940^2673196112Hans Havermann07/2020
793922640^17583+17583^2264096109Hans Havermann07/2020
7940(19178^22441-1)/1917796107Serge Batalov06/2022
79412^319237+6583596100Lelio R Paula03/2016
79422^319194-184196087Yves Minet03/2013
794323949^10280+10280^2394996084Hans Havermann07/2020
7944(1927^29251-1)/192696083Serge Batalov06/2022
794520^73847-3196078Lelio R Paula05/2016
7946(60229^20101-1)/6022896075Serge Batalov06/2022
7947(28044^21601-1)/2804396074Serge Batalov06/2022
794850^56543-4996065Norbert Schneider09/2018
79492^319107-10955596061Enzo Doria04/2014
7950(3*2^319114-1)/262796060Lelio R Paula02/2014
79512^319098-11215796059Enzo Doria06/2014
795215^81673+9496055Lelio R Paula07/2016
7953(85761^19471-1)/8576096052Serge Batalov06/2022
79542^319074+187174996051Enzo Doria05/2016
795525670^5517+5517^2567096050Hans Havermann06/2020
79566*10^96037+1996038Robert Price11/2021
79572^319007-11211196031Enzo Doria06/2014
7958(57987^20161-1)/5798696029Serge Batalov06/2022
79602^318946-142196013Yves Minet01/2013
7959(68310^19861-1)/6830996013Serge Batalov06/2022
7961(20294^22291-1)/2029396012Serge Batalov06/2022
7962(304^38669-1)/30396008Serge Batalov06/2022
7963(1840^29401-1)/183995986Serge Batalov06/2022
796422830^16003+16003^2283095982Hans Havermann02/2020
79652^318834-11041195979Enzo Doria05/2014
79662^318831-196595978Lelio R Paula03/2016
7967(5*10^95976+7)/395977Erik Branger03/2014
7968(12797^23369-1)/1279695975Serge Batalov06/2022
7969(10534^23857-1)/1053395963Serge Batalov06/2022
797022871^15696+15696^2287195962Hans Havermann01/2020
7971(2^318760+858)/295957Stefano Morozzi02/2021
797223167^13860+13860^2316795953Hans Havermann01/2020
7973(823^32911-1)/82295946Serge Batalov06/2022
79755*3^201089-895945Lelio R Paula08/2014
7974(81783^19531-1)/8178295945Serge Batalov06/2022
79762^318711-13995942Lelio R Paula11/2012
79772^318635-116795919Lelio R Paula03/2016
797815^81555+1695917Lelio R Paula07/2016
7979(37*10^95895+377)/995896Robert Price10/2017
7980(22699*2^318527+1)/2195890Lelio R Paula07/2014
79812^318496-9730595877Lelio R Paula03/2016
798222129^21496+21496^2212995871Hans Havermann07/2020
79842^318466+1501595868Lelio R Paula03/2016
798324847^7216+7216^2484795868Hans Havermann07/2020
798523706^11065+11065^2370695866Hans Havermann07/2020
7986(2863^27733-1)/286295865Serge Batalov06/2022
79876^123187-17312995859Mike Oakes04/2011
79882^318423-48795855Yves Minet03/2012
7989(2^318359+678)/295836Stefano Morozzi09/2020
7990(10223*2^318350+1)/156395834Lelio R Paula07/2014
7991(8060^24533-1)/805995831Serge Batalov06/2022
7992(9853^23993-1)/985295814Serge Batalov06/2022
7994(2^318267+2550)/295808Stefano Morozzi09/2020
7993(5048^25873-1)/504795808Serge Batalov06/2022
79964*10^95799+1395800Robert Price02/2021
7995(65533^19891-1)/6553295800Serge Batalov06/2022
799745369!2+102495787Robert Price02/2015
79983^200758-8695786Lelio R Paula05/2016
7999(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
8000(2^318171+2030)/295779Stefano Morozzi09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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