PRP Records

Probable Primes Top 10000

(288949 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 ?
750121969^15878+15878^2196992288Hans Havermann08/2020
750221690^17959+17959^2169092276Hans Havermann08/2020
7503(7613^23773-1)/761292273Serge Batalov08/2020
7504(31*2^306487-1)/229192260Lelio R Paula02/2014
75052^306467-183561192256Enzo Doria04/2015
75062^306433+7642792246Enzo Doria05/2016
75072^306430-11331392245Enzo Doria07/2014
7508(23*10^92244-59)/992245Robert Price03/2017
7509(47*2^306398+1)/138480392231Lelio R Paula04/2015
751021436^20043+20043^2143692217Hans Havermann09/2020
7511(25*10^92186+59)/392187Robert Price05/2016
75122^306213-28618392180Enzo Doria06/2015
751310^92178+6192179Robert Price04/2011
751410^92178-17550992178Patrick De Geest07/2013
75152^306200+118592176Lelio R Paula02/2016
7516(2^306171+1514)/292167Stefano Morozzi09/2020
75172^306153+1192162Lelio R Paula11/2012
7518(2^306141-7)/592157Lelio R Paula06/2013
751921725^17454+17454^2172592156Hans Havermann09/2020
7520(26*10^92152-23)/392153Robert Price08/2016
7521(2*10^92152+67)/392152Robert Price04/2017
752221368^20457+20457^2136892115Hans Havermann08/2020
7523(2^305996+3018)/292114Stefano Morozzi09/2020
75244*10^92099+3*7^9209992100Mike Oakes12/2010
752530504^1045+1045^3050492096Hans Havermann08/2020
752624334^6085+6085^2433492087Hans Havermann08/2020
7527(2^305898+2262)/292085Stefano Morozzi01/2021
7528(4591^25147-1)/459092083Serge Batalov08/2020
7529115^44684+11492081Norbert Schneider07/2018
7530(416771^16384+1)/292077Richard Fischer08/2020
7531(2^305867-2^152934+1)/59207511/2006
75322^305851-10949592071Enzo Doria04/2014
7533(416213^16384+1)/292067Richard Fischer08/2020
753512^85300+3592055Lelio R Paula06/2016
7534((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
753621732^17201+17201^2173292048Hans Havermann08/2020
75377*10^92043-3992044Robert Price07/2020
75383^192911+9292042Lelio R Paula04/2016
75392^305723-27627192032Enzo Doria07/2015
7540(2^305714+3738)/292029Stefano Morozzi09/2020
7541(2^305707+798)/292027Stefano Morozzi01/2021
7542(2^305682+3202)/292020Stefano Morozzi09/2020
75432^305676+9392018Donovan Johnson06/2008
75443^192819+491999Lelio R Paula04/2013
7545(38*10^91997-83)/9991997Ray Chandler07/2011
75462^305539+7291191977Enzo Doria04/2016
7547Phi(212014,10)91960Makoto Kamada04/2019
7548(2^305423+2666)/291942Stefano Morozzi09/2020
7549(2^305427-5)/129799821391934Lelio R Paula06/2013
755082077!4-12891928Robert Price11/2019
755185^47642+8491922Norbert Schneider10/2015
755210^91920+18765191921Patrick De Geest07/2013
755310^91920-3991920Robert Price05/2011
7554(3975^25537-1)/397491913Serge Batalov08/2020
7555(22*10^91903+41)/991904Robert Price02/2015
75572^305275-2791897Lelio R Paula11/2012
75563^192607-772691897Enzo Doria05/2014
7558(2^305243+2274)/291887Stefano Morozzi02/2021
7559(2^305220+1278)/291881Stefano Morozzi01/2021
7561(6958^23911-1)/695791874Serge Batalov08/2020
75609*10^91873-9191874Robert Price06/2021
7562(7*10^91856-61)/991856Erik Branger12/2009
7563(2^305107+1274)/291847Stefano Morozzi01/2021
7564(89*10^91839-53)/991840Robert Price11/2015
75651678^28479+28479^167891839Norbert Schneider08/2020
7566(2^304996+406)/291813Stefano Morozzi02/2021
75678*5^131351+791812Lelio R Paula10/2014
75683^192426-6891811Lelio R Paula04/2016
75702^304973+11791807Lelio R Paula11/2012
7569(2^304974+234)/291807Stefano Morozzi09/2020
75712^304939-186372791796Enzo Doria03/2016
75722^304902+841591785Lelio R Paula02/2016
757318^73119+6191785Lelio R Paula06/2016
7574(78557*2^304740+1)/15991739Lelio R Paula06/2014
75752^304747+7135591738Lelio R Paula02/2016
7576(2^304738+2262)/291735Stefano Morozzi01/2021
75778*3^192251+591728Lelio R Paula08/2014
7578(2^304693+3746)/291722Stefano Morozzi01/2021
75792^304674-8791717Lelio R Paula11/2012
7580(28*10^91715+701)/991716Robert Price11/2017
7582(2^304698+9)/136280995391715Lelio R Paula06/2013
7581(2^304671+1046)/291715Stefano Morozzi09/2020
7583(2^304667+3614)/291714Stefano Morozzi09/2020
7584(5*10^91707-119)/391708Robert Price04/2016
75852^304633-11277191704Enzo Doria06/2014
7586(395347^16384+1)/291701Richard Fischer06/2020
75879*10^91693+2391694Robert Price11/2017
75882^304578-1671391688Enzo Doria05/2013
75896^117824-1871391685Enzo Doria03/2013
7590(17^74509-1)/1691679Paul Bourdelais03/2010
7591(2^304551-7)/891223191673Lelio R Paula06/2013
7592(2^304532-3)/301391670Lelio R Paula06/2013
75932^304507-1664591666Enzo Doria04/2013
7594(29*2^304489+1)/3191661Lelio R Paula09/2013
759521221^20860+20860^2122191661Hans Havermann08/2020
75962^304471-183612791655Enzo Doria04/2015
75972^304433+3276991644Lelio R Paula02/2016
75982^304410-1662591637Enzo Doria04/2013
7599183^40500-291630Lelio R Paula10/2017
7600(2^304373+1850)/291626Stefano Morozzi02/2021
7601(203*10^91613+1)/391615Robert Price09/2017
76024*5^131052+791603Lelio R Paula10/2014
760421725^16458+16458^2172591601Hans Havermann08/2020
7603(2^304290+3270)/291601Stefano Morozzi02/2021
76052^304278-400191597Yves Minet04/2017
76062^304272-186637791595Enzo Doria03/2016
76072^304268+1968391594Lelio R Paula02/2016
760821718^16497+16497^2171891594Hans Havermann08/2020
760922759^10576+10576^2275991590Hans Havermann08/2020
7610(29*10^91584-119)/991585Robert Price12/2021
76112^304162-16191562Lelio R Paula11/2012
76125*7^108331+691552Lelio R Paula10/2014
76132^304082-278782191538Enzo Doria03/2016
76142^304015+6413391518David Broadhurst06/2002
7615(7*2^303963+1)/391503Lelio R Paula09/2013
7616(2^303945-9)/361791494Lelio R Paula06/2013
7617(384007^16384+1)/291494Richard Fischer05/2020
76182^303930+188052791493Enzo Doria10/2016
761924810^4859+4859^2481091464Hans Havermann08/2020
76202*10^91457+2991458Robert Price02/2021
76213^191684-6891457Lelio R Paula04/2016
7622(21*2^303813-1)/16991456Lelio R Paula02/2014
7623(298*10^91446+11)/391448Robert Price11/2020
762411^87797-12091432Enzo Doria07/2012
76252^303698-184723191423Enzo Doria07/2015
7626(38^28933-1)^2-291416Norbert Schneider06/2016
762725660^3643+3643^2566091388Hans Havermann08/2020
76282^303554+7729991379Enzo Doria05/2016
76292^303542+1270591376Lelio R Paula02/2016
763031^61269-291375Lelio R Paula09/2013
7631(2^303525+2774)/291370Stefano Morozzi01/2021
76322^303516-6487591368Lelio R Paula02/2016
7633(2^303497+1266)/291362Stefano Morozzi09/2020
7634(2^303497+3710)/291362Stefano Morozzi09/2020
7635(31*10^91352+257)/991353Robert Price12/2021
763621856^15121+15121^2185691349Hans Havermann09/2020
7637(24737*2^303428+1)/391345Lelio R Paula06/2014
7638(21181*2^303357+1)/3236191320Lelio R Paula06/2014
763923081^9046+9046^2308191319Hans Havermann09/2020
76402^303344-278696991316Enzo Doria03/2016
76416^117346+6591313Lelio R Paula05/2016
76422^303321+85591309Lelio R Paula02/2016
7643(2^303315+3746)/291307Stefano Morozzi01/2021
764412^84606+4791306Lelio R Paula06/2016
76452^303288+187431191299Enzo Doria06/2016
7646197^39788-291293Lelio R Paula10/2017
764711^87663-171091292Enzo Doria12/2012
7648(4*10^91284-61)/391285Robert Price12/2021
76502^303224+253391280Henri Lifchitz05/2005
7649(2^303226+1830)/291280Stefano Morozzi02/2021
76516^117302+14391279Lelio R Paula05/2016
76523^191306-11288091277Enzo Doria07/2014
7653(10052^22807-1)/1005191276Serge Batalov08/2020
76542^303207+1291591275Lelio R Paula02/2016
76552^303191-11125991270Enzo Doria05/2014
765681539!4+3291267Robert Price09/2019
7657(2^303116+3570)/291247Stefano Morozzi09/2020
765810^91230+9^(91230+1)91231Robert Price08/2016
765910^91230+792191231Patrick De Geest11/2016
766010^91230-91114191230Patrick De Geest11/2016
766110^91229+34879391230Patrick De Geest07/2019
766210^91229-247191229Patrick De Geest01/2019
76632996^26241+26241^299691228Norbert Schneider01/2020
766510^91225+527191226Patrick De Geest01/2019
76642816^26445+26445^281691226Norbert Schneider02/2020
76676^117232-1742391225Enzo Doria02/2013
766610^91225-14721991225Patrick De Geest07/2019
76687*10^91215+391216Erik Branger11/2009
766910^91215+23061191216Patrick De Geest07/2019
767010^91215-453991215Patrick De Geest01/2019
7671(2^303007+606)/291214Stefano Morozzi09/2020
76729*10^91212-4791213Robert Price11/2021
7673(2^302998+3102)/291212Stefano Morozzi09/2020
767410^91210+242191211Patrick De Geest01/2019
767510^91210-173791210Patrick De Geest01/2019
767697*10^91205-391207Robert Price01/2017
76772^302979-16118191206Enzo Doria04/2013
7678(166*10^91199-7)/391201Robert Price11/2020
76792^302949+8191197Henri Lifchitz02/2007
768010^91194+20036191195Patrick De Geest07/2019
76824*6^117192-591194Lelio R Paula10/2014
768110^91194-866391194Patrick De Geest01/2019
76832^302918+9991188Lelio R Paula11/2012
768410^91186+26811191187Patrick De Geest07/2019
768510^91186-776391186Patrick De Geest01/2019
768610^91181+55047191182Patrick De Geest07/2019
7687(26*10^91181-83)/391182Robert Price12/2021
768810^91181-136791181Patrick De Geest01/2019
768910^91178+7188391179Patrick De Geest07/2019
769010^91178-471991178Patrick De Geest01/2019
769124686^4935+4935^2468691173Hans Havermann08/2020
769210^91165+304391166Patrick De Geest01/2019
769310^91165-39941391165Patrick De Geest07/2019
769410^91156+386191157Patrick De Geest01/2019
769510^91156-23149791156Patrick De Geest07/2019
76962^302797+186958791151Enzo Doria05/2016
7697265^37614+37614^26591148Norbert Schneider01/2015
76987^107852+8291146Lelio R Paula04/2016
7699(38*10^91144-11)/991145Robert Price05/2015
7700(55*10^91142+377)/991143Robert Price10/2017
770110^91128+996191129Patrick De Geest01/2019
7703249^38030+38030^24991128Norbert Schneider01/2015
770210^91128-18915391128Patrick De Geest07/2019
7704(2^302718+2814)/291127Stefano Morozzi02/2021
77056^117094-21104991117Mike Oakes05/2011
770621353^18472+18472^2135391103Hans Havermann05/2020
77082^302602-186718191093Enzo Doria03/2016
770710^91092+5612791093Patrick De Geest07/2019
770910^91092-910791092Patrick De Geest01/2019
7710(1017*2^302592-1)/5391091Lelio R Paula04/2015
771115^77445-1691083Lelio R Paula07/2016
771221656^16053+16053^2165691076Hans Havermann05/2020
77132^302505+8191064Henri Lifchitz02/2007
77142^302496-11234991061Enzo Doria06/2014
7715(2^302475+1790)/291054Stefano Morozzi01/2021
771617^73999-7291052Lelio R Paula07/2016
771710^91047+933191048Patrick De Geest01/2019
771810^91047-67116991047Patrick De Geest07/2019
771910^91044+207791045Patrick De Geest01/2019
772010^91044-13635991044Patrick De Geest07/2019
772110^91041+934991042Patrick De Geest01/2019
772210^91041-782391041Patrick De Geest01/2019
772310^91040+407791041Patrick De Geest01/2019
772410^91040-11942191040Patrick De Geest07/2019
772510^91037+276991038Patrick De Geest01/2019
772610^91037-2264991037Patrick De Geest07/2019
7727(16*10^91032+41)/391033Robert Price10/2017
772810^91023+5803991024Patrick De Geest07/2019
772910^91023-647191023Patrick De Geest01/2019
773010^91018+787391019Patrick De Geest01/2019
773110^91018-33317791018Patrick De Geest07/2019
773210^91017+6876791018Patrick De Geest07/2019
773310^91017-42832791017Patrick De Geest07/2019
773410^91016+7311191017Patrick De Geest07/2019
773510^91016-797391016Patrick De Geest01/2019
77361949^27666+27666^194991016Norbert Schneider04/2020
77372^302332+57729457591012Lelio R Paula08/2016
773810^91004+907391005Patrick De Geest01/2019
773910^91004-49151991004Patrick De Geest07/2019
774010^91003+7426991004Patrick De Geest07/2019
774110^91003-390391003Patrick De Geest01/2019
77422^302274+7420990994Enzo Doria04/2016
774310^90991+8114790992Patrick De Geest07/2019
774410^90991-627990991Patrick De Geest01/2019
774510^90983+139390984Patrick De Geest01/2019
774611*10^90982+990984Robert Price08/2020
774710^90983-56238390983Patrick De Geest07/2019
7748(311^36497-1)/31090976Eric Chen09/2017
7749(2^302210+1014)/290974Stefano Morozzi09/2020
7750(3^190668+2)/8990970Lelio R Paula04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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