PRP Records

Probable Primes Top 10000

(255169 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 ?
775165^37636+1668231Lelio R Paula01/2016
77525^97615-4^(97615+1)68230Robert Price04/2016
775312^63200-4368205Lelio R Paula07/2013
7754-330*Bern(21940)/22379062073368201Serge Batalov04/2015
77553^142925+868068193Lelio R Paula06/2013
77563*2^226512-768188Lelio R Paula04/2014
775714^59484+5768177Lelio R Paula08/2013
775811^65438-219068147Enzo Doria12/2012
775991^34784-268144Lelio R Paula09/2013
776016589^12810+12810^1658968141Hans Havermann10/2019
7761(2^226336-3)*6-768135Gilbert Mozzo06/2016
7762(22*10^68133-37)/368134Robert Price05/2017
77635^97476+3668133Lelio R Paula06/2013
77643*5^97474-268132Lelio R Paula09/2014
776512^63130+4968129Lelio R Paula07/2013
77662^226281+538568118Lelio R Paula04/2012
77672^226257-304968111Yves Minet10/2014
7768(28*10^68107-43)/368108Robert Price04/2016
77692^226243-258768106Yves Minet07/2014
777020^52346-1168104Lelio R Paula09/2013
77712^226205-9968095Lelio R Paula02/2012
77722^226187-4968090Lelio R Paula02/2012
77733^142708+7668090Lelio R Paula06/2013
77747*10^68088-8968089Robert Price01/2017
777518562^4653+4653^1856268081Hans Havermann09/2019
77762^226154+7183968080Enzo Doria04/2016
7777(10^68078+59)/368078Serge Batalov12/2014
777914^59387+6968066Lelio R Paula08/2013
77782^226108-11342968066Enzo Doria07/2014
7780(62*10^68059-197)/968060Robert Price10/2017
7781(24^49307-1)/2368053Robert Price04/2012
778215^57859-2868048Lelio R Paula08/2013
7783(509203*2^226003-1)/1368039Lelio R Paula04/2015
77842^226015-11136168038Enzo Doria05/2014
7785(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
77864*10^68020+9168021Robert Price11/2017
778716181^15948+15948^1618168004Hans Havermann09/2019
7788156*(10^(4*17000)-1)/101-168001Robert Price05/2014
77892^225878-101767997Lelio R Paula04/2012
77903*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
77913*2^225865+567993Lelio R Paula04/2014
779211^65284-582067987Enzo Doria01/2013
779319^53166+7067987Lelio R Paula08/2013
77942^225837+7540767984Enzo Doria04/2016
77953^142464-11265467973Enzo Doria06/2014
779616851^10802+10802^1685167969Hans Havermann09/2019
77972^225777+9567966Lelio R Paula02/2012
7798(2^225641-1017)/13881567920Lelio R Paula04/2012
77992^225609-1844567916Enzo Doria05/2013
78002^225542-17767895Lelio R Paula02/2012
78012^225536-2967894Henri Lifchitz05/2005
780211^65190-339067889Enzo Doria12/2012
780316971^9986+9986^1697167874Hans Havermann09/2019
78043^142249-2^(142249-1)67871Robert Price01/2016
780511^65168-483067866Enzo Doria01/2013
780610^67863+5862767864Patrick De Geest01/2016
780716258^14933+14933^1625867864Hans Havermann09/2019
780810^67863-1167863Robert Price05/2011
7809(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
7810(19*2^225357-1)/1167840Lelio R Paula01/2014
78119*6^87164-767828Lelio R Paula09/2014
7812131^32034+13067825Norbert Schneider03/2015
7813(29*2^225314+1)/1088167824Lelio R Paula08/2012
781417761^6586+6586^1776167823Hans Havermann09/2019
7815(134*10^67816+7)/367818Robert Price02/2017
78162^225261+85567811Lelio R Paula04/2012
7817(29*2^225252-1)/293367806Lelio R Paula01/2014
7818(4*10^67796+23)/967796Robert Price11/2014
781915477^16180-16180^1547767790Norbert Schneider09/2018
7820(23*2^225177+1)/3167785Lelio R Paula08/2012
7821(4*10^67784+149)/967784Robert Price03/2017
78228177^17322+17322^817767774Norbert Schneider03/2019
78232^225120+15167768Lelio R Paula02/2012
7824(44^41233+1)/4567763Robert Price11/2013
782589933!6-1667747Robert Price08/2018
78268*10^67742+967743Dmitry Domanov11/2010
78272^224977+108967725Lelio R Paula04/2012
7828(2^224950+5)/1950967713Lelio R Paula04/2012
782911^65011-597067702Enzo Doria01/2013
783088*10^67691+767693Robert Price11/2016
783111^65000-714067691Enzo Doria01/2013
78322^224841+5967684Lelio R Paula02/2012
783333129!2+2^3312967684Robert Price09/2015
78342^224827+841567680Lelio R Paula02/2013
7835(9913*2^224821-1)/1982567678Lelio R Paula04/2015
78362^224815-4978967677Henri Lifchitz04/2005
78377257^17528+17528^725767672Norbert Schneider08/2019
7838(43*10^67664+11)/967665Robert Price06/2015
7839(292*10^67659-1)/367661Robert Price01/2017
7840(17*2^224766+1)/2900767659Lelio R Paula06/2012
78412^224744+57729457567655Lelio R Paula02/2016
7842((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
7843(2^224721+78557)/173967645Lelio R Paula05/2012
78442^224700+191567642Lelio R Paula04/2012
7845(29*2^224694-1)/19890567636Lelio R Paula01/2014
78462^224658-9367629Lelio R Paula02/2012
78472^224624-1307767619Enzo Doria10/2012
784818^53860-331967609Enzo Doria03/2013
7849(21181*2^224570+1)/567606Lelio R Paula06/2014
785089762!6-367606Robert Price08/2018
78512^224578-11104167605Enzo Doria05/2014
78522^224569-11323367603Enzo Doria07/2014
78532^224562-11317167600Enzo Doria07/2014
78542^224556-11312967599Enzo Doria07/2014
78556*7^79980-567592Lelio R Paula09/2014
7856(6883*2^224523-1)/1603167588Lelio R Paula04/2015
785710^67579+16477967580Patrick De Geest07/2017
7859(52*10^67578-61)/967579Robert Price09/2015
785810^67579-40167579Robert Price06/2017
7860(17^54919-1)/1667574Paul Bourdelais03/2010
786122115^1134+1134^2211567553Hans Havermann08/2019
7862((10^33771-1)*10000/9+6389)*10^33771+(10^33771-1)/967546Hans Havermann05/2019
7863(2^224363-9)/195167537Lelio R Paula04/2012
7864(709*10^67517-7)/967519Robert Price09/2017
786547719!3-5904967516Robert Price12/2015
786616356^13411+13411^1635667509Hans Havermann09/2019
7867(22^50287+1)/2367506Robert Price06/2013
786816671^11198+11198^1667167504Hans Havermann09/2019
78693*10^67499+6767500Robert Price11/2017
787011^64811-582067494Enzo Doria01/2013
7871131^31870+31870^13167478Serge Batalov05/2014
78729*10^67468+767469Dmitry Domanov11/2010
7873(31*2^224115-1)/4772367463Lelio R Paula01/2014
7874128^32001+32001^12867433Serge Batalov05/2014
7875(89*10^67431-17)/967432Robert Price11/2015
78762^223912-11105967405Enzo Doria05/2014
78782^223913+7369767405Enzo Doria04/2016
7877(2*10^67405-23)/367405Robert Price09/2017
7879(10^67404+179)/967404Serge Batalov12/2014
788018738^3955+3955^1873867404Hans Havermann09/2016
78819*7^79728-267379Lelio R Paula09/2014
7882(28*10^67378-43)/367379Robert Price04/2016
7883(3^141234-7)/43024128267378Lelio R Paula04/2012
7884211^28988-267377Lelio R Paula09/2013
78854*10^67375+9167376Robert Price11/2017
78862^223793-1806967369Enzo Doria05/2013
78872^223777-252167364Yves Minet07/2014
7888(15185*2^223775-1)/1518367363Lelio R Paula04/2015
7889(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
7890V(340138)67336Serge Batalov03/2015
789143125^14528-10667334Enzo Doria07/2012
789215275^16086-16086^1527567304Norbert Schneider09/2018
78938*10^67302-5167303Robert Price10/2017
789417458^7153+7153^1745867292Hans Havermann08/2016
789516366^12925+12925^1636667288Hans Havermann08/2016
789637^42906-267286Lelio R Paula08/2013
789718^53592-1367273Lelio R Paula08/2013
7898V(396221)67256Serge Batalov03/2015
7900(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
7899(14*10^67235-101)/367236Robert Price04/2017
790153^38993-52^3899367235Robert Price01/2013
7902(2^223349-7)/648567231Lelio R Paula04/2012
79032^223333+31567230Lelio R Paula04/2012
79042^223278-11104167214Enzo Doria05/2014
7905(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
79062^223256-4567207Lelio R Paula02/2012
79072^223253-11211167206Enzo Doria06/2014
790818407^4474+4474^1840767199Hans Havermann08/2016
790947^40182+40182^4767189Norbert Schneider11/2014
791013^60309+9467181Lelio R Paula07/2013
791111^64503-8467173Lelio R Paula07/2013
79123^140781+23667170Lelio R Paula06/2013
79132^223107-86505767162Paul Bourdelais03/2013
79142^223100-5967160Lelio R Paula02/2012
79152^223087+7196367156Enzo Doria04/2016
791718^53481-377967134Enzo Doria03/2013
7916(326^26713-1)/32567134Eric Chen09/2017
79184^111473-6257367114Mike Oakes02/2011
79192^222943+2967113Henri Lifchitz08/2005
7920(2^222939-9)/10367110Lelio R Paula04/2012
79212^222862-45916167089Enzo Doria05/2015
79222^222828+819367078Lelio R Paula04/2012
79233^140570+266067069Lelio R Paula06/2013
792420731^1716+1716^2073167055Hans Havermann08/2019
79252^222744+85567053Lelio R Paula04/2012
792613^60189+8467048Lelio R Paula07/2013
79272*10^67043-5167044Robert Price11/2017
792822588^929+929^2258867042Hans Havermann08/2019
79292^222701+57729457567040Lelio R Paula02/2016
7930(13*10^67038-31)/967039Serge Batalov11/2008
7931(151*10^67027-7)/967029Robert Price07/2017
7932(58695*2^222620-1)/6167019Lelio R Paula04/2015
79332^222614-11104167014Enzo Doria05/2014
793416255^13242+13242^1625567003Hans Havermann08/2019
793516477^11650+11650^1647767001Hans Havermann08/2019
7936118^32333-11766991Norbert Schneider08/2018
79372^222520-190766986Yves Minet03/2013
7938(4^111231+23)/366968Robert Price02/2017
793916206^13549+13549^1620666962Hans Havermann08/2019
79402^222408-11127566952Enzo Doria05/2014
794110^66949-9^6694966949Jean-Louis Charton12/2005
79422^222378-100566943Lelio R Paula04/2012
7943(9*2^222366+1)/7366938Lelio R Paula08/2012
79447^79202-6^(79202+1)66934Robert Price06/2016
79452^222325-11225566927Enzo Doria06/2014
794621789^1178+1178^2178966918Hans Havermann08/2019
794720^51428+3366910Lelio R Paula08/2013
79482^222224-1850966897Enzo Doria05/2013
7949(38*10^66896+187)/966897Robert Price11/2017
79502^222192-86968810566887Lelio R Paula02/2016
7951(19*10^66878-43)/366879Robert Price10/2017
795211^64219-6466878Lelio R Paula07/2013
79532^222151-1729566875Lelio R Paula04/2012
7954gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
79552^222085-11103166855Enzo Doria05/2014
79568*10^66848-1366849Robert Price05/2017
7957(3^140087+4)/1366838Lelio R Paula04/2012
7958(3^140102+4)/884360943766836Lelio R Paula04/2012
795919^52265+5266835Lelio R Paula08/2013
79602*10^66826-2766827Robert Price02/2017
79614*6^85867+566819Lelio R Paula09/2014
796211955^16384+266807Matt Stath12/2018
796315^56800+866802Lelio R Paula08/2013
7964(2^221891-2^110946+1)/56679611/2006
796510^66793+6944166794Patrick De Geest05/2013
796610^66793-6366793Robert Price05/2011
796735^43256-170466791Enzo Doria03/2013
79693^139976+2^(139976-1)66786Robert Price05/2016
796888769!6-4866786Robert Price08/2018
79707^79023-5466783Lelio R Paula06/2013
7971104^33109-10366782Norbert Schneider11/2016
7972(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
7973(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
79752^221768+18366759Lelio R Paula02/2012
7974gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
7976(154*10^66755-1)/966757Serge Batalov12/2014
797711^64097+4866751Lelio R Paula07/2013
7978(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
7979(19*10^66748+413)/966749Robert Price10/2017
7980(3*2^221696-1)/1366737Lelio R Paula01/2014
79818*6^85758-766734Lelio R Paula09/2014
7982135^31325+266733Lelio R Paula05/2013
7983(49*10^66729+41)/966730Robert Price07/2015
7984(349*10^66720-7)/966722Robert Price03/2017
7985(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
7986(25*10^66714+71)/366715Robert Price01/2017
798711^64061-78066713Enzo Doria11/2012
79887^78929+466703Lelio R Paula06/2013
798911^64048-93066700Enzo Doria11/2012
7990120^32079-11966699Norbert Schneider09/2018
79912*7^78921+566697Lelio R Paula09/2014
7992(25*2^221526+1)/40966685Lelio R Paula08/2012
799316330^12117+12117^1633066682Hans Havermann08/2019
7994(2^221509-1)/29239188166673Jens K. Andersen02/2009
79952^221479+7295366672Enzo Doria04/2016
799710^66666+27540366667Patrick De Geest03/2010
799616317^12182+12182^1631766667Hans Havermann08/2019
799810^66666-11552166666Patrick De Geest03/2010
7999(18*10^66657-81)/9966657Ray Chandler01/2011
80004*10^66653+2166654Robert Price08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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