PRP Records

Probable Primes Top 10000

(252538 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 ?
7001(529^25693+1)/53069972Richard Fischer12/2017
70027^82778+4869956Lelio R Paula09/2013
70037*2^232381+369955Lelio R Paula04/2014
70042^232362-11054169948Enzo Doria05/2014
70052^232326-11239169938Enzo Doria06/2014
70063^146575+23669935Lelio R Paula09/2013
700730^47341-2969929Norbert Schneider02/2014
70085^100040-6869925Lelio R Paula09/2013
7009(35*10^69866-593)/969867Robert Price08/2017
70102^232045-1729569853Lelio R Paula04/2012
7011(2^231987+78557)/9569834Lelio R Paula05/2012
70122^231955+7424369826Yves Minet03/2011
70132^231946-1587369823Enzo Doria04/2013
701418^55618+9569816Lelio R Paula09/2013
70156^89712+5^(89712-1)69810Robert Price02/2016
70162^231870+13569800Lelio R Paula02/2012
7017(23*2^231827-1)/417969785Lelio R Paula01/2014
70182^231778+5461569773Lelio R Paula04/2012
7019(19*2^231780+1)/23569772Lelio R Paula08/2012
702014^60866+2769761Lelio R Paula09/2013
702113^62619-4469755Lelio R Paula09/2013
7022(2^231715-509203)/3569752Lelio R Paula05/2012
70232^231711-11046769752Enzo Doria05/2014
7024(19^54547+18^54547)/3769751Robert Price08/2013
7025(23*2^231697-1)/4569748Lelio R Paula01/2014
70262^231696-186149969748Enzo Doria03/2016
70272^231684-14769744Lelio R Paula02/2012
7028(23*2^231686-1)/118369743Lelio R Paula01/2014
70292^231591-47739769716Paul Bourdelais03/2013
703011^66916-42069686Enzo Doria08/2012
70325^99680-1370669674Enzo Doria02/2013
7031(8*10^69674-53)/969674Robert Price11/2014
7033(44*10^69663-413)/969664Robert Price10/2017
7034(77*10^69656-23)/969657Robert Price10/2015
70356^89509+13169652Lelio R Paula09/2013
7036(78557*2^231349+1)/3569647Lelio R Paula06/2014
7037(11*10^69645+19)/369646Robert Price03/2016
703811^66875-2869644Lelio R Paula09/2013
70392^231347+7148369643Enzo Doria04/2016
7040(14^60763+3^60763)/1769641Robert Price04/2013
7041(4*10^69626+173)/369627Robert Price01/2017
70422^231289+25569625Lelio R Paula04/2012
70432^231234-11291369609Enzo Doria06/2014
7044(265*10^69602-7)/369604Robert Price07/2016
70452^231182-11284169593Enzo Doria06/2014
7046(15*2^231129+1)/2369577Lelio R Paula08/2012
70473^145806-2869568Lelio R Paula09/2013
7048(265*10^69554-7)/369556Robert Price07/2016
70492^231052-11315969554Enzo Doria07/2014
705011^66784-869549Lelio R Paula09/2013
7051Phi(104409,10)/229699969546Maksym Voznyy07/2015
70522^231016-11052369543Enzo Doria05/2014
70532^231014+57729457569543Lelio R Paula02/2016
705414^60658+6769522Lelio R Paula09/2013
70555^99418+3669491Lelio R Paula06/2013
70567^82203-3069470Lelio R Paula09/2013
7057(63^38609-1)/6269469Paul Bourdelais08/2017
70585^99359-2^9936069449Mike Oakes12/2010
7059(29*2^230684+1)/139569442Lelio R Paula08/2012
7060(19*10^69424+77)/369425Robert Price08/2016
706119^54287-9669420Lelio R Paula09/2013
70622^230541+5890569400Lelio R Paula04/2012
70632^230506+1270569390Lelio R Paula02/2013
70648*6^89156-569378Lelio R Paula09/2014
70652^230438-11134769369Enzo Doria05/2014
70662^230428-9969366Lelio R Paula02/2012
7067(62^38699+1)/6369362Paul Bourdelais08/2017
70683*10^69354+1769355Robert Price03/2017
7069(493*10^69340-7)/969342Robert Price07/2016
7070(41*10^69321+373)/969322Robert Price04/2017
70716^89072+5369312Lelio R Paula09/2013
7072155^31639+269300Lelio R Paula05/2013
70733*7^81965-469269Lelio R Paula09/2014
7074(16*10^69265+41)/369266Robert Price10/2017
7075(86*10^69260-77)/969261Robert Price05/2016
70769*5^99087+469260Lelio R Paula09/2014
70773^145145+266069252Lelio R Paula09/2013
707911^66492-114069245Enzo Doria11/2012
70785*3^145129-469245Lelio R Paula04/2014
70807*3^145126+869244Lelio R Paula04/2014
708111^66480-237069232Enzo Doria12/2012
70822^229962-6569226Lelio R Paula02/2012
70832^229958-11073369225Enzo Doria05/2014
7084V(332407)69225Serge Batalov03/2015
70856^88959+769224Lelio R Paula09/2013
708615^58855-9469219Lelio R Paula09/2013
7087159773#-p(159773)69212Henri Lifchitz12/2018
7088(2^229838+47)/1208169185Lelio R Paula04/2012
70893^144952+9869160Lelio R Paula09/2013
70905^98941-7269157Lelio R Paula06/2013
7091(17*2^229604-1)/22969117Lelio R Paula01/2014
70922^229585-106369112Yves Minet11/2012
7093(13*2^229567-1)/1969107Lelio R Paula01/2014
7094(13*2^229393-1)/569055Lelio R Paula01/2014
7095(53*10^69050-17)/969051Robert Price09/2015
7096(43*10^69048+47)/969049Robert Price12/2017
70972^229305-186853369028Enzo Doria04/2016
70982^229297+138569026Lelio R Paula04/2012
709918^54986-244169023Enzo Doria03/2013
7100(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
71015^98736-1463669014Enzo Doria02/2013
7102(13^61949-5^61949)/869007Robert Price03/2013
7103(2^229227+5)/61169002Lelio R Paula04/2012
71042^229216-11327969001Enzo Doria07/2014
710510^68994+5191368995Patrick De Geest03/2016
710710^68994-10^5814-168994Serge Batalov01/2011
710610^68994-8294768994Patrick De Geest03/2016
7108(17*2^229136-1)/238168975Lelio R Paula01/2014
71092^229113+10768970Lelio R Paula02/2012
711011^66202-441068943Enzo Doria01/2013
711112^63883+568942Lelio R Paula07/2013
7112(9913*2^229002-1)/39990368935Lelio R Paula04/2015
71132^228962-11158168925Enzo Doria05/2014
71142^228944+8168920Henri Lifchitz01/2007
711511^66174-5468914Lelio R Paula09/2013
71162^228913-11126568910Enzo Doria05/2014
71172^228902+7351968907Enzo Doria04/2016
7118(47*2^228884+1)/6368901Lelio R Paula04/2015
71192^228821+7642768882Enzo Doria05/2016
71203^144340+5068868Lelio R Paula09/2013
71212^228758-11296768864Enzo Doria06/2014
71222^228743-11137968859Enzo Doria05/2014
71232^228741-11091168858Enzo Doria05/2014
7125lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
71243*5^98511-868857Lelio R Paula09/2014
71262^228717+46768851Lelio R Paula02/2011
7127Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
7128(509203*2^228665-1)/3568840Lelio R Paula04/2015
71298^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
713011^66074-105068809Enzo Doria11/2012
7131(68*10^68798-11)/368800Robert Price10/2017
71322^228484+18168781Lelio R Paula02/2012
71332^228479-5869568780Lelio R Paula04/2012
71342^228465-1585368775Enzo Doria04/2013
713511^66040-540068774Enzo Doria01/2013
7136(13*2^228441-1)/57568766Lelio R Paula01/2014
7137(17*2^228393+1)/29568752Lelio R Paula08/2012
71382*10^68744+4168745Robert Price01/2017
713911^66011-15068744Enzo Doria08/2012
7140(13*2^228304-1)/8168726Lelio R Paula01/2014
71412^228295-11107968724Enzo Doria05/2014
7142(3^144039+7)/2268723Lelio R Paula04/2012
7143(8*10^68722+49)/368723Robert Price03/2016
7144(35*10^68718+1)/968719Serge Batalov11/2010
71452^228271-22827168717Henri Lifchitz11/2004
71462^228257+8287568713Lelio R Paula02/2013
71473^144013+4068712Lelio R Paula09/2013
714813^61671-8668699Lelio R Paula09/2013
7149(46*10^68698+683)/968699Robert Price12/2017
715017^55828-7268694Lelio R Paula09/2013
71516^88259+6168679Lelio R Paula09/2013
715218^54699-568663Lelio R Paula09/2013
715333^45216+268662Lelio R Paula05/2013
7154(2^228073-5)/368657Lelio R Paula04/2012
7155(2^(6*38012+1)-5)/368657Kevin Acres11/2013
71562^228055-11160768652Enzo Doria05/2014
71572^228054-11476168652Enzo Doria05/2015
71582^228041+118568648Lelio R Paula04/2012
71592^228040-103768647Yves Minet11/2012
71602*F(328450)-168642Henri Lifchitz12/2009
71615^98201-3468640Lelio R Paula06/2013
71629^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
71637*2^227780-368570Lelio R Paula04/2014
716415327^16382-16382^1532768567Norbert Schneider11/2018
71652^227733-12168555Lelio R Paula02/2012
71662^227702-1696768546Enzo Doria05/2013
71672^227689-11165568542Enzo Doria05/2014
7168gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
71695^98051+268535Ray Chandler07/2011
71705*10^68524+5168525Robert Price01/2017
7171(11*10^68520-149)/368521Robert Price01/2017
717219^53573-7868507Lelio R Paula09/2013
7173(68*10^68504+13)/968505Ray Chandler10/2010
71749*5^98003+468503Lelio R Paula09/2014
71752^227528+5168493Lelio R Paula02/2012
7176(146*28^47316+1)/368476Karsten Bonath06/2018
71773^143497+868466Lelio R Paula04/2012
71782^227430-9568464Lelio R Paula02/2012
7179(8*10^68455+13)/368456Robert Price11/2017
71803*5^97934-268454Lelio R Paula09/2014
718120^52613+7768452Lelio R Paula09/2013
71822^227371+3276968446Lelio R Paula04/2012
7183(3^143465+4)/2127042006768440Lelio R Paula04/2012
7184CopelandErdos(68433)68433Eric W. Weisstein08/2013
71852^227323+7543168432Enzo Doria04/2016
71862^227314-196568429Lelio R Paula04/2012
71872^227303-11061768426Enzo Doria05/2014
71897^80963+6668422Lelio R Paula07/2013
71882^227290+7384968422Enzo Doria04/2016
7190(14^59693-1)/1368415Paul Bourdelais06/2008
71912^227256-278624968411Enzo Doria03/2016
71938*10^68400-768401Dmitry Domanov11/2010
7192(15*2^227228-1)/58368401Lelio R Paula01/2014
71942^227210+186916968398Enzo Doria05/2016
71952^227159-183863568382Enzo Doria05/2015
719644*10^68368+368370Robert Price08/2017
71972^227115-780768369Lelio R Paula10/2009
71982^227078-4735568358Lelio R Paula04/2012
7199(2^227063-1017)/34968351Lelio R Paula04/2012
72002^227057+14809168351Lelio R Paula04/2012
72012^227046+18768348Lelio R Paula02/2012
72029*10^68331+5968332Robert Price10/2017
720311^65608-72068324Enzo Doria11/2012
7204(32*10^68320+319)/968321Robert Price10/2017
720533408!2-2^33408-168315Joe McLean05/2017
72062^226894-12368302Lelio R Paula02/2012
720710^68297+14155968298Patrick De Geest05/2013
720810^68297-9368297Robert Price05/2011
7209680^24107-679^2410768284Jean-Louis Charton07/2010
721012^63267+5968277Lelio R Paula07/2013
72112^226785-115968270Yves Minet11/2012
72127^80769+9068258Lelio R Paula07/2013
7213(88*10^68256-1)/368258Robert Price10/2017
72142^226741+6658768256Yves Minet10/2010
72152^226720-11240368250Enzo Doria06/2014
7216(78557*2^226694+1)/368247Lelio R Paula06/2014
7217(83*10^68231+7)/968232Robert Price10/2015
721865^37636+1668231Lelio R Paula01/2016
72195^97615-4^(97615+1)68230Robert Price04/2016
722012^63200-4368205Lelio R Paula07/2013
7221-330*Bern(21940)/22379062073368201Serge Batalov04/2015
72223^142925+868068193Lelio R Paula06/2013
72233*2^226512-768188Lelio R Paula04/2014
722414^59484+5768177Lelio R Paula08/2013
722511^65438-219068147Enzo Doria12/2012
722691^34784-268144Lelio R Paula09/2013
7227(2^226336-3)*6-768135Gilbert Mozzo06/2016
7228(22*10^68133-37)/368134Robert Price05/2017
72295^97476+3668133Lelio R Paula06/2013
72303*5^97474-268132Lelio R Paula09/2014
723112^63130+4968129Lelio R Paula07/2013
72322^226281+538568118Lelio R Paula04/2012
72332^226257-304968111Yves Minet10/2014
7234(28*10^68107-43)/368108Robert Price04/2016
72352^226243-258768106Yves Minet07/2014
723620^52346-1168104Lelio R Paula09/2013
72372^226205-9968095Lelio R Paula02/2012
72382^226187-4968090Lelio R Paula02/2012
72393^142708+7668090Lelio R Paula06/2013
72407*10^68088-8968089Robert Price01/2017
72412^226154+7183968080Enzo Doria04/2016
7242(10^68078+59)/368078Serge Batalov12/2014
724414^59387+6968066Lelio R Paula08/2013
72432^226108-11342968066Enzo Doria07/2014
7245(62*10^68059-197)/968060Robert Price10/2017
7246(24^49307-1)/2368053Robert Price04/2012
724715^57859-2868048Lelio R Paula08/2013
7248(509203*2^226003-1)/1368039Lelio R Paula04/2015
72492^226015-11136168038Enzo Doria05/2014
7250(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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