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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
7501((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
7502(2^756839/10^36014)%10^7000070000Michael Vang12/2016
7503(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
750410^69999-8825169999Patrick De Geest08/2009
75052^232507+108969992Lelio R Paula04/2012
7506(17*2^232445+1)/569974Lelio R Paula08/2012
7507(529^25693+1)/53069972Richard Fischer12/2017
75087^82778+4869956Lelio R Paula09/2013
75107*2^232381+369955Lelio R Paula04/2014
750919305^4204+4204^1930569955Hans Havermann10/2019
75112^232362-11054169948Enzo Doria05/2014
751219442^3957+3957^1944269940Hans Havermann09/2019
75132^232326-11239169938Enzo Doria06/2014
75143^146575+23669935Lelio R Paula09/2013
751530^47341-2969929Norbert Schneider02/2014
75165^100040-6869925Lelio R Paula09/2013
75179946^17491+17491^994669923Norbert Schneider07/2019
7518(35*10^69866-593)/969867Robert Price08/2017
75192^232045-1729569853Lelio R Paula04/2012
7520(2^231987+78557)/9569834Lelio R Paula05/2012
75212^231955+7424369826Yves Minet03/2011
75222^231946-1587369823Enzo Doria04/2013
752318^55618+9569816Lelio R Paula09/2013
75246^89712+5^(89712-1)69810Robert Price02/2016
75252^231870+13569800Lelio R Paula02/2012
7526(23*2^231827-1)/417969785Lelio R Paula01/2014
75272^231778+5461569773Lelio R Paula04/2012
7528(19*2^231780+1)/23569772Lelio R Paula08/2012
752914^60866+2769761Lelio R Paula09/2013
753013^62619-4469755Lelio R Paula09/2013
7531(2^231715-509203)/3569752Lelio R Paula05/2012
75322^231711-11046769752Enzo Doria05/2014
7533(19^54547+18^54547)/3769751Robert Price08/2013
7534(23*2^231697-1)/4569748Lelio R Paula01/2014
75352^231696-186149969748Enzo Doria03/2016
75362^231684-14769744Lelio R Paula02/2012
7537(23*2^231686-1)/118369743Lelio R Paula01/2014
75382^231591-47739769716Paul Bourdelais03/2013
753916916^13209+13209^1691669709Hans Havermann09/2019
754016568^16095+16095^1656869697Hans Havermann09/2019
754111^66916-42069686Enzo Doria08/2012
75425^99680-1370669674Enzo Doria02/2013
7543(8*10^69674-53)/969674Robert Price11/2014
7544(44*10^69663-413)/969664Robert Price10/2017
754518950^4743+4743^1895069662Hans Havermann10/2019
7546(77*10^69656-23)/969657Robert Price10/2015
75476^89509+13169652Lelio R Paula09/2013
7548(78557*2^231349+1)/3569647Lelio R Paula06/2014
7549(11*10^69645+19)/369646Robert Price03/2016
755011^66875-2869644Lelio R Paula09/2013
75512^231347+7148369643Enzo Doria04/2016
7552(14^60763+3^60763)/1769641Robert Price04/2013
7553(4*10^69626+173)/369627Robert Price01/2017
75542^231289+25569625Lelio R Paula04/2012
755519794^3287+3287^1979469612Hans Havermann09/2019
75562^231234-11291369609Enzo Doria06/2014
7557(265*10^69602-7)/369604Robert Price07/2016
75582^231182-11284169593Enzo Doria06/2014
7559(15*2^231129+1)/2369577Lelio R Paula08/2012
75603^145806-2869568Lelio R Paula09/2013
7561(265*10^69554-7)/369556Robert Price07/2016
75622^231052-11315969554Enzo Doria07/2014
7563(10^9+1)*(10^129+1)*(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)69552Makoto Kamada03/2019
756411^66784-869549Lelio R Paula09/2013
7565Phi(104409,10)/229699969546Maksym Voznyy07/2015
75662^231016-11052369543Enzo Doria05/2014
75672^231014+57729457569543Lelio R Paula02/2016
756814^60658+6769522Lelio R Paula09/2013
75695^99418+3669491Lelio R Paula06/2013
75707^82203-3069470Lelio R Paula09/2013
7571(63^38609-1)/6269469Paul Bourdelais08/2017
75725^99359-2^9936069449Mike Oakes12/2010
7573(29*2^230684+1)/139569442Lelio R Paula08/2012
757417692^8411+8411^1769269439Hans Havermann09/2019
7575(19*10^69424+77)/369425Robert Price08/2016
757619^54287-9669420Lelio R Paula09/2013
757720739^2222+2222^2073969409Hans Havermann09/2019
75782^230541+5890569400Lelio R Paula04/2012
75792^230506+1270569390Lelio R Paula02/2013
75808*6^89156-569378Lelio R Paula09/2014
75812^230438-11134769369Enzo Doria05/2014
75822^230428-9969366Lelio R Paula02/2012
7583(62^38699+1)/6369362Paul Bourdelais08/2017
75843*10^69354+1769355Robert Price03/2017
7585(493*10^69340-7)/969342Robert Price07/2016
7586(41*10^69321+373)/969322Robert Price04/2017
75876^89072+5369312Lelio R Paula09/2013
7588155^31639+269300Lelio R Paula05/2013
75893*7^81965-469269Lelio R Paula09/2014
7590(16*10^69265+41)/369266Robert Price10/2017
7591(86*10^69260-77)/969261Robert Price05/2016
75929*5^99087+469260Lelio R Paula09/2014
75933^145145+266069252Lelio R Paula09/2013
759411^66492-114069245Enzo Doria11/2012
75955*3^145129-469245Lelio R Paula04/2014
75967*3^145126+869244Lelio R Paula04/2014
759711^66480-237069232Enzo Doria12/2012
75982^229962-6569226Lelio R Paula02/2012
75992^229958-11073369225Enzo Doria05/2014
7600V(332407)69225Serge Batalov03/2015
76016^88959+769224Lelio R Paula09/2013
760215^58855-9469219Lelio R Paula09/2013
7603159773#-p(159773)69212Henri Lifchitz12/2018
760420223^2638+2638^2022369189Hans Havermann09/2019
7605(2^229838+47)/1208169185Lelio R Paula04/2012
76063^144952+9869160Lelio R Paula09/2013
76075^98941-7269157Lelio R Paula06/2013
760863329!4+25669147Robert Price09/2019
760916422^16229+16229^1642269142Hans Havermann09/2019
7610(17*2^229604-1)/22969117Lelio R Paula01/2014
76112^229585-106369112Yves Minet11/2012
7612(13*2^229567-1)/1969107Lelio R Paula01/2014
7613(13*2^229393-1)/569055Lelio R Paula01/2014
7614(53*10^69050-17)/969051Robert Price09/2015
7615(43*10^69048+47)/969049Robert Price12/2017
76162^229305-186853369028Enzo Doria04/2016
76172^229297+138569026Lelio R Paula04/2012
761818^54986-244169023Enzo Doria03/2013
7619(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
76205^98736-1463669014Enzo Doria02/2013
7621(13^61949-5^61949)/869007Robert Price03/2013
7622(2^229227+5)/61169002Lelio R Paula04/2012
76232^229216-11327969001Enzo Doria07/2014
762410^68994+5191368995Patrick De Geest03/2016
762610^68994-10^5814-168994Serge Batalov01/2011
762510^68994-8294768994Patrick De Geest03/2016
7627(17*2^229136-1)/238168975Lelio R Paula01/2014
76282^229113+10768970Lelio R Paula02/2012
762916877^12198+12198^1687768965Hans Havermann09/2019
763011^66202-441068943Enzo Doria01/2013
763112^63883+568942Lelio R Paula07/2013
7632(9913*2^229002-1)/39990368935Lelio R Paula04/2015
76332^228962-11158168925Enzo Doria05/2014
76342^228944+8168920Henri Lifchitz01/2007
763511^66174-5468914Lelio R Paula09/2013
763616756^12959+12959^1675668911Hans Havermann09/2019
76372^228913-11126568910Enzo Doria05/2014
763818917^4392+4392^1891768909Hans Havermann09/2019
76392^228902+7351968907Enzo Doria04/2016
7640(47*2^228884+1)/6368901Lelio R Paula04/2015
764116542^14591+14591^1654268883Hans Havermann09/2019
76422^228821+7642768882Enzo Doria05/2016
76433^144340+5068868Lelio R Paula09/2013
76442^228758-11296768864Enzo Doria06/2014
76452^228743-11137968859Enzo Doria05/2014
76462^228741-11091168858Enzo Doria05/2014
7648lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
76473*5^98511-868857Lelio R Paula09/2014
76492^228717+46768851Lelio R Paula02/2011
7650Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
7651(509203*2^228665-1)/3568840Lelio R Paula04/2015
76528^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
765311^66074-105068809Enzo Doria11/2012
7654(68*10^68798-11)/368800Robert Price10/2017
76552^228484+18168781Lelio R Paula02/2012
76562^228479-5869568780Lelio R Paula04/2012
76572^228465-1585368775Enzo Doria04/2013
765811^66040-540068774Enzo Doria01/2013
7659(13*2^228441-1)/57568766Lelio R Paula01/2014
7660(17*2^228393+1)/29568752Lelio R Paula08/2012
766117859^7072+7072^1785968749Hans Havermann09/2019
76622*10^68744+4168745Robert Price01/2017
766311^66011-15068744Enzo Doria08/2012
7664(13*2^228304-1)/8168726Lelio R Paula01/2014
76652^228295-11107968724Enzo Doria05/2014
7667(3^144039+7)/2268723Lelio R Paula04/2012
7666(8*10^68722+49)/368723Robert Price03/2016
7668(35*10^68718+1)/968719Serge Batalov11/2010
76692^228271-22827168717Henri Lifchitz11/2004
76702^228257+8287568713Lelio R Paula02/2013
76713^144013+4068712Lelio R Paula09/2013
767213^61671-8668699Lelio R Paula09/2013
7673(46*10^68698+683)/968699Robert Price12/2017
767417^55828-7268694Lelio R Paula09/2013
767518675^4762+4762^1867568683Hans Havermann09/2019
76766^88259+6168679Lelio R Paula09/2013
767718^54699-568663Lelio R Paula09/2013
767833^45216+268662Lelio R Paula05/2013
7680(2^228073-5)/368657Lelio R Paula04/2012
7679(2^(6*38012+1)-5)/368657Kevin Acres11/2013
76812^228055-11160768652Enzo Doria05/2014
76822^228054-11476168652Enzo Doria05/2015
76832^228041+118568648Lelio R Paula04/2012
76842^228040-103768647Yves Minet11/2012
76852*F(328450)-168642Henri Lifchitz12/2009
76865^98201-3468640Lelio R Paula06/2013
76879^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
768818177^5948+5948^1817768607Hans Havermann09/2019
76897*2^227780-368570Lelio R Paula04/2014
769015327^16382-16382^1532768567Norbert Schneider11/2018
76912^227733-12168555Lelio R Paula02/2012
769216460^14607+14607^1646068549Hans Havermann09/2019
76932^227702-1696768546Enzo Doria05/2013
76942^227689-11165568542Enzo Doria05/2014
7695gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
76965^98051+268535Ray Chandler07/2011
76975*10^68524+5168525Robert Price01/2017
7698(11*10^68520-149)/368521Robert Price01/2017
769916624^13235+13235^1662468520Hans Havermann09/2019
770016359^15430+15430^1635968518Hans Havermann08/2019
770119^53573-7868507Lelio R Paula09/2013
7702(68*10^68504+13)/968505Ray Chandler10/2010
77039*5^98003+468503Lelio R Paula09/2014
770421121^1750+1750^2112168497Hans Havermann10/2019
77052^227528+5168493Lelio R Paula02/2012
7706(146*28^47316+1)/368476Karsten Bonath06/2018
77073^143497+868466Lelio R Paula04/2012
77082^227430-9568464Lelio R Paula02/2012
7709(8*10^68455+13)/368456Robert Price11/2017
77103*5^97934-268454Lelio R Paula09/2014
771120^52613+7768452Lelio R Paula09/2013
77122^227371+3276968446Lelio R Paula04/2012
7713(3^143465+4)/2127042006768440Lelio R Paula04/2012
7714CopelandErdos(68433)68433Eric W. Weisstein08/2013
77152^227323+7543168432Enzo Doria04/2016
77162^227314-196568429Lelio R Paula04/2012
77172^227303-11061768426Enzo Doria05/2014
77197^80963+6668422Lelio R Paula07/2013
77182^227290+7384968422Enzo Doria04/2016
7720(14^59693-1)/1368415Paul Bourdelais06/2008
77212^227256-278624968411Enzo Doria03/2016
77238*10^68400-768401Dmitry Domanov11/2010
7722(15*2^227228-1)/58368401Lelio R Paula01/2014
77242^227210+186916968398Enzo Doria05/2016
77252^227159-183863568382Enzo Doria05/2015
772644*10^68368+368370Robert Price08/2017
77272^227115-780768369Lelio R Paula10/2009
772818469^5032+5032^1846968368Hans Havermann08/2019
77292^227078-4735568358Lelio R Paula04/2012
773016927^10920+10920^1692768355Hans Havermann10/2019
7731(2^227063-1017)/34968351Lelio R Paula04/2012
77322^227057+14809168351Lelio R Paula04/2012
77332^227046+18768348Lelio R Paula02/2012
77342^227009-469368337Yves Minet05/2019
77359*10^68331+5968332Robert Price10/2017
773611^65608-72068324Enzo Doria11/2012
7737(32*10^68320+319)/968321Robert Price10/2017
773833408!2-2^33408-168315Joe McLean05/2017
77392^226894-12368302Lelio R Paula02/2012
774010^68297+14155968298Patrick De Geest05/2013
774110^68297-9368297Robert Price05/2011
7742680^24107-679^2410768284Jean-Louis Charton07/2010
774312^63267+5968277Lelio R Paula07/2013
77442^226785-115968270Yves Minet11/2012
77457^80769+9068258Lelio R Paula07/2013
7746(88*10^68256-1)/368258Robert Price10/2017
77472^226741+6658768256Yves Minet10/2010
77482^226720-11240368250Enzo Doria06/2014
7749(78557*2^226694+1)/368247Lelio R Paula06/2014
7750(83*10^68231+7)/968232Robert Price10/2015


Find by discoverer :


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

Go back
Valid XHTML 1.0!    Valid CSS!