PRP Records

Probable Primes Top 10000

(212140 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 (> 30000) Who ? When ?
6501(29*10^70194-11)/970195Robert Price04/2015
65023^147109+19670189Lelio R Paula05/2014
6503(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
65049^73538+8^(73538+1)70174Robert Price06/2016
65052*5^100391+770171Lelio R Paula10/2014
650699^35156-270159Lelio R Paula08/2013
6507(68*10^70148+7)/370150Robert Price03/2016
650811^67360-603070149Enzo Doria01/2013
6509(35*10^70130-377)/970131Robert Price12/2017
651049391!3+3^4939170128Robert Price09/2015
6511(229*10^70122-1)/370124Robert Price12/2016
65127^82975-9270123Lelio R Paula07/2014
651365^38670+5870106Lelio R Paula01/2016
6514105^34684+34684^10570103Serge Batalov05/2014
6515134^32955-13370099Norbert Schneider03/2015
65172^232836-22790370091Enzo Doria12/2012
65162^232837-185917370091Enzo Doria03/2016
65183*2^232820+570087Lelio R Paula04/2014
65202^232799+9019570080Lelio R Paula02/2013
65192^232799-11223770080Enzo Doria06/2014
65212^232759+26214570068Lelio R Paula04/2012
65223*2^232750+770066Lelio R Paula04/2014
652312^64918-1170059Lelio R Paula01/2015
65247^82899-1270058Lelio R Paula09/2013
6525(22*10^70051-13)/970052Robert Price03/2015
6526(2^232685-7)/251462570039Lelio R Paula04/2012
652718^55786-536370027Enzo Doria03/2013
6528(2^(77537*3+1)+243)/770023Kevin Acres11/2013
65292^232602+16970021Lelio R Paula02/2012
6530(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
65312^232580+7213370014Enzo Doria04/2016
65324*6^89958-770002Lelio R Paula09/2014
653310^70000+8048770001Milton L. Brown05/2006
653410^69999+13485770000Patrick De Geest02/2007
653910^70000-927370000Patrick De Geest08/2009
6535(79*10^69999-7)/970000Robert Price01/2015
6536((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6537(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6538(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
654010^69999-8825169999Patrick De Geest08/2009
65412^232507+108969992Lelio R Paula04/2012
6542(17*2^232445+1)/569974Lelio R Paula08/2012
6543(529^25693+1)/53069972Richard Fischer12/2017
65447^82778+4869956Lelio R Paula09/2013
65457*2^232381+369955Lelio R Paula04/2014
65462^232362-11054169948Enzo Doria05/2014
65472^232326-11239169938Enzo Doria06/2014
65483^146575+23669935Lelio R Paula09/2013
654930^47341-2969929Norbert Schneider02/2014
65505^100040-6869925Lelio R Paula09/2013
6551(35*10^69866-593)/969867Robert Price08/2017
65522^232045-1729569853Lelio R Paula04/2012
6553(2^231987+78557)/9569834Lelio R Paula05/2012
65542^231955+7424369826Yves Minet03/2011
65552^231946-1587369823Enzo Doria04/2013
655618^55618+9569816Lelio R Paula09/2013
65576^89712+5^(89712-1)69810Robert Price02/2016
65582^231870+13569800Lelio R Paula02/2012
6559(23*2^231827-1)/417969785Lelio R Paula01/2014
65602^231778+5461569773Lelio R Paula04/2012
6561(19*2^231780+1)/23569772Lelio R Paula08/2012
656214^60866+2769761Lelio R Paula09/2013
656313^62619-4469755Lelio R Paula09/2013
6564(2^231715-509203)/3569752Lelio R Paula05/2012
65652^231711-11046769752Enzo Doria05/2014
6566(19^54547+18^54547)/3769751Robert Price08/2013
6567(23*2^231697-1)/4569748Lelio R Paula01/2014
65682^231696-186149969748Enzo Doria03/2016
65692^231684-14769744Lelio R Paula02/2012
6570(23*2^231686-1)/118369743Lelio R Paula01/2014
65712^231591-47739769716Paul Bourdelais03/2013
657211^66916-42069686Enzo Doria08/2012
65735^99680-1370669674Enzo Doria02/2013
6574(8*10^69674-53)/969674Robert Price11/2014
6575(44*10^69663-413)/969664Robert Price10/2017
6576(77*10^69656-23)/969657Robert Price10/2015
65776^89509+13169652Lelio R Paula09/2013
6578(78557*2^231349+1)/3569647Lelio R Paula06/2014
6579(11*10^69645+19)/369646Robert Price03/2016
658011^66875-2869644Lelio R Paula09/2013
65812^231347+7148369643Enzo Doria04/2016
6582(14^60763+3^60763)/1769641Robert Price04/2013
6583(4*10^69626+173)/369627Robert Price01/2017
65842^231289+25569625Lelio R Paula04/2012
65852^231234-11291369609Enzo Doria06/2014
6586(265*10^69602-7)/369604Robert Price07/2016
65872^231182-11284169593Enzo Doria06/2014
6588(15*2^231129+1)/2369577Lelio R Paula08/2012
65893^145806-2869568Lelio R Paula09/2013
6590(265*10^69554-7)/369556Robert Price07/2016
65912^231052-11315969554Enzo Doria07/2014
659211^66784-869549Lelio R Paula09/2013
6593Phi(104409,10)/229699969546Maksym Voznyy07/2015
65942^231016-11052369543Enzo Doria05/2014
65952^231014+57729457569543Lelio R Paula02/2016
659614^60658+6769522Lelio R Paula09/2013
65975^99418+3669491Lelio R Paula06/2013
65987^82203-3069470Lelio R Paula09/2013
6599(63^38609-1)/6269469Paul Bourdelais08/2017
66005^99359-2^9936069449Mike Oakes12/2010
6601(29*2^230684+1)/139569442Lelio R Paula08/2012
6602(19*10^69424+77)/369425Robert Price08/2016
660319^54287-9669420Lelio R Paula09/2013
66042^230541+5890569400Lelio R Paula04/2012
66052^230506+1270569390Lelio R Paula02/2013
66068*6^89156-569378Lelio R Paula09/2014
66072^230438-11134769369Enzo Doria05/2014
66082^230428-9969366Lelio R Paula02/2012
6609(62^38699+1)/6369362Paul Bourdelais08/2017
66103*10^69354+1769355Robert Price03/2017
6611(493*10^69340-7)/969342Robert Price07/2016
6612(41*10^69321+373)/969322Robert Price04/2017
66136^89072+5369312Lelio R Paula09/2013
6614155^31639+269300Lelio R Paula05/2013
66153*7^81965-469269Lelio R Paula09/2014
6616(16*10^69265+41)/369266Robert Price10/2017
6617(86*10^69260-77)/969261Robert Price05/2016
66189*5^99087+469260Lelio R Paula09/2014
66193^145145+266069252Lelio R Paula09/2013
662011^66492-114069245Enzo Doria11/2012
66215*3^145129-469245Lelio R Paula04/2014
66227*3^145126+869244Lelio R Paula04/2014
662311^66480-237069232Enzo Doria12/2012
66242^229962-6569226Lelio R Paula02/2012
66252^229958-11073369225Enzo Doria05/2014
6626V(332407)69225Serge Batalov03/2015
66276^88959+769224Lelio R Paula09/2013
662815^58855-9469219Lelio R Paula09/2013
6629(2^229838+47)/1208169185Lelio R Paula04/2012
66303^144952+9869160Lelio R Paula09/2013
66315^98941-7269157Lelio R Paula06/2013
6632(17*2^229604-1)/22969117Lelio R Paula01/2014
66332^229585-106369112Yves Minet11/2012
6634(13*2^229567-1)/1969107Lelio R Paula01/2014
6635(13*2^229393-1)/569055Lelio R Paula01/2014
6636(53*10^69050-17)/969051Robert Price09/2015
6637(43*10^69048+47)/969049Robert Price12/2017
66382^229305-186853369028Enzo Doria04/2016
66392^229297+138569026Lelio R Paula04/2012
664018^54986-244169023Enzo Doria03/2013
6641(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
66425^98736-1463669014Enzo Doria02/2013
6643(13^61949-5^61949)/869007Robert Price03/2013
6644(2^229227+5)/61169002Lelio R Paula04/2012
66452^229216-11327969001Enzo Doria07/2014
664610^68994+5191368995Patrick De Geest03/2016
664810^68994-10^5814-168994Serge Batalov01/2011
664710^68994-8294768994Patrick De Geest03/2016
6649(17*2^229136-1)/238168975Lelio R Paula01/2014
66502^229113+10768970Lelio R Paula02/2012
665111^66202-441068943Enzo Doria01/2013
665212^63883+568942Lelio R Paula07/2013
6653(9913*2^229002-1)/39990368935Lelio R Paula04/2015
66542^228962-11158168925Enzo Doria05/2014
66552^228944+8168920Henri Lifchitz01/2007
665611^66174-5468914Lelio R Paula09/2013
66572^228913-11126568910Enzo Doria05/2014
66582^228902+7351968907Enzo Doria04/2016
6659(47*2^228884+1)/6368901Lelio R Paula04/2015
66602^228821+7642768882Enzo Doria05/2016
66613^144340+5068868Lelio R Paula09/2013
66622^228758-11296768864Enzo Doria06/2014
66632^228743-11137968859Enzo Doria05/2014
66642^228741-11091168858Enzo Doria05/2014
6666lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
66653*5^98511-868857Lelio R Paula09/2014
66672^228717+46768851Lelio R Paula02/2011
6668Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6669(509203*2^228665-1)/3568840Lelio R Paula04/2015
66708^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
667111^66074-105068809Enzo Doria11/2012
6672(68*10^68798-11)/368800Robert Price10/2017
66732^228484+18168781Lelio R Paula02/2012
66742^228479-5869568780Lelio R Paula04/2012
66752^228465-1585368775Enzo Doria04/2013
667611^66040-540068774Enzo Doria01/2013
6677(13*2^228441-1)/57568766Lelio R Paula01/2014
6678(17*2^228393+1)/29568752Lelio R Paula08/2012
66792*10^68744+4168745Robert Price01/2017
668011^66011-15068744Enzo Doria08/2012
6681(13*2^228304-1)/8168726Lelio R Paula01/2014
66822^228295-11107968724Enzo Doria05/2014
6684(3^144039+7)/2268723Lelio R Paula04/2012
6683(8*10^68722+49)/368723Robert Price03/2016
6685(35*10^68718+1)/968719Serge Batalov11/2010
66862^228271-22827168717Henri Lifchitz11/2004
66872^228257+8287568713Lelio R Paula02/2013
66883^144013+4068712Lelio R Paula09/2013
668913^61671-8668699Lelio R Paula09/2013
6690(46*10^68698+683)/968699Robert Price12/2017
669117^55828-7268694Lelio R Paula09/2013
66926^88259+6168679Lelio R Paula09/2013
669318^54699-568663Lelio R Paula09/2013
669433^45216+268662Lelio R Paula05/2013
6696(2^228073-5)/368657Lelio R Paula04/2012
6695(2^(6*38012+1)-5)/368657Kevin Acres11/2013
66972^228055-11160768652Enzo Doria05/2014
66982^228054-11476168652Enzo Doria05/2015
66992^228041+118568648Lelio R Paula04/2012
67002^228040-103768647Yves Minet11/2012
67012*F(328450)-168642Henri Lifchitz12/2009
67025^98201-3468640Lelio R Paula06/2013
67039^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
67047*2^227780-368570Lelio R Paula04/2014
67052^227733-12168555Lelio R Paula02/2012
67062^227702-1696768546Enzo Doria05/2013
67072^227689-11165568542Enzo Doria05/2014
6708gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
67095^98051+268535Ray Chandler07/2011
67105*10^68524+5168525Robert Price01/2017
6711(11*10^68520-149)/368521Robert Price01/2017
671219^53573-7868507Lelio R Paula09/2013
6713(68*10^68504+13)/968505Ray Chandler10/2010
67149*5^98003+468503Lelio R Paula09/2014
67152^227528+5168493Lelio R Paula02/2012
67163^143497+868466Lelio R Paula04/2012
67172^227430-9568464Lelio R Paula02/2012
6718(8*10^68455+13)/368456Robert Price11/2017
67193*5^97934-268454Lelio R Paula09/2014
672020^52613+7768452Lelio R Paula09/2013
67212^227371+3276968446Lelio R Paula04/2012
6722(3^143465+4)/2127042006768440Lelio R Paula04/2012
6723CopelandErdos(68433)68433Eric W. Weisstein08/2013
67242^227323+7543168432Enzo Doria04/2016
67252^227314-196568429Lelio R Paula04/2012
67262^227303-11061768426Enzo Doria05/2014
67277^80963+6668422Lelio R Paula07/2013
67282^227290+7384968422Enzo Doria04/2016
6729(14^59693-1)/1368415Paul Bourdelais06/2008
67302^227256-278624968411Enzo Doria03/2016
67328*10^68400-768401Dmitry Domanov11/2010
6731(15*2^227228-1)/58368401Lelio R Paula01/2014
67332^227210+186916968398Enzo Doria05/2016
67342^227159-183863568382Enzo Doria05/2015
673544*10^68368+368370Robert Price08/2017
67362^227115-780768369Lelio R Paula10/2009
67372^227078-4735568358Lelio R Paula04/2012
6738(2^227063-1017)/34968351Lelio R Paula04/2012
67392^227057+14809168351Lelio R Paula04/2012
67402^227046+18768348Lelio R Paula02/2012
67419*10^68331+5968332Robert Price10/2017
674211^65608-72068324Enzo Doria11/2012
6743(32*10^68320+319)/968321Robert Price10/2017
674433408!2-2^33408-168315Joe McLean05/2017
67452^226894-12368302Lelio R Paula02/2012
674610^68297+14155968298Patrick De Geest05/2013
674710^68297-9368297Robert Price05/2011
6748680^24107-679^2410768284Jean-Louis Charton07/2010
674912^63267+5968277Lelio R Paula07/2013
67502^226785-115968270Yves Minet11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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