PRP Records

Probable Primes Top 10000

(202632 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 ?
62512^235308+13570835Lelio R Paula02/2012
6252r(35414,90)*1000+91170831Patrick De Geest07/2004
62532^235274+15970825Lelio R Paula02/2012
62543^148409+7070810Lelio R Paula11/2014
6255(19*10^70794+17)/970795Robert Price03/2015
62562^235108-23270970775Paul Bourdelais03/2013
6257(2^235099-2^117550+1)/57077211/2006
625819^55325-670748Lelio R Paula08/2014
6259257^29356+29356^25770746Norbert Schneider10/2014
626022*10^70729+370731Robert Price10/2017
62612^234956+1171570729Lelio R Paula05/2012
6262(7*10^70727-43)/970727Robert Price10/2014
62632^234890-3034170709Enzo Doria11/2012
626417^57461+1470703Lelio R Paula01/2015
6265(9179*2^234834-1)/570696Lelio R Paula04/2015
62662*10^70688+5170689Robert Price10/2017
6267123^33822-12270685Norbert Schneider01/2015
62687*10^70680-9970681Robert Price11/2017
6269(21*2^234772-1)/209570672Lelio R Paula01/2014
6270(29*2^234686-1)/2114570645Lelio R Paula01/2014
6271(15*2^234688-1)/527814170643Lelio R Paula01/2014
62732^234655-6770639Lelio R Paula02/2012
6272(79*10^70638-61)/970639Robert Price10/2015
62742^234652-17370638Lelio R Paula02/2012
62752^234618-364570628Lelio R Paula05/2012
6276(2^234610-5)/1970624Lelio R Paula05/2012
62774*5^101038+970624Lelio R Paula10/2014
62782^234603+7196370623Enzo Doria04/2016
62792^234600-11312970622Enzo Doria07/2014
62802^234586+970618Lelio R Paula02/2012
62813^148008+2670618Robert Price11/2013
6282(7*10^70616-151)/970616Robert Price09/2017
628365^38947+3270608Lelio R Paula01/2016
6284(2^234488-3)/1170587Lelio R Paula05/2012
6285(3*2^234451+1)/3570576Lelio R Paula08/2012
6286Phi(159495,10)70560Maksym Voznyy09/2015
62872^234383-403570557Lelio R Paula05/2012
62882^234315-11124170536Enzo Doria05/2014
628914^61526+9770517Lelio R Paula01/2015
6290(3*2^234170+1)/1370492Lelio R Paula08/2012
629151^41281-50^4128170491Robert Price02/2013
62922^234141-11212370484Enzo Doria06/2014
62932^234139+1228570483Lelio R Paula04/2012
62942^234133-316370482Yves Minet04/2009
62952^234115+8370476Lelio R Paula02/2012
62962^234114-159570476Lelio R Paula05/2012
629724^51061-23^5106170475Robert Price07/2012
629819471^16428-270467Faysal YAtim09/2005
62997^83381+1270466Robert Price01/2014
63002^234067-11142770462Enzo Doria05/2014
6301(266*10^70457+1)/370459Robert Price02/2016
6302(31*2^234041-1)/9770453Lelio R Paula01/2014
63032^234026+1290970449Lelio R Paula04/2012
63042^233965-1970431Lelio R Paula02/2012
6305(5*2^233932-1)/17970419Lelio R Paula01/2014
63062^233908-1710970414Enzo Doria05/2013
6307695^24772+24772^69570402Norbert Schneider09/2016
63083*5^100719-270401Lelio R Paula10/2014
63092^233829-11135570390Enzo Doria05/2014
6310(19775^16384+1)/270388Henri Lifchitz03/2007
63117*3^147519+870386Lelio R Paula04/2014
6312141^32749-270385Lelio R Paula10/2017
63135*7^83265+270368Lelio R Paula10/2014
6314(23*10^70363+97)/370364Robert Price02/2017
6315(23*2^233749-1)/3532570363Lelio R Paula01/2014
63165^100652-1391670353Enzo Doria02/2013
631745^42555-270353Lelio R Paula08/2013
63182^233661-6170339Lelio R Paula02/2012
63192^233523-11224970298Enzo Doria06/2014
63205*3^147324-870293Lelio R Paula04/2014
63212^233488-1306570287Enzo Doria11/2012
6322(3^147322+8)/4285170286Lelio R Paula06/2012
6323(22*10^70259+161)/370260Robert Price02/2017
63242^233388+46570257Lelio R Paula11/2012
632514^61299+5970257Lelio R Paula01/2015
63262^233383+9406570256Lelio R Paula04/2012
632749471!3-656170253Robert Price11/2015
63287^83121+6^(83121-1)70246Robert Price03/2016
6329(197*10^70241-11)/370243Robert Price10/2017
633023*10^70240-770242Robert Price03/2016
6331(71*10^70227-53)/970228Robert Price10/2015
6332(2^233247-9)/1770214Lelio R Paula05/2012
6333(11^67421-2^67421)/970211Robert Price01/2013
6334(23*10^70209-41)/970210Robert Price03/2015
6335(29*10^70194-11)/970195Robert Price04/2015
63363^147109+19670189Lelio R Paula05/2014
6337(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
63389^73538+8^(73538+1)70174Robert Price06/2016
63392*5^100391+770171Lelio R Paula10/2014
634099^35156-270159Lelio R Paula08/2013
6341(68*10^70148+7)/370150Robert Price03/2016
634211^67360-603070149Enzo Doria01/2013
6343(35*10^70130-377)/970131Robert Price12/2017
634449391!3+3^4939170128Robert Price09/2015
6345(229*10^70122-1)/370124Robert Price12/2016
63467^82975-9270123Lelio R Paula07/2014
634765^38670+5870106Lelio R Paula01/2016
6348105^34684+34684^10570103Serge Batalov05/2014
6349134^32955-13370099Norbert Schneider03/2015
63512^232836-22790370091Enzo Doria12/2012
63502^232837-185917370091Enzo Doria03/2016
63523*2^232820+570087Lelio R Paula04/2014
63542^232799+9019570080Lelio R Paula02/2013
63532^232799-11223770080Enzo Doria06/2014
63552^232759+26214570068Lelio R Paula04/2012
63563*2^232750+770066Lelio R Paula04/2014
635712^64918-1170059Lelio R Paula01/2015
63587^82899-1270058Lelio R Paula09/2013
6359(22*10^70051-13)/970052Robert Price03/2015
6360(2^232685-7)/251462570039Lelio R Paula04/2012
636118^55786-536370027Enzo Doria03/2013
6362(2^(77537*3+1)+243)/770023Kevin Acres11/2013
63632^232602+16970021Lelio R Paula02/2012
63642^232580+7213370014Enzo Doria04/2016
63654*6^89958-770002Lelio R Paula09/2014
636610^70000+8048770001Milton L. Brown05/2006
636710^69999+13485770000Patrick De Geest02/2007
637210^70000-927370000Patrick De Geest08/2009
6368(79*10^69999-7)/970000Robert Price01/2015
6371((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6369(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6370(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
637310^69999-8825169999Patrick De Geest08/2009
63742^232507+108969992Lelio R Paula04/2012
6375(17*2^232445+1)/569974Lelio R Paula08/2012
6376(529^25693+1)/53069972Richard Fischer12/2017
63777^82778+4869956Lelio R Paula09/2013
63787*2^232381+369955Lelio R Paula04/2014
63792^232362-11054169948Enzo Doria05/2014
63802^232326-11239169938Enzo Doria06/2014
63813^146575+23669935Lelio R Paula09/2013
638230^47341-2969929Norbert Schneider02/2014
63835^100040-6869925Lelio R Paula09/2013
6384(35*10^69866-593)/969867Robert Price08/2017
63852^232045-1729569853Lelio R Paula04/2012
6386(2^231987+78557)/9569834Lelio R Paula05/2012
63872^231955+7424369826Yves Minet03/2011
63882^231946-1587369823Enzo Doria04/2013
638918^55618+9569816Lelio R Paula09/2013
63906^89712+5^(89712-1)69810Robert Price02/2016
63912^231870+13569800Lelio R Paula02/2012
6392(23*2^231827-1)/417969785Lelio R Paula01/2014
63932^231778+5461569773Lelio R Paula04/2012
6394(19*2^231780+1)/23569772Lelio R Paula08/2012
639514^60866+2769761Lelio R Paula09/2013
639613^62619-4469755Lelio R Paula09/2013
6397(2^231715-509203)/3569752Lelio R Paula05/2012
63982^231711-11046769752Enzo Doria05/2014
6399(19^54547+18^54547)/3769751Robert Price08/2013
6400(23*2^231697-1)/4569748Lelio R Paula01/2014
64012^231696-186149969748Enzo Doria03/2016
64022^231684-14769744Lelio R Paula02/2012
6403(23*2^231686-1)/118369743Lelio R Paula01/2014
64042^231591-47739769716Paul Bourdelais03/2013
640511^66916-42069686Enzo Doria08/2012
64075^99680-1370669674Enzo Doria02/2013
6406(8*10^69674-53)/969674Robert Price11/2014
6408(44*10^69663-413)/969664Robert Price10/2017
6409(77*10^69656-23)/969657Robert Price10/2015
64106^89509+13169652Lelio R Paula09/2013
6411(78557*2^231349+1)/3569647Lelio R Paula06/2014
6412(11*10^69645+19)/369646Robert Price03/2016
641311^66875-2869644Lelio R Paula09/2013
64142^231347+7148369643Enzo Doria04/2016
6415(14^60763+3^60763)/1769641Robert Price04/2013
6416(4*10^69626+173)/369627Robert Price01/2017
64172^231289+25569625Lelio R Paula04/2012
64182^231234-11291369609Enzo Doria06/2014
6419(265*10^69602-7)/369604Robert Price07/2016
64202^231182-11284169593Enzo Doria06/2014
6421(15*2^231129+1)/2369577Lelio R Paula08/2012
64223^145806-2869568Lelio R Paula09/2013
6423(265*10^69554-7)/369556Robert Price07/2016
64242^231052-11315969554Enzo Doria07/2014
642511^66784-869549Lelio R Paula09/2013
6426Phi(104409,10)/229699969546Maksym Voznyy07/2015
64272^231016-11052369543Enzo Doria05/2014
64282^231014+57729457569543Lelio R Paula02/2016
642914^60658+6769522Lelio R Paula09/2013
64305^99418+3669491Lelio R Paula06/2013
64317^82203-3069470Lelio R Paula09/2013
6432(63^38609-1)/6269469Paul Bourdelais08/2017
64335^99359-2^9936069449Mike Oakes12/2010
6434(29*2^230684+1)/139569442Lelio R Paula08/2012
6435(19*10^69424+77)/369425Robert Price08/2016
643619^54287-9669420Lelio R Paula09/2013
64372^230541+5890569400Lelio R Paula04/2012
64382^230506+1270569390Lelio R Paula02/2013
64398*6^89156-569378Lelio R Paula09/2014
64402^230438-11134769369Enzo Doria05/2014
64412^230428-9969366Lelio R Paula02/2012
6442(62^38699+1)/6369362Paul Bourdelais08/2017
64433*10^69354+1769355Robert Price03/2017
6444(493*10^69340-7)/969342Robert Price07/2016
6445(41*10^69321+373)/969322Robert Price04/2017
64466^89072+5369312Lelio R Paula09/2013
6447155^31639+269300Lelio R Paula05/2013
64483*7^81965-469269Lelio R Paula09/2014
6449(16*10^69265+41)/369266Robert Price10/2017
6450(86*10^69260-77)/969261Robert Price05/2016
64519*5^99087+469260Lelio R Paula09/2014
64523^145145+266069252Lelio R Paula09/2013
645411^66492-114069245Enzo Doria11/2012
64535*3^145129-469245Lelio R Paula04/2014
64557*3^145126+869244Lelio R Paula04/2014
645611^66480-237069232Enzo Doria12/2012
64572^229962-6569226Lelio R Paula02/2012
64582^229958-11073369225Enzo Doria05/2014
6459V(332407)69225Serge Batalov03/2015
64606^88959+769224Lelio R Paula09/2013
646115^58855-9469219Lelio R Paula09/2013
6462(2^229838+47)/1208169185Lelio R Paula04/2012
64633^144952+9869160Lelio R Paula09/2013
64645^98941-7269157Lelio R Paula06/2013
6465(17*2^229604-1)/22969117Lelio R Paula01/2014
64662^229585-106369112Yves Minet11/2012
6467(13*2^229567-1)/1969107Lelio R Paula01/2014
6468(13*2^229393-1)/569055Lelio R Paula01/2014
6469(53*10^69050-17)/969051Robert Price09/2015
6470(43*10^69048+47)/969049Robert Price12/2017
64712^229305-186853369028Enzo Doria04/2016
64722^229297+138569026Lelio R Paula04/2012
647318^54986-244169023Enzo Doria03/2013
6474(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
64755^98736-1463669014Enzo Doria02/2013
6476(13^61949-5^61949)/869007Robert Price03/2013
6477(2^229227+5)/61169002Lelio R Paula04/2012
64782^229216-11327969001Enzo Doria07/2014
647910^68994+5191368995Patrick De Geest03/2016
648110^68994-10^5814-168994Serge Batalov01/2011
648010^68994-8294768994Patrick De Geest03/2016
6482(17*2^229136-1)/238168975Lelio R Paula01/2014
64832^229113+10768970Lelio R Paula02/2012
648411^66202-441068943Enzo Doria01/2013
648512^63883+568942Lelio R Paula07/2013
6486(9913*2^229002-1)/39990368935Lelio R Paula04/2015
64872^228962-11158168925Enzo Doria05/2014
64882^228944+8168920Henri Lifchitz01/2007
648911^66174-5468914Lelio R Paula09/2013
64902^228913-11126568910Enzo Doria05/2014
64912^228902+7351968907Enzo Doria04/2016
6492(47*2^228884+1)/6368901Lelio R Paula04/2015
64932^228821+7642768882Enzo Doria05/2016
64943^144340+5068868Lelio R Paula09/2013
64952^228758-11296768864Enzo Doria06/2014
64962^228743-11137968859Enzo Doria05/2014
64972^228741-11091168858Enzo Doria05/2014
6499lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
64983*5^98511-868857Lelio R Paula09/2014
65002^228717+46768851Lelio R Paula02/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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