PRP Records

Probable Primes Top 10000

(252932 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 ?
62517^91966-3277721Lelio R Paula02/2015
625235^50327+277709Lelio R Paula05/2013
625324^56298+2377704Norbert Schneider12/2016
6254(2^258105+78557)/1977697Lelio R Paula10/2012
62552^258079+17977690Lelio R Paula03/2012
62562^258062-11311177685Enzo Doria07/2014
625780^40807-7977660Norbert Schneider03/2015
6258(10^77637+359)/977637Serge Batalov12/2014
62592^257862-16577625Lelio R Paula03/2012
6260(25*2^257853+1)/377623Lelio R Paula07/2012
6261(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
62626^99728+7177604Lelio R Paula01/2015
62632^257778-11276777599Enzo Doria06/2014
6264(31*2^257771+1)/53777596Lelio R Paula07/2012
62652^257729-7377585Lelio R Paula03/2012
62662^257689-6377573Lelio R Paula03/2012
6267(47*10^77572+493)/977573Robert Price11/2017
6268(78557*2^257665+1)/610872577564Lelio R Paula06/2014
6269(3^162563+8)/288577559Lelio R Paula10/2012
62702^257636-11023577557Enzo Doria05/2014
6271(23*10^77556+97)/377557Robert Price02/2017
62722^257621-11007177552Enzo Doria04/2014
62732^257567-6487577536Lelio R Paula06/2013
62742*7^91674+977474Lelio R Paula10/2014
6275(17*10^77427-47)/377428Robert Price05/2017
627610^77418+84168377419Patrick De Geest06/2013
627710^77418-3377418Robert Price05/2011
627819^60539-3677415Lelio R Paula03/2015
627937401!!-102477397Robert Price11/2015
628011^74313-1875077390Enzo Doria12/2012
62822^257044-11288377378Enzo Doria06/2014
62818*10^77377+5177378Robert Price05/2017
62832*7^91553+977372Lelio R Paula10/2014
6284713^27118+27118^71377371Norbert Schneider12/2016
62852^256920-11115577341Enzo Doria05/2014
62862^256896-655577334Lelio R Paula06/2013
6287(52*10^77322-7)/977323Robert Price12/2014
62882^256849-11293977320Enzo Doria06/2014
6289(4*10^77309-31)/977309Erik Branger05/2011
6290(3^161988+7)/4186477284Lelio R Paula10/2012
6291(14^67421-1)/1377272Paul Bourdelais09/2008
62925*3^161923-477258Lelio R Paula06/2014
62932^256552-149977230Yves Minet05/2013
62942^256460-11275777203Enzo Doria06/2014
62952^256398+2329977184Yves Minet02/2011
62962^256391-1155*25639177182Henri Lifchitz03/2005
6297(2^256391-9)/5659377177Lelio R Paula10/2012
6298(2^256308+9)/1058577153Lelio R Paula10/2012
630021^58348-277149Lelio R Paula08/2013
6299(17*2^256291-1)/478577149Lelio R Paula02/2014
6301(5*2^256274-1)/214177144Lelio R Paula02/2014
630219^60321+8277136Lelio R Paula03/2015
63035*2^256233-377135Lelio R Paula06/2014
63043*2^256149+777110Lelio R Paula06/2014
63053^161594-10677100Lelio R Paula02/2015
63062^256114-18577098Lelio R Paula03/2012
63078^85349-85349^877078Norbert Schneider05/2017
63082^256043-278637777077Enzo Doria03/2016
63092^255973+186994777056Enzo Doria05/2016
631012^71393-4377046Lelio R Paula02/2015
631115^65490+4477023Lelio R Paula02/2015
6312(3^161411-7)/94077010Lelio R Paula10/2012
6313lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
6314(570^27943-1)/56977005Serge Batalov12/2016
63152^255750-7576989Lelio R Paula03/2012
63163*6^98926-576980Lelio R Paula10/2014
631718^61320-143376974Enzo Doria03/2013
63186^98916-1709376972Enzo Doria02/2013
63192^255659-11013176962Enzo Doria04/2014
632012^71303+9176949Lelio R Paula02/2015
632118^61298+5976946Lelio R Paula02/2015
6322(223^32768+1)/13107476945Lelio R Paula02/2009
6323(2^255613-5)/28151776942Lelio R Paula10/2012
632418^61290-1176936Lelio R Paula02/2015
632663^42752-276926Lelio R Paula08/2013
6325(11*2^255545-1)/11776926Lelio R Paula02/2014
63272^255517+5638776919Yves Minet02/2011
63282^255499-11256776913Enzo Doria06/2014
63292^255492+34576911Lelio R Paula06/2013
633010^76875+21759176876Patrick De Geest05/2013
633210^76875-5376875Robert Price05/2011
633111^73819-588076875Enzo Doria01/2013
63332^255313+1891576857Lelio R Paula06/2013
6334(2^255320-1017)/144666776853Lelio R Paula10/2012
63352^255296+577576852Lelio R Paula06/2013
633614^67052-2976851Lelio R Paula02/2015
6337(8*10^76840+43)/376841Robert Price10/2017
6338(7*10^76818-313)/976818Robert Price11/2016
633910^76801+6976802Robert Price03/2011
634010^76801-8094376801Patrick De Geest06/2013
63412^255105+5776795Lelio R Paula03/2012
6342(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
6343(2^255097-7)/2002005576785Lelio R Paula10/2012
63442^255055+186935376780Enzo Doria05/2016
634517^62396-9076776Lelio R Paula03/2015
63467^90833-6076763Lelio R Paula02/2015
634713^68901-5676752Lelio R Paula03/2015
63482^254961+186991776751Enzo Doria05/2016
63499*5^109791-876742Lelio R Paula10/2014
635082^40089+40089^8276723Serge Batalov02/2012
63512^254861-279001376721Enzo Doria03/2016
6352(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
635310^76705+1376706Robert Price01/2011
635410^76705-9407776705Patrick De Geest06/2013
6355(5*2^254785-1)/99976696Lelio R Paula02/2014
63562^254758-11040576690Enzo Doria05/2014
63572^254716-377976678Yves Minet04/2017
63582^254708-11050776675Enzo Doria05/2014
6359(47*10^76672+133)/976673Robert Price04/2017
63602^254670-11290176664Enzo Doria06/2014
6361(3^160665+7)/98135076651Lelio R Paula10/2012
63622^254598-11318376642Enzo Doria07/2014
636319^59932+2276639Lelio R Paula01/2015
63642^254569-11221376633Enzo Doria06/2014
63652*5^109626+976626Lelio R Paula10/2014
63662^254521+187252776619Enzo Doria05/2016
6367(76*10^76615+167)/976616Robert Price08/2016
636825^54799-24^5479976606Robert Price07/2012
6369(24737*2^254464+1)/976605Lelio R Paula06/2014
637012^70961-8576580Lelio R Paula02/2015
63717^90590-3876558Lelio R Paula02/2015
63722^254304+522776554Lelio R Paula06/2013
6373(76*10^76547-211)/976548Robert Price10/2017
637418^60979-536376546Enzo Doria03/2013
6375(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
6377(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
6376(7*10^76536-313)/976536Robert Price11/2016
63792^254239-2776534Lelio R Paula03/2012
63782^254238-184176534Yves Minet03/2013
6380(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
63812^254189-11222576519Enzo Doria06/2014
638218^60938-139776494Enzo Doria03/2013
63832^254075-278841776485Enzo Doria03/2016
63847*10^76483-2376484Robert Price04/2016
63852^254042-11291376475Enzo Doria06/2014
638614^66723-3776474Lelio R Paula02/2015
63872^254037-11030576473Enzo Doria05/2014
63882^253931-11110976441Enzo Doria05/2014
63892^253926-116776440Lelio R Paula05/2013
6390(49*10^76438-13)/976439Robert Price07/2015
6391(21*2^253845-1)/14376415Lelio R Paula02/2014
639210^76374+3176375Robert Price03/2011
639310^76374-22215976374Patrick De Geest05/2013
63942^253561-11053376330Enzo Doria05/2014
6395gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
63969*5^109182+276316Lelio R Paula10/2014
639711^73279-369076313Enzo Doria12/2012
6398(598*10^76309-31)/976311Robert Price02/2017
639911^73274-2400076308Enzo Doria12/2012
64007^90291-676305Theodore Burton11/2005
6401(21181*2^253432+1)/2143776291Lelio R Paula06/2014
64026^98025+14576279Lelio R Paula01/2015
64032^253355+115576268Lelio R Paula05/2013
6404(73*10^76262+413)/976263Robert Price10/2017
64052^253292-7121976249Enzo Doria04/2016
64067^90221-3676246Lelio R Paula02/2015
640718^60727-347376229Enzo Doria03/2013
6408(78557*2^253184+1)/376221Lelio R Paula06/2014
6409(8*10^76220-83)/376221Robert Price10/2017
6410(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
641111^73163-201076192Enzo Doria12/2012
64122^253060+5461576179Lelio R Paula05/2013
64132^253029+186976176170Enzo Doria05/2016
64142^252955-11100776148Enzo Doria05/2014
64152*5^108931+776140Lelio R Paula10/2014
6416(86*10^76128+121)/976129Robert Price03/2017
641722154*29^52050+976123Curtis Bright05/2015
64183^159530-11235876116Enzo Doria06/2014
641911^73089-4876115Lelio R Paula02/2015
642086^39337-8576098Norbert Schneider10/2015
6421(3^159505-7)/31329731676095Lelio R Paula06/2012
64226^97783+7776090Lelio R Paula01/2015
64232^252712-10576074Lelio R Paula03/2012
6424(10^76069-19)/976069Robert Price10/2017
6426131^35927+276068Lelio R Paula05/2013
6425(41*10^76067+373)/976068Robert Price04/2017
64272^252683-13976066Lelio R Paula03/2012
6428137^35597-13676061Norbert Schneider05/2015
64293^159413+10676060Lelio R Paula01/2015
64309^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
6431(2^252557-9)/7176026Lelio R Paula07/2012
6432(85*10^76021-103)/976022Robert Price10/2017
643311^72989+8076011Lelio R Paula02/2015
643499877!6-3675996Robert Price11/2018
64352^252449-45952375995Enzo Doria05/2015
643620^58408+7375991Lelio R Paula01/2015
64372^252418-142175986Yves Minet01/2013
6438(11*2^252396-1)/575980Lelio R Paula02/2014
64392^252365-11068975970Enzo Doria05/2014
644011^72949-102075969Enzo Doria11/2012
6441(2^252294+47)/654975945Lelio R Paula07/2012
64422^252261-11059575939Enzo Doria05/2014
64437^89853+7675935Lelio R Paula01/2015
64443^159132+5675926Lelio R Paula01/2015
6445730^26513+26513^73075916Norbert Schneider11/2016
6446(27*2^252163-1)/194575907Lelio R Paula01/2014
64475^108596-1484675906Enzo Doria02/2013
64485^108560-1484675881Enzo Doria02/2013
64492^252051-11035975875Enzo Doria05/2014
64502^251971-11050975851Enzo Doria05/2014
6451(42457^16384+1)/32768275819Lelio R Paula11/2011
64522^251842-471575812Yves Minet05/2019
645399655!6-275811Robert Price07/2017
645414*10^75798+108975800Jens K. Andersen11/2007
64552^251784-45575795Yves Minet03/2012
64562^251780-128975794Yves Minet01/2013
64572^251760-21560975788Paul Bourdelais03/2013
645899^37973+275781Lelio R Paula05/2013
6459(185*10^75777+7)/375779Robert Price02/2017
64605*2^251690+375767Lelio R Paula06/2014
64616^97366+9575766Lelio R Paula01/2015
6462s(23010)75760Hans Havermann11/2017
64638*6^97337-775744Lelio R Paula10/2014
64642^251588-11167775736Enzo Doria05/2014
64655^108346-1325675731Enzo Doria02/2013
6466(31^50777+1)/3275726Robert Price07/2013
6467(10^75707+77)/375707Robert Price01/2017
6468(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
64692^251466+19375699Lelio R Paula03/2012
6470(5*2^251464+1)/942375695Lelio R Paula07/2012
64712^251422-10999175686Enzo Doria04/2014
647291*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
64734*5^108245-375661Lelio R Paula10/2014
647412^70067-11^7006775615Jean-Louis Charton11/2006
647512^70066+9575614Lelio R Paula02/2015
6476-E20534/206375607Thomas Ritschel02/2017
647719^59120-5075600Lelio R Paula01/2015
647818^60222-469775596Enzo Doria03/2013
647918^60211-435575582Enzo Doria03/2013
64807*2^251014-975564Lelio R Paula06/2014
64816^97101-2575560Lelio R Paula01/2015
64828^83663-7^8366375556Jean-Louis Charton01/2004
64833^158331-14075544Lelio R Paula01/2015
6485(37^48157-1)/3675519Robert Price03/2012
6484(19*10^75518-43)/375519Robert Price10/2017
64862^250868-422975519Yves Minet08/2018
648710^75516+3146775517Patrick De Geest03/2016
648910^75516-10^2256-175516Serge Batalov01/2011
648810^75516-6659175516Patrick De Geest03/2016
64902^250851-18775514Lelio R Paula03/2012
6491(43*10^75498-7)/975499Robert Price12/2014
6492(3^158244-5)/24791675497Lelio R Paula06/2012
64934*5^107971-375470Lelio R Paula10/2014
6494(25*10^75465+71)/375466Robert Price01/2017
6495(5*2^250681-1)/99975461Lelio R Paula01/2014
6496(182*10^75456+1)/375458Robert Price02/2017
6497(2^250669-9)/9889772975451Lelio R Paula07/2012
649810^75441+1375442Robert Price01/2011
649910^75441-992375441Patrick De Geest05/2013
6500(27*2^250546-1)/645775420Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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