PRP Records

Probable Primes Top 10000

(177649 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 ?
525118^60979-536376546Enzo Doria03/2013
5252(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5254(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5253(7*10^76536-313)/976536Robert Price11/2016
52562^254239-2776534Lelio R Paula03/2012
52552^254238-184176534Yves Minet03/2013
5257(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
52582^254189-11222576519Enzo Doria06/2014
525918^60938-139776494Enzo Doria03/2013
52602^254075-278841776485Enzo Doria03/2016
52617*10^76483-2376484Robert Price04/2016
52622^254042-11291376475Enzo Doria06/2014
526314^66723-3776474Lelio R Paula02/2015
52642^254037-11030576473Enzo Doria05/2014
52652^253931-11110976441Enzo Doria05/2014
52662^253926-116776440Lelio R Paula05/2013
5267(49*10^76438-13)/976439Robert Price07/2015
5268(21*2^253845-1)/14376415Lelio R Paula02/2014
526910^76374+3176375Robert Price03/2011
527010^76374-22215976374Patrick De Geest05/2013
52712^253561-11053376330Enzo Doria05/2014
5272gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
52739*5^109182+276316Lelio R Paula10/2014
527411^73279-369076313Enzo Doria12/2012
5275(598*10^76309-31)/976311Robert Price02/2017
527611^73274-2400076308Enzo Doria12/2012
52777^90291-676305Theodore Burton11/2005
5278(21181*2^253432+1)/2143776291Lelio R Paula06/2014
52796^98025+14576279Lelio R Paula01/2015
52802^253355+115576268Lelio R Paula05/2013
52812^253292-7121976249Enzo Doria04/2016
52827^90221-3676246Lelio R Paula02/2015
528318^60727-347376229Enzo Doria03/2013
5284(78557*2^253184+1)/376221Lelio R Paula06/2014
5285(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
528611^73163-201076192Enzo Doria12/2012
52872^253060+5461576179Lelio R Paula05/2013
52882^253029+186976176170Enzo Doria05/2016
52892^252955-11100776148Enzo Doria05/2014
52902*5^108931+776140Lelio R Paula10/2014
5291(86*10^76128+121)/976129Robert Price03/2017
529222154*29^52050+976123Curtis Bright05/2015
52933^159530-11235876116Enzo Doria06/2014
529411^73089-4876115Lelio R Paula02/2015
529586^39337-8576098Norbert Schneider10/2015
5296(3^159505-7)/31329731676095Lelio R Paula06/2012
52976^97783+7776090Lelio R Paula01/2015
52982^252712-10576074Lelio R Paula03/2012
5299131^35927+276068Lelio R Paula05/2013
5300(41*10^76067+373)/976068Robert Price04/2017
53012^252683-13976066Lelio R Paula03/2012
5302137^35597-13676061Norbert Schneider05/2015
53033^159413+10676060Lelio R Paula01/2015
53049^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5305(2^252557-9)/7176026Lelio R Paula07/2012
530611^72989+8076011Lelio R Paula02/2015
53072^252449-45952375995Enzo Doria05/2015
530820^58408+7375991Lelio R Paula01/2015
53092^252418-142175986Yves Minet01/2013
5310(11*2^252396-1)/575980Lelio R Paula02/2014
53112^252365-11068975970Enzo Doria05/2014
531211^72949-102075969Enzo Doria11/2012
5313(2^252294+47)/654975945Lelio R Paula07/2012
53142^252261-11059575939Enzo Doria05/2014
53157^89853+7675935Lelio R Paula01/2015
53163^159132+5675926Lelio R Paula01/2015
5317730^26513+26513^73075916Norbert Schneider11/2016
5318(27*2^252163-1)/194575907Lelio R Paula01/2014
53195^108596-1484675906Enzo Doria02/2013
53205^108560-1484675881Enzo Doria02/2013
53212^252051-11035975875Enzo Doria05/2014
53222^251971-11050975851Enzo Doria05/2014
5323(42457^16384+1)/32768275819Lelio R Paula11/2011
532499655!6-275811Robert Price07/2017
532514*10^75798+108975800Jens K. Andersen11/2007
53262^251784-45575795Yves Minet03/2012
53272^251780-128975794Yves Minet01/2013
53282^251760-21560975788Paul Bourdelais03/2013
532999^37973+275781Lelio R Paula05/2013
5330(185*10^75777+7)/375779Robert Price02/2017
53315*2^251690+375767Lelio R Paula06/2014
53326^97366+9575766Lelio R Paula01/2015
53338*6^97337-775744Lelio R Paula10/2014
53342^251588-11167775736Enzo Doria05/2014
53355^108346-1325675731Enzo Doria02/2013
5336(31^50777+1)/3275726Robert Price07/2013
5337(10^75707+77)/375707Robert Price01/2017
53382^251466+19375699Lelio R Paula03/2012
5339(5*2^251464+1)/942375695Lelio R Paula07/2012
53402^251422-10999175686Enzo Doria04/2014
53414*5^108245-375661Lelio R Paula10/2014
534212^70067-11^7006775615Jean-Louis Charton11/2006
534312^70066+9575614Lelio R Paula02/2015
5344-E20534/206375607Thomas Ritschel02/2017
534519^59120-5075600Lelio R Paula01/2015
534618^60222-469775596Enzo Doria03/2013
534718^60211-435575582Enzo Doria03/2013
53487*2^251014-975564Lelio R Paula06/2014
53496^97101-2575560Lelio R Paula01/2015
53508^83663-7^8366375556Jean-Louis Charton01/2004
53513^158331-14075544Lelio R Paula01/2015
5352(37^48157-1)/3675519Robert Price03/2012
535310^75516+3146775517Patrick De Geest03/2016
535510^75516-10^2256-175516Serge Batalov01/2011
535410^75516-6659175516Patrick De Geest03/2016
53562^250851-18775514Lelio R Paula03/2012
5357(43*10^75498-7)/975499Robert Price12/2014
5358(3^158244-5)/24791675497Lelio R Paula06/2012
53594*5^107971-375470Lelio R Paula10/2014
5360(25*10^75465+71)/375466Robert Price01/2017
5361(5*2^250681-1)/99975461Lelio R Paula01/2014
5362(182*10^75456+1)/375458Robert Price02/2017
5363(2^250669-9)/9889772975451Lelio R Paula07/2012
536410^75441+1375442Robert Price01/2011
536510^75441-992375441Patrick De Geest05/2013
5366(27*2^250546-1)/645775420Lelio R Paula01/2014
53675*7^89231-675410Lelio R Paula10/2014
53692^250503-1699575409Lelio R Paula05/2013
536811^72411-2875409Lelio R Paula02/2015
53703*5^107860-875392Lelio R Paula10/2014
53722^250426+2983575386Lelio R Paula05/2013
53718*3^157999-775386Lelio R Paula05/2014
5373(88*10^75381-43)/975382Robert Price11/2015
53742^250382-11175575373Enzo Doria05/2014
53752^250374-279805175371Eric Chen03/2016
5376(22*10^75368-1)/375369Robert Price12/2014
5377(19*10^75338+119)/375339Robert Price02/2017
53782^250223-185916775325Enzo Doria03/2016
5379(3^157854-7)/6602528275308Lelio R Paula06/2012
53803^157831-9875305Lelio R Paula01/2015
5381(46^45281+11^45281)/5775290Serge Batalov12/2016
538292^38335-9175282Norbert Schneider01/2016
53832^250020+1891575264Lelio R Paula05/2013
53842^250002+819375259Lelio R Paula05/2013
5385(11*2^249977-7)/1575251Renaud Lifchitz02/2011
5386(2^249968+78557)/6375247Lelio R Paula07/2012
5387(5*10^75244+91)/375245Robert Price11/2016
5388(10489!)^2+Prime(10489)75242Robert Price08/2014
538914^65644+6775237Lelio R Paula01/2015
5390(2^249928-5)/1185905975229Lelio R Paula06/2012
5391129^35638+275218Lelio R Paula05/2013
53922^249853-11047575214Enzo Doria05/2014
53932^249762+7540975186Enzo Doria04/2016
5394565^27318+27318^56575181Norbert Schneider12/2016
5395(2^249741-7)/68575177Lelio R Paula06/2012
53962^249726-11218175176Enzo Doria06/2014
53972^249721+1171575174Lelio R Paula05/2013
5398(38661^16384+1)/275158Lelio R Paula11/2011
53992^249658-4735575155Lelio R Paula05/2013
5400155^34311+275153Lelio R Paula05/2013
5401(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
5402(23*2^249602+1)/9375138Lelio R Paula08/2012
54032^249522+841575114Lelio R Paula05/2013
54042^249489-11091175104Enzo Doria05/2014
5405(28*10^75078+131)/375079Robert Price02/2017
5406(206*10^75073-17)/975075Robert Price03/2017
54072^249368-11057375068Enzo Doria05/2014
5408NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
5409(2^249375+78557)/4505612575062Lelio R Paula07/2012
54102^249272+19375039Lelio R Paula03/2012
541114^65468+4375035Lelio R Paula01/2015
541237^47844+3675030Norbert Schneider05/2014
5413(52*10^75027-7)/975028Robert Price12/2014
541420^57653+8975009Lelio R Paula01/2015
54152^249061-186835374975Enzo Doria04/2016
54167^88713+2*3^8871374972Mike Oakes07/2010
54172*6^96313+574947Lelio R Paula10/2014
5418(8*10^74944+49)/374945Robert Price03/2016
5419300^30247+30247^30074926Norbert Schneider11/2014
54202^248866-17174917Lelio R Paula03/2012
54216*5^107168-774908Lelio R Paula10/2014
542211^71926+7874904Lelio R Paula02/2015
54232^248824+186939174904Enzo Doria05/2016
54242^248816+111174902Lelio R Paula01/2011
5425V(388219)74890Serge Batalov03/2015
54262*F(358297)-174880Henri Lifchitz12/2009
5427(22*10^74874-31)/974875Robert Price04/2015
542811^71892-7680000074868Enzo Doria01/2013
54299*5^107107-474866Lelio R Paula10/2014
54302^248678-71011174860Paul Bourdelais03/2013
543113^67194+1274851Lelio R Paula01/2015
5432(7*2^248634+1)/7174846Lelio R Paula08/2012
543311^71867-309074842Enzo Doria12/2012
54342^248609+26214574839Lelio R Paula05/2013
54353^156852+5074838Lelio R Paula01/2015
543618^59607-1174824Lelio R Paula01/2015
54372^248556-11050774823Enzo Doria05/2014
54387^88531-3674818Lelio R Paula01/2015
5439p(15738)#/2+102474814Robert Price07/2017
54404*3^156740-574785Lelio R Paula05/2014
5441(32*10^74773-41)/974774Robert Price05/2015
5442(29*2^248384-1)/1374772Lelio R Paula01/2014
544319401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
54442^248357-1279741374763Enzo Doria03/2016
544542^46057+4174762Lelio R Paula07/2012
544611^71784-300074756Enzo Doria12/2012
544719^58458+1874754Lelio R Paula01/2015
544812^69265-3574750Lelio R Paula02/2015
544911^71771-4800074742Enzo Doria12/2012
5450(7*10^74741+197)/374742Robert Price07/2017
5451(2^248282-5)/5012974736Lelio R Paula06/2012
54522^248252-11010574732Enzo Doria04/2014
5453(7*10^74729+71)/374730Robert Price03/2016
54543^156614-5074724Lelio R Paula01/2015
5455(7*2^248213+1)/13574719Lelio R Paula07/2012
5456(2^248173+78557)/76774705Lelio R Paula07/2012
5457125^35622+12474697Norbert Schneider02/2015
5458(19*2^248099-1)/2974686Lelio R Paula01/2014
5459(86*10^74676-41)/974677Robert Price11/2015
546010^74670+3174671Robert Price01/2011
546110^74670-12246374670Patrick De Geest05/2013
54622^248036-6974667Lelio R Paula03/2012
546311^71698-600074666Enzo Doria12/2012
546458*(10^(3*24887)-1)/111-174661Robert Price10/2014
546514^65139-4574658Lelio R Paula01/2015
54666^95921-13374642Lelio R Paula01/2015
546711^71675+7874642Lelio R Paula02/2015
546818^59449-9174625Lelio R Paula01/2015
54696^95864-1604374597Enzo Doria02/2013
54705*7^88261+674590Lelio R Paula10/2014
54719*5^106710+474589Lelio R Paula10/2014
5472(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
5473(265*10^74579+17)/374581Robert Price05/2016
5474(2^247759-1017)/331831171774574Lelio R Paula07/2012
54755^106682-2474568Lelio R Paula08/2014
5476474^27863+27863^47474556Norbert Schneider01/2017
5477(35365^16384+1)/274524Lelio R Paula11/2011
54783^156161+266074508Lelio R Paula01/2015
54792^247474-5869574498Lelio R Paula05/2013
548011^71519-9074480Enzo Doria07/2012
5481(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5483(2^247394-7)/374473Lelio R Paula06/2012
548218^59328+1774473Lelio R Paula01/2015
54842^247379-18174469Lelio R Paula03/2012
5485(15*2^247370-1)/47974465Lelio R Paula01/2014
54862^247344+204774458Lelio R Paula05/2013
54872^247311-101774449Lelio R Paula05/2013
54882^247280+774439Lelio R Paula03/2012
5489(68*10^74434+13)/974435Ray Chandler11/2010
54903^156004-6274433Lelio R Paula01/2015
549136095!2-6474416Robert Price06/2015
54922^247165-374405M. Frind & P. Underwood07/2002
54932^247150+3276974400Lelio R Paula05/2013
549412^68911+7374368Lelio R Paula01/2015
54952^246999+7490374355Enzo Doria04/2016
54962^246989-11064374352Enzo Doria05/2014
5497(10^74350+11)/374350Robert Price11/2014
549810^74350-40000000174350Robert Price07/2017
549910^74335+1365974336Patrick De Geest05/2013
550010^74335-5374335Robert Price05/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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