PRP Records

Probable Primes Top 10000

(271019 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 ?
55012^308650+51392913Lelio R Paula02/2016
55025*7^109936+692908Lelio R Paula10/2014
55032*10^92897+8992898Robert Price07/2016
5504(2^308585+3182)/292894Stefano Morozzi09/2020
550512^86073-2992889Lelio R Paula06/2016
55062^308566-11792888Lelio R Paula11/2012
5507(17*10^92869-11)/392870Robert Price07/2015
55082^308459+7543192856Enzo Doria04/2016
55092^308426-186637792846Enzo Doria03/2016
551024810^5521+5521^2481092840Hans Havermann09/2020
5511(96^46831-1)/9592830Paul Bourdelais09/2017
55122^308349-11211192823Enzo Doria06/2014
55139*10^92821+1992822Robert Price05/2016
55142^308337-7592819Lelio R Paula11/2012
55154*3^194508+792805Lelio R Paula08/2014
551622*25^66379-11392796Curtis Bright05/2015
551724538^6047+6047^2453892792Hans Havermann09/2020
551811^89101-108092790Enzo Doria12/2012
55192^308236-186785992789Enzo Doria04/2016
552012^85963+2592770Lelio R Paula06/2016
552123692^8221+8221^2369292753Hans Havermann08/2020
55227^109750-6692750Lelio R Paula04/2016
55239*10^92742+1192743Robert Kinser01/2017
5524(2^308054+778)/292734Stefano Morozzi09/2020
5525(21*2^308046-1)/885792729Lelio R Paula02/2014
55262^307997-11065592717Enzo Doria05/2014
5527L(443609)92709Renaud Lifchitz11/2003
552810^92691+992692Robert Price03/2011
552910^92691-25229192691Patrick De Geest08/2013
5530(2^307883+3506)/292682Stefano Morozzi09/2020
55312^307879-252192681Yves Minet07/2014
553221269^21412+21412^2126992666Norbert Schneider04/2020
5533(2^307780-7)/1995966992644Lelio R Paula06/2013
553414^80831+4792643Lelio R Paula06/2016
553515^78744+9292611Lelio R Paula07/2016
553665^51083-6492610Norbert Schneider11/2014
5537(2^307639+506)/292609Stefano Morozzi09/2020
5538131^43737-13092604Norbert Schneider02/2019
55396^118996-1694392597Enzo Doria02/2013
5540(16*10^92591+41)/392592Robert Price10/2017
5541(2^307566+3094)/292587Stefano Morozzi09/2020
5542(2^307528+1578)/292575Stefano Morozzi09/2020
5543(3^194014-7)/292568Lelio R Paula04/2013
5544(2^307498+570)/292566Stefano Morozzi09/2020
5545(63^51439+1)/6492555Paul Bourdelais08/2017
5546(26*10^92546-77)/392547Robert Price02/2017
55473^193954+34092540Lelio R Paula04/2016
55482^307407-307407^292539Henri Lifchitz05/2005
554924299^6430+6430^2429992536Hans Havermann08/2020
5550(17*10^92513-11)/392514Robert Price07/2015
55512^307318-421192512Yves Minet06/2011
55522^307280+19392501Lelio R Paula11/2012
555320^71075-3392471Lelio R Paula05/2016
55542^307126-7879592455Lelio R Paula02/2016
55552^307125-4978992454Henri Lifchitz08/2005
55562^307099+2392447Lelio R Paula11/2012
5557129^43798+12892440Norbert Schneider01/2019
555821826^17181+17181^2182692435Hans Havermann09/2020
5559Phi(277314,10)/332776992430Makoto Kamada05/2019
5560(2^307022+1038)/292423Stefano Morozzi09/2020
55617*10^92414-6992415Robert Price01/2017
5562(9787*2^306975-1)/212915592407Lelio R Paula04/2015
556322280^14037+14037^2228092402Hans Havermann09/2020
55642^306915+187337392391Enzo Doria06/2016
55652^306908+1291592389Lelio R Paula02/2016
556621620^18759+18759^2162092387Hans Havermann09/2020
5567(2^306897+1142)/292385Stefano Morozzi09/2020
556819^72244-8092383Lelio R Paula06/2016
55702^306849+7592371Lelio R Paula11/2012
5569(397*10^92369+53)/992371Robert Price11/2017
55712^306813-86968810592360Lelio R Paula08/2016
5572(2^306797+2694)/292355Stefano Morozzi09/2020
557321713^17914+17914^2171392350Hans Havermann09/2020
55742^306672-10905992318Enzo Doria04/2014
5575(430463^16384+1)/292307Richard Fischer09/2020
55766^118604-1706392292Enzo Doria02/2013
557721969^15878+15878^2196992288Hans Havermann08/2020
557821690^17959+17959^2169092276Hans Havermann08/2020
5579(7613^23773-1)/761292273Serge Batalov08/2020
5580(31*2^306487-1)/229192260Lelio R Paula02/2014
55812^306467-183561192256Enzo Doria04/2015
55822^306433+7642792246Enzo Doria05/2016
55832^306430-11331392245Enzo Doria07/2014
5584(23*10^92244-59)/992245Robert Price03/2017
5585(47*2^306398+1)/138480392231Lelio R Paula04/2015
558621436^20043+20043^2143692217Hans Havermann09/2020
5587(25*10^92186+59)/392187Robert Price05/2016
55882^306213-28618392180Enzo Doria06/2015
558910^92178+6192179Robert Price04/2011
559010^92178-17550992178Patrick De Geest07/2013
55912^306200+118592176Lelio R Paula02/2016
5592(2^306171+1514)/292167Stefano Morozzi09/2020
55932^306153+1192162Lelio R Paula11/2012
5594(2^306141-7)/592157Lelio R Paula06/2013
559521725^17454+17454^2172592156Hans Havermann09/2020
5596(26*10^92152-23)/392153Robert Price08/2016
5597(2*10^92152+67)/392152Robert Price04/2017
559821368^20457+20457^2136892115Hans Havermann08/2020
5599(2^305996+3018)/292114Stefano Morozzi09/2020
56004*10^92099+3*7^9209992100Mike Oakes12/2010
560130504^1045+1045^3050492096Hans Havermann08/2020
560224334^6085+6085^2433492087Hans Havermann08/2020
5603(4591^25147-1)/459092083Serge Batalov08/2020
5604115^44684+11492081Norbert Schneider07/2018
5605(416771^16384+1)/292077Richard Fischer08/2020
5606(2^305867-2^152934+1)/59207511/2006
56072^305851-10949592071Enzo Doria04/2014
5608(416213^16384+1)/292067Richard Fischer08/2020
560912^85300+3592055Lelio R Paula06/2016
5610((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
561121732^17201+17201^2173292048Hans Havermann08/2020
56127*10^92043-3992044Robert Price07/2020
56133^192911+9292042Lelio R Paula04/2016
56142^305723-27627192032Enzo Doria07/2015
5615(2^305714+3738)/292029Stefano Morozzi09/2020
5616(2^305682+3202)/292020Stefano Morozzi09/2020
56172^305676+9392018Donovan Johnson06/2008
56183^192819+491999Lelio R Paula04/2013
5619(38*10^91997-83)/9991997Ray Chandler07/2011
56202^305539+7291191977Enzo Doria04/2016
5621Phi(212014,10)91960Makoto Kamada04/2019
5622(2^305423+2666)/291942Stefano Morozzi09/2020
5623(2^305427-5)/129799821391934Lelio R Paula06/2013
562482077!4-12891928Robert Price11/2019
562585^47642+8491922Norbert Schneider10/2015
562610^91920+18765191921Patrick De Geest07/2013
562710^91920-3991920Robert Price05/2011
5628(3975^25537-1)/397491913Serge Batalov08/2020
5629(22*10^91903+41)/991904Robert Price02/2015
56312^305275-2791897Lelio R Paula11/2012
56303^192607-772691897Enzo Doria05/2014
5632(6958^23911-1)/695791874Serge Batalov08/2020
5633(7*10^91856-61)/991856Erik Branger12/2009
5634(89*10^91839-53)/991840Robert Price11/2015
56351678^28479+28479^167891839Norbert Schneider08/2020
56368*5^131351+791812Lelio R Paula10/2014
56373^192426-6891811Lelio R Paula04/2016
56392^304973+11791807Lelio R Paula11/2012
5638(2^304974+234)/291807Stefano Morozzi09/2020
56402^304939-186372791796Enzo Doria03/2016
56412^304902+841591785Lelio R Paula02/2016
564218^73119+6191785Lelio R Paula06/2016
5643(78557*2^304740+1)/15991739Lelio R Paula06/2014
56442^304747+7135591738Lelio R Paula02/2016
56458*3^192251+591728Lelio R Paula08/2014
56462^304674-8791717Lelio R Paula11/2012
5647(28*10^91715+701)/991716Robert Price11/2017
5649(2^304698+9)/136280995391715Lelio R Paula06/2013
5648(2^304671+1046)/291715Stefano Morozzi09/2020
5650(2^304667+3614)/291714Stefano Morozzi09/2020
5651(5*10^91707-119)/391708Robert Price04/2016
56522^304633-11277191704Enzo Doria06/2014
5653(395347^16384+1)/291701Richard Fischer06/2020
56549*10^91693+2391694Robert Price11/2017
56552^304578-1671391688Enzo Doria05/2013
56566^117824-1871391685Enzo Doria03/2013
5657(17^74509-1)/1691679Paul Bourdelais03/2010
5658(2^304551-7)/891223191673Lelio R Paula06/2013
5659(2^304532-3)/301391670Lelio R Paula06/2013
56602^304507-1664591666Enzo Doria04/2013
5661(29*2^304489+1)/3191661Lelio R Paula09/2013
566221221^20860+20860^2122191661Hans Havermann08/2020
56632^304471-183612791655Enzo Doria04/2015
56642^304433+3276991644Lelio R Paula02/2016
56652^304410-1662591637Enzo Doria04/2013
5666183^40500-291630Lelio R Paula10/2017
5667(203*10^91613+1)/391615Robert Price09/2017
56684*5^131052+791603Lelio R Paula10/2014
566921725^16458+16458^2172591601Hans Havermann08/2020
56702^304278-400191597Yves Minet04/2017
56712^304272-186637791595Enzo Doria03/2016
56722^304268+1968391594Lelio R Paula02/2016
567321718^16497+16497^2171891594Hans Havermann08/2020
567422759^10576+10576^2275991590Hans Havermann08/2020
56752^304162-16191562Lelio R Paula11/2012
56765*7^108331+691552Lelio R Paula10/2014
56772^304082-278782191538Enzo Doria03/2016
56782^304015+6413391518David Broadhurst06/2002
5679(7*2^303963+1)/391503Lelio R Paula09/2013
5680(2^303945-9)/361791494Lelio R Paula06/2013
5681(384007^16384+1)/291494Richard Fischer05/2020
56822^303930+188052791493Enzo Doria10/2016
568324810^4859+4859^2481091464Hans Havermann08/2020
56843^191684-6891457Lelio R Paula04/2016
5685(21*2^303813-1)/16991456Lelio R Paula02/2014
568611^87797-12091432Enzo Doria07/2012
56872^303698-184723191423Enzo Doria07/2015
5688(38^28933-1)^2-291416Norbert Schneider06/2016
568925660^3643+3643^2566091388Hans Havermann08/2020
56902^303554+7729991379Enzo Doria05/2016
56912^303542+1270591376Lelio R Paula02/2016
569231^61269-291375Lelio R Paula09/2013
56932^303516-6487591368Lelio R Paula02/2016
5694(2^303497+1266)/291362Stefano Morozzi09/2020
5695(2^303497+3710)/291362Stefano Morozzi09/2020
569621856^15121+15121^2185691349Hans Havermann09/2020
5697(24737*2^303428+1)/391345Lelio R Paula06/2014
5698(21181*2^303357+1)/3236191320Lelio R Paula06/2014
569923081^9046+9046^2308191319Hans Havermann09/2020
57002^303344-278696991316Enzo Doria03/2016
57016^117346+6591313Lelio R Paula05/2016
57022^303321+85591309Lelio R Paula02/2016
570312^84606+4791306Lelio R Paula06/2016
57042^303288+187431191299Enzo Doria06/2016
5705197^39788-291293Lelio R Paula10/2017
570611^87663-171091292Enzo Doria12/2012
57072^303224+253391280Henri Lifchitz05/2005
57086^117302+14391279Lelio R Paula05/2016
57093^191306-11288091277Enzo Doria07/2014
5710(10052^22807-1)/1005191276Serge Batalov08/2020
57112^303207+1291591275Lelio R Paula02/2016
57122^303191-11125991270Enzo Doria05/2014
571381539!4+3291267Robert Price09/2019
5714(2^303116+3570)/291247Stefano Morozzi09/2020
571510^91230+9^(91230+1)91231Robert Price08/2016
571610^91230+792191231Patrick De Geest11/2016
571710^91230-91114191230Patrick De Geest11/2016
571810^91229+34879391230Patrick De Geest07/2019
571910^91229-247191229Patrick De Geest01/2019
57202996^26241+26241^299691228Norbert Schneider01/2020
572210^91225+527191226Patrick De Geest01/2019
57212816^26445+26445^281691226Norbert Schneider02/2020
57246^117232-1742391225Enzo Doria02/2013
572310^91225-14721991225Patrick De Geest07/2019
57257*10^91215+391216Erik Branger11/2009
572610^91215+23061191216Patrick De Geest07/2019
572710^91215-453991215Patrick De Geest01/2019
5728(2^303007+606)/291214Stefano Morozzi09/2020
5729(2^302998+3102)/291212Stefano Morozzi09/2020
573010^91210+242191211Patrick De Geest01/2019
573110^91210-173791210Patrick De Geest01/2019
573297*10^91205-391207Robert Price01/2017
57332^302979-16118191206Enzo Doria04/2013
57342^302949+8191197Henri Lifchitz02/2007
573510^91194+20036191195Patrick De Geest07/2019
57374*6^117192-591194Lelio R Paula10/2014
573610^91194-866391194Patrick De Geest01/2019
57382^302918+9991188Lelio R Paula11/2012
573910^91186+26811191187Patrick De Geest07/2019
574010^91186-776391186Patrick De Geest01/2019
574110^91181+55047191182Patrick De Geest07/2019
574210^91181-136791181Patrick De Geest01/2019
574310^91178+7188391179Patrick De Geest07/2019
574410^91178-471991178Patrick De Geest01/2019
574524686^4935+4935^2468691173Hans Havermann08/2020
574610^91165+304391166Patrick De Geest01/2019
574710^91165-39941391165Patrick De Geest07/2019
574810^91156+386191157Patrick De Geest01/2019
574910^91156-23149791156Patrick De Geest07/2019
57502^302797+186958791151Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

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