PRP Records

Probable Primes Top 10000

(277054 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 ?
650110^90209-72479790209Patrick De Geest07/2019
650210^90208+18953190209Patrick De Geest07/2019
650310^90208-224790208Patrick De Geest09/2018
6504(629^32233-1)/62890207Michael Stocker05/2020
6505116^43693-11590203Norbert Schneider08/2018
650610^90202+355390203Patrick De Geest09/2018
65083^189053+28090202Lelio R Paula04/2016
650710^90202-6779390202Patrick De Geest07/2019
65092^299639-18790201Lelio R Paula10/2012
651010^90199+25403190200Patrick De Geest07/2019
651110^90199-289190199Patrick De Geest09/2018
65132^299631+18390198Lelio R Paula10/2012
651221567^15212+15212^2156790198Hans Havermann08/2020
651410^90196+18753990197Patrick De Geest07/2019
651610^90196-968390196Patrick De Geest09/2018
651521708^14287+14287^2170890196Hans Havermann08/2020
651710^90193+10497390194Patrick De Geest07/2019
651810^90193-980990193Patrick De Geest09/2018
6519(21*2^299611-1)/2990192Lelio R Paula02/2014
6520(2277^26863-1)/227690186Serge Batalov08/2020
65212^299567+11390179Lelio R Paula10/2012
65222^299550+18990174Lelio R Paula10/2012
652310^90170+37606390171Patrick De Geest07/2019
652410^90170-674990170Patrick De Geest09/2018
6525(2^299535+3)/2990168Lelio R Paula01/2013
6526(2^299521+13)/1590164Stefano Morozzi03/2020
652722316^10971+10971^2231690163Hans Havermann08/2020
652810^90160+27194790161Patrick De Geest07/2019
652910^90160-561390160Patrick De Geest09/2018
6530(97*10^90155-1)/390157Serge Batalov12/2014
65323^188938+868090147Lelio R Paula04/2016
653110^90146+16020990147Patrick De Geest07/2019
653310^90146-202790146Patrick De Geest09/2018
65346^115840-5590142Lelio R Paula05/2016
6535(5*10^90142-473)/990142Robert Price12/2017
65368*7^106659+590139Lelio R Paula10/2014
65392^299406-1665390131Enzo Doria05/2013
6537(317057^16384+1)/290131Richard Fischer10/2019
6538(2^299409+834)/290131Stefano Morozzi01/2020
654010^90128+28867390129Patrick De Geest07/2019
6542208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
654110^90128-838790128Patrick De Geest09/2018
6543(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
65446^115819-5390125Lelio R Paula05/2016
654510^90123+631390124Patrick De Geest09/2018
65476^115816-1685390123Enzo Doria02/2013
654610^90123-2261790123Patrick De Geest07/2019
65486^115813-2390121Lelio R Paula05/2016
6549(22*10^90110+161)/390111Robert Price02/2017
6551(2^299330-509203)/6990106Lelio R Paula01/2013
655010^90105+91575990106Patrick De Geest07/2019
655310^90105-76790105Patrick De Geest09/2018
655210^90104+4818990105Patrick De Geest07/2019
6554(6050^23827-1)/604990105Serge Batalov08/2020
655510^90104-770390104Patrick De Geest09/2018
655610^90103+915990104Patrick De Geest09/2018
655710^90103-20845790103Patrick De Geest07/2019
655810^90102+7301190103Patrick De Geest07/2019
655910^90102-60243390102Patrick De Geest07/2019
656010^90101+122553790102Patrick De Geest07/2019
656110^90101-320790101Patrick De Geest09/2018
656221730^14007+14007^2173090101Hans Havermann08/2020
6563(29*10^90096-17)/390097Erik Branger09/2014
656410^90089+14318190090Patrick De Geest07/2019
656510^90089-357390089Patrick De Geest09/2018
65662^299247+187052990083Enzo Doria05/2016
656710^90079+160990080Patrick De Geest09/2018
656810^90079-23004390079Patrick De Geest07/2019
65692^299229-279778390077Enzo Doria04/2016
65702^299220-1631790075Enzo Doria04/2013
657111^86491-135090072Enzo Doria12/2012
657210^90071+5233390072Patrick De Geest07/2019
657410^90071-123390071Patrick De Geest09/2018
6573(314401^16384+1)/290071Richard Fischer10/2019
657510^90069+15852790070Patrick De Geest07/2019
657610^90069-784190069Patrick De Geest09/2018
6577(31*10^90064-1)/390066Robert Price03/2017
657810^90060+14943190061Patrick De Geest07/2019
657910^90060-83990060Patrick De Geest09/2018
658010^90052+236190053Patrick De Geest09/2018
658110^90052-9092990052Patrick De Geest07/2019
658210^90047+61990048Patrick De Geest09/2018
658310^90047-15107190047Patrick De Geest07/2019
6584L(430949)/861899/144038756153990045Serge Batalov07/2017
658522996^8233+8233^2299690043Hans Havermann08/2020
65862^299112+7395190042Enzo Doria04/2016
65878^99702+7^(99702-1)90040Robert Price02/2016
658810^90038+15780390039Patrick De Geest07/2019
658910^90038-968790038Patrick De Geest09/2018
65915*10^90033+390034Dmitry Domanov11/2010
6590(17574^21211-1)/1757390034Serge Batalov08/2020
659210^90030+22581390031Patrick De Geest07/2019
659310^90030-146190030Patrick De Geest09/2018
6594243^37738+37738^24390029Norbert Schneider01/2015
659510^90025+7056990026Patrick De Geest07/2019
659610^90025-870390025Patrick De Geest09/2018
65972^299048-11329790023Enzo Doria07/2014
659810^90015+84990016Patrick De Geest09/2018
659910^90015-22838790015Patrick De Geest07/2019
660010^90010+681190011Patrick De Geest09/2018
660110^90010-18359790010Patrick De Geest11/2018
660210^90009+5832190010Patrick De Geest11/2018
660310^90008+84790009Patrick De Geest09/2018
660410^90009-35601390009Patrick De Geest11/2018
660525696^3183+3183^2569690009Hans Havermann08/2020
66073^188648+9290008Lelio R Paula12/2015
660610^90008-70604990008Patrick De Geest11/2018
66085*2^298991+790006Lelio R Paula08/2014
6609(25*2^298997+1)/326790005Lelio R Paula01/2013
661010^90000+886990001Patrick De Geest12/2009
661210^89999+8293990000Dirk Augustin04/2007
661110^90000-14034390000Patrick De Geest12/2009
661310^89999-19489189999Patrick De Geest11/2009
6614(2^298918+1798)/289983Stefano Morozzi01/2020
661519^70365-7889980Lelio R Paula12/2015
6616NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
66172^298852-6487589964Lelio R Paula11/2013
6618(2^298825+1010)/289955Stefano Morozzi01/2020
661918^71659+3789952Lelio R Paula12/2015
6620(2908*29^61501-3)/789942Curtis Bright05/2015
6621(2^298769+1202)/289939Stefano Morozzi01/2020
6622(5941^23827-1)/594089916Serge Batalov08/2020
662317^73067+2089906Lelio R Paula11/2015
66242^298637-9989899Lelio R Paula10/2012
662525513^3336+3336^2551389889Hans Havermann08/2020
662629748^1051+1051^2974889887Hans Havermann08/2020
66279^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
6628(2^298558+3654)/289875Stefano Morozzi01/2020
66299*10^89858+1989859Robert Price05/2016
66302^298501+187006789858Enzo Doria05/2016
6631(286*10^89852-1)/389854Robert Price11/2020
663211^86280-9889852Lelio R Paula11/2015
66332^298473-11005989850Enzo Doria04/2014
663419^70263-3289850Lelio R Paula12/2015
663521208^17221+17221^2120889839Hans Havermann08/2020
6636(299*10^89836-17)/389838Robert Price01/2017
66373^188286+1489836Robert Price09/2013
6638(2^298408+450)/289830Stefano Morozzi01/2020
6639gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
66402^298367+5890589818Lelio R Paula11/2013
664121966^12269+12269^2196689815Hans Havermann08/2020
6642(2^298333+3126)/289807Stefano Morozzi01/2020
66432^298319-10965789803Enzo Doria04/2014
66448*10^89800+8189801Robert Price05/2017
664521354^16037+16037^2135489797Hans Havermann08/2020
6646(2^298249+714)/289782Stefano Morozzi01/2020
664721227^16954+16954^2122789775Hans Havermann08/2020
6648(733^31333-1)/73289770Serge Batalov08/2020
665118^71505-9189759Lelio R Paula12/2015
6649(2^298171+1586)/289759Stefano Morozzi01/2020
6650(4788^24391-1)/478789759Serge Batalov08/2020
6652(2^298161+3530)/289756Stefano Morozzi01/2020
6653(7^106187+1)/889738Paul Bourdelais04/2008
66542^298079-10953189731Enzo Doria04/2014
6655(9255^22621-1)/925489720Serge Batalov08/2020
6656117^43380+11689718Norbert Schneider08/2018
6657(22699*2^298016+1)/38589714Lelio R Paula06/2014
6658156*(10^(4*22427)-1)/101-189709Robert Price05/2014
66592^298003-6694589708Lelio R Paula11/2013
6660(23*10^89705-83)/389706Robert Price09/2017
666117^72900-5489700Lelio R Paula11/2015
6662(2^297968+2482)/289698Stefano Morozzi01/2020
66633*2^297956+589695Lelio R Paula08/2014
6664(2^297952+3558)/289693Stefano Morozzi01/2020
6665(3992^24907-1)/399189692Serge Batalov08/2020
666620^68938-1189691Lelio R Paula01/2016
666789*10^89687-789689Robert Price03/2017
6668(6882^23371-1)/688189688Serge Batalov08/2020
6669(297847^16384+1)/289686Richard Fischer08/2019
66702^297923+7778389684Enzo Doria05/2016
6671(2^297893+1694)/289675Stefano Morozzi01/2020
667211^86107-2457600089672Enzo Doria02/2013
66732^297878-11191189671Enzo Doria05/2014
667420823^20236+20236^2082389667Hans Havermann08/2020
667525708^3075+3075^2570889666Hans Havermann08/2020
667621002^18585+18585^2100289661Hans Havermann08/2020
6677(2^297830+3670)/289656Stefano Morozzi01/2020
66787^106084+4089652Lelio R Paula10/2015
6679(2^297815+618)/289651Stefano Morozzi01/2020
668021223^16752+16752^2122389648Hans Havermann08/2020
6682(86*10^89640-311)/989641Robert Price10/2017
6681(2^297781+2094)/289641Stefano Morozzi01/2020
6683(2^297741+3326)/289629Stefano Morozzi01/2020
6684(2^297724+3606)/289624Stefano Morozzi01/2020
66853*10^89608-5989609Robert Price10/2017
6686(2^297650+3250)/289602Stefano Morozzi01/2020
66873^187780-1103889594Enzo Doria05/2014
6688(13*2^297560-1)/4915178789568Lelio R Paula02/2014
66895^128141-3689567Lelio R Paula10/2015
66904*7^105951+989540Lelio R Paula10/2014
6691(7*10^89539-439)/989539Robert Price09/2017
6692(9772^22441-1)/977189536Serge Batalov08/2020
669322823^8374+8374^2282389534Hans Havermann08/2020
6694(2^297401+2954)/289527Stefano Morozzi01/2020
6695(2^297403+1670)/289527Stefano Morozzi01/2020
66962^297397+17725789526Enzo Doria05/2016
66982^297346-1624189511Enzo Doria04/2013
6697(5*10^89510+79)/389511Robert Price11/2017
66994^148663-3^14866389505Jean-Louis Charton11/2005
67002^297328-86968810589505Lelio R Paula07/2016
67012^297325-45904389504Enzo Doria05/2015
67022^297310-11239189500Enzo Doria06/2014
67032^297296-11215789496Enzo Doria06/2014
670457^50966-289490Lelio R Paula08/2013
6705(266*10^89482+1)/389484Robert Price02/2016
6706(14*10^89480-101)/389481Robert Price04/2017
67072618^26175+26175^261889466Norbert Schneider01/2020
6708(2^297150+3922)/289451Stefano Morozzi01/2020
6709(2^297141+1842)/289449Stefano Morozzi01/2020
6710(2^297140+1458)/289448Stefano Morozzi01/2020
6711(2^297129+726)/289445Stefano Morozzi01/2020
67122^297122+9989443Lelio R Paula10/2012
6713(3^187435-5)/128689427Lelio R Paula01/2013
6714(28*10^89425+101)/389426Robert Price09/2020
6715(2^297037+3522)/289417Stefano Morozzi01/2020
6716(25*10^89413+161)/389414Robert Price01/2017
671729080^1187+1187^2908089406Hans Havermann08/2020
67182^296990+187069989403Enzo Doria05/2016
67192^296972-101789398Lelio R Paula11/2013
6720(7*10^89383+167)/389384Robert Kinser10/2017
6721(85*10^89375-31)/989376Robert Price11/2015
67229*2^296870+789368Lelio R Paula08/2014
6723100^44683-99^4468389366Robert Price07/2013
67242^296810+7651989349Enzo Doria05/2016
6725(2747^25981-1)/274689342Serge Batalov08/2020
67268^98928+7^(98928+1)89341Robert Price06/2016
6728(3^187247+4)/102789337Lelio R Paula01/2013
672721832^12359+12359^2183289337Hans Havermann08/2020
6729(3^187235-2)/204589331Lelio R Paula01/2013
67302^296736-43214989327Paul Bourdelais05/2013
67312^296737-11251989327Enzo Doria06/2014
67322^296718-364589322Lelio R Paula11/2013
6733(2^296702+2338)/289316Stefano Morozzi01/2020
67342^296681-1622189310Enzo Doria04/2013
67352^296669-1651389307Enzo Doria04/2013
6736(2^296626+1282)/289294Stefano Morozzi01/2020
67372^296619-1635789292Enzo Doria04/2013
67382^296614-11005189290Enzo Doria04/2014
6739(2^296601+1730)/289286Stefano Morozzi01/2020
6740(3^187138+8)/8314789283Lelio R Paula01/2013
6741(2*10^89279+457)/989279Robert Price01/2017
6742(2^296568+1222)/289276Stefano Morozzi01/2020
674315^75907-2889274Lelio R Paula11/2015
67442^296547-3789270Yves Minet01/2012
67452^296485+19189251Lelio R Paula10/2012
67462^296467-7589246Lelio R Paula10/2012
6747(2^296462+1674)/289244Stefano Morozzi01/2020
67482^296416-10953589231Enzo Doria04/2014
6749(23*2^296406+1)/389228Lelio R Paula01/2013
675066^49037-6589225Norbert Schneider11/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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