PRP Records

Probable Primes Top 10000

(290751 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 ?
47512^368946-3623111064Yves Minet03/2017
47522^368929+29835111059Lelio R Paula05/2017
47534^184463-3^184463111058Jean-Louis Charton12/2004
4754111^54298+110111057Norbert Schneider04/2017
4755(4*10^111032-7)/3111033Ray Chandler04/2011
475635799^1262+1262^35799111015Hans Havermann10/2020
4757(298*10^111004+11)/3111006Robert Price11/2020
475827648^10349+10349^27648111004Hans Havermann11/2020
475928899^6932+6932^28899110997Hans Havermann11/2020
47602^368641-460303110972Enzo Doria06/2015
47612^368619-109087110966Enzo Doria04/2014
4762(74*10^110961+313)/9110962Robert Price06/2019
476325258^24711+24711^25258110956Hans Havermann11/2020
4764(2^368539+1290)/2110941Stefano Morozzi01/2021
47653*2^368489+7110927Lelio R Paula09/2014
4766(14*10^110922+61)/3110923Robert Price12/2018
476797411!4-2110913Robert Price07/2017
4768(301*10^110903+23)/9110905Robert Price06/2021
4769(9179*2^368330-1)/35110881Lelio R Paula05/2015
477025830^19619+19619^25830110880Hans Havermann10/2020
4771(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
477226022^18191+18191^26022110850Hans Havermann10/2020
4773(2^368211+2250)/2110843Stefano Morozzi01/2021
4774(37*10^110813+251)/9110814Robert Price09/2021
47752^368050-64875110795Lelio R Paula05/2017
47762^368048+25110794Lelio R Paula02/2013
4777(2^368017+2262)/2110784Stefano Morozzi02/2021
477869^60239-2110771Lelio R Paula10/2013
4779(23*2^367952+1)/15717110762Lelio R Paula03/2014
47802^367924-69110757Lelio R Paula02/2013
4781(23*10^110738+61)/3110739Robert Price01/2022
4782(2^367779+3750)/2110713Stefano Morozzi01/2021
47832^367709-109723110692Enzo Doria04/2014
4784(3*2^367644-1)/107110671Lelio R Paula03/2014
4785(2^367626+3514)/2110667Stefano Morozzi09/2020
4786(23*2^367398+1)/57963110595Lelio R Paula03/2014
4787140^51515-139110558Norbert Schneider04/2019
47882^367215+1879223110543Enzo Doria09/2016
478925782^19375+19375^25782110534Hans Havermann10/2020
479026117^17058+17058^26117110526Hans Havermann10/2020
47912^367141+41110521Lelio R Paula02/2013
47922^367126+29835110516Lelio R Paula05/2017
4793(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
4794(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
4795(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
4796(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
4797(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
4798(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
4799(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
4800(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
4801(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
4802(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
4803(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
48043*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
48053*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
48063*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
48073*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
48083*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
48093*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
48103*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
48117*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
48127*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
48137*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
48147*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
48157*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
48167*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
48177*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
48187*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
48197*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
48207*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
48217*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
48227*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
48237*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
48247*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
48257*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
4826(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
4827(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
4828(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
4829(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
4830(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
4831(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
4832(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
4833(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
4834(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
4835(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
4836(11*10^110496+49)/3110497Robert Price07/2018
483725447^21958+21958^25447110481Hans Havermann11/2020
4838(31*2^366976+1)/7110472Lelio R Paula03/2014
48397*10^110468-23110469Robert Price07/2019
48402^366853+5711110434Lelio R Paula05/2017
4841(21181*2^366833+1)/3110432Lelio R Paula07/2014
48422^366816+315110423Lelio R Paula05/2017
48432^366775-2787037110411Enzo Doria03/2016
4844(112*10^110405-1)/3110407Serge Batalov12/2014
48452^366751+2797553110404Enzo Doria03/2016
484625276^23331+23331^25276110404Hans Havermann10/2020
48472^366748+255110403Lelio R Paula05/2017
48482^366738-2985110400Yves Minet09/2014
4849(23*2^366739+1)/74575110396Lelio R Paula03/2014
4850(2^366722+1314)/2110395Stefano Morozzi02/2021
48512^366716+1871791110393Enzo Doria05/2016
48522^366649+1871687110373Enzo Doria05/2016
48532^366629-351205110367Enzo Doria06/2015
4854(31*10^110363+257)/9110364Robert Price12/2021
48562^366558+1874479110345Enzo Doria06/2016
485525132^24581+24581^25132110345Hans Havermann10/2020
4857(2^366539+770)/2110339Stefano Morozzi09/2020
485826368^15285+15285^26368110331Hans Havermann10/2020
4859(23*10^110290+19)/3110291Robert Price07/2019
486018^87853-4409110280Enzo Doria03/2013
486128490^7419+7419^28490110267Hans Havermann11/2020
48622^366218-23110243Lelio R Paula02/2013
4863(21*2^366193-1)/197110235Lelio R Paula03/2014
48642^366178-343991110231Enzo Doria07/2015
486525777^18798+18798^25777110174Hans Havermann10/2020
48662^365944+1871341110161Enzo Doria05/2016
48672^365838-461267110129Enzo Doria07/2015
486830152^4491+4491^30152110126Hans Havermann11/2020
486910^110111+464019110112Patrick De Geest05/2021
487010^110111-40001110111Robert Price01/2021
48712^365763-6555110106Lelio R Paula04/2017
4872(2^365689+2^182845+1)/511008311/2006
48732^365666-459161110077Enzo Doria05/2015
48743*10^110076-7110077Robert Price08/2015
487513^98785-72110041Lelio R Paula03/2017
4876(25^78707+1)/26110027Robert Price06/2013
4877(7*10^110027-277)/9110027Robert Price02/2022
4878(16*10^110014-73)/3110015Robert Price07/2020
4879(7*10^110006-151)/9110006Robert Price02/2018
48806^141361-7110001Lelio R Paula11/2014
488120^84536+81109984Lelio R Paula03/2017
48825*2^365347-9109982Lelio R Paula09/2014
48839*6^141303+7109957Lelio R Paula11/2014
488427635^9522+9522^27635109953Hans Havermann11/2020
488578^58099+77109929Norbert Schneider02/2015
48862*10^109928-7109929Robert Price10/2015
488730580^3933+3933^30580109927Hans Havermann11/2020
488826380^14689+14689^26380109926Hans Havermann11/2020
4889(2^365161+1130)/2109925Stefano Morozzi09/2020
4890(27*2^365137-1)/2021109916Lelio R Paula03/2014
4891(4441*29^75152-24)/7109905Curtis Bright05/2015
4892(2^365087+7)/6015109899Lelio R Paula01/2014
4893(2^365069+3774)/2109897Stefano Morozzi02/2021
489429652^5083+5083^29652109894Mark Rodenkirch10/2020
4895(2^365049+722)/2109891Stefano Morozzi09/2020
4896(35*10^109888-89)/9109889Robert Price02/2022
489718^87533-11109878Lelio R Paula04/2017
48982^364982-5109871Henri Lifchitz04/2006
48993*10^109861+59109862Robert Price08/2018
49005*10^109860-69109861Robert Price02/2021
49012^364936-1867979109857Enzo Doria04/2016
490227013^11652+11652^27013109846Hans Havermann10/2020
49032^364867-112087109836Enzo Doria06/2014
49044^182415-85061109825Mike Oakes06/2011
4905(2^364809+1034)/2109819Stefano Morozzi09/2020
4906(53*10^109809-287)/9109810Robert Price02/2022
4907(52*10^109807-133)/9109808Robert Price09/2021
490825708^18675+18675^25708109806Hans Havermann10/2020
4909(17^89227+16^89227)/33109788Robert Price08/2013
49102^364687-187109782Lelio R Paula01/2012
49112^364644+67109769Lelio R Paula01/2012
4912(9787*2^364625-1)/24947109763Lelio R Paula05/2015
4913(2^364616+5)/9109760Lelio R Paula01/2014
4914(55*10^109759+89)/9109760Robert Price03/2019
491512^101694+73109747Lelio R Paula03/2017
491613^98518-66109744Lelio R Paula03/2017
4917(8*10^109721-269)/9109721Robert Price09/2021
49182^364478-113261109719Enzo Doria07/2014
4919(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
4920(24737*2^364454+1)/3109716Lelio R Paula07/2014
492127814^8777+8777^27814109681Hans Havermann10/2020
4922(62*10^109673+1)/9109674Serge Batalov11/2010
49233^229824+340109654Lelio R Paula03/2017
4924(2*10^109645-71)/3109645Robert Price12/2017
49252^364169-112813109626Enzo Doria06/2014
492628822^6359+6359^28822109622Hans Havermann11/2020
492710^109615+21109616Lelio R Paula03/2017
492810^109615-456267109615Patrick De Geest03/2017
49292^364094-113109604Lelio R Paula01/2012
493025251^21898+21898^25251109600Hans Havermann11/2020
4931(4^182026+11)/3109591Robert Price02/2017
49322^364041-6883109588Lelio R Paula09/2011
493312^101545+11109586Lelio R Paula03/2017
493426536^13475+13475^26536109582Hans Havermann11/2020
49352^363842-2787101109528Enzo Doria03/2016
4936(2^363812+3570)/2109519Stefano Morozzi09/2020
4937(22699*2^363782+1)/763109511Lelio R Paula07/2014
49382^363769+5711109506Lelio R Paula04/2017
4939(31*2^363748+1)/49109499Lelio R Paula03/2014
4940(2^363670+100280245065)109476Paul Bourdelais05/2022
4941p(22245)#/2-8109462Robert Price01/2017
49422^363556+55109442Lelio R Paula01/2012
4943(2^363437+1682)/2109406Stefano Morozzi09/2020
4944(55459*2^363411+1)/81109401Lelio R Paula07/2014
49452^363406+1871569109397Enzo Doria05/2016
4946(2^363370+1338)/2109385Stefano Morozzi02/2021
4947(2^363349+7)/9109378Lelio R Paula01/2014
49483^229236+100109374Lelio R Paula03/2017
4949(2^363315+3258)/2109369Stefano Morozzi02/2021
49502^363268-58695109355Lelio R Paula04/2017
49512^363191-112321109332Enzo Doria06/2014
495226231^14718+14718^26231109327Hans Havermann10/2020
495325461^19672+19672^25461109326Hans Havermann10/2020
49544*10^109316-63109317Robert Price10/2018
49552^363120+3109311Donovan Johnson04/2006
4956(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
49572^363042-114641109287Enzo Doria04/2015
49582^363020-112793109280Enzo Doria06/2014
4959(85*10^109253+203)/9109254Robert Price09/2020
496024990^23431+23431^24990109202Hans Havermann10/2020
4961(2^362746+3738)/2109198Stefano Morozzi09/2020
4962(2^362716+1282)/2109189Stefano Morozzi01/2021
4963(67607*2^362695+1)/70499109183Lelio R Paula07/2014
496425060^22737+22737^25060109180Hans Havermann10/2020
4965(9*2^362644+1)/5109167Lelio R Paula03/2014
49665^156181+38109166Lelio R Paula02/2017
4967(2^362623+3618)/2109161Stefano Morozzi09/2020
496825138^21993+21993^25138109157Hans Havermann10/2020
49694*10^109142+91109143Robert Price08/2018
49703^228750+68109142Lelio R Paula03/2017
4971(2^362561+786)/2109142Stefano Morozzi09/2020
4972(23*10^109113+61)/3109114Robert Price01/2022
49732*10^109100-49109101Robert Price09/2020
4974(10223*2^362376+1)/9109090Lelio R Paula07/2014
497565^60167-64^60167109078Robert Price08/2013
49767*3^228589-2109066Lelio R Paula09/2014
497724874^24243+24243^24874109063Hans Havermann11/2020
4978(17*10^109059-161)/9109060Robert Price02/2021
497929158^5495+5495^29158109050Hans Havermann11/2020
4980(78557*2^362188+1)/189109033Lelio R Paula07/2014
49812*7^129008+9109025Lelio R Paula11/2014
498288*10^109022+7109024Robert Price03/2020
498328194^7337+7337^28194108985Hans Havermann10/2020
4984(5*10^108960+91)/3108961Robert Price04/2018
49852^361957+76367108960Enzo Doria05/2016
49862^361873-1411108935Yves Minet01/2013
4987(24737*2^361857+1)/35108933Lelio R Paula07/2014
4988115^52842-114108892Norbert Schneider07/2018
498913^97745-24108883Lelio R Paula03/2017
4990(2^361696+2562)/2108882Stefano Morozzi09/2020
499117^88475+8108864Lelio R Paula04/2017
49922^361567+51108843Lelio R Paula01/2012
49932^361563-109501108842Enzo Doria04/2014
499412^100852+83108838Lelio R Paula03/2017
49952^361497+767108822Lelio R Paula01/2012
499628019^7630+7630^28019108785Hans Havermann10/2020
499724723^24758-24758^24723108765Norbert Schneider11/2020
49982^361280-112349108757Enzo Doria06/2014
49992^361271-5955108754Lelio R Paula04/2017
500012^100757+19108736Lelio R Paula03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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