PRP Records

Probable Primes Top 10000

(291192 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 ?
4751(91*10^112098-1)/9112100Robert Price04/2015
4752(68*10^112087-149)/9112088Robert Price07/2022
47532^372310-85061112077Paul Bourdelais02/2012
4754(10^112067+53)/9112067Serge Batalov07/2015
4755(2^372237+2082)/2112055Stefano Morozzi09/2020
475675^59760+2112054Lelio R Paula08/2013
4757(2^372200+1710)/2112044Stefano Morozzi09/2020
4758(10^112048+7)/8747/373157112039Alfred Reich06/2021
4759(2^372181+2250)/2112038Stefano Morozzi01/2021
4760(2^372161+2574)/2112032Stefano Morozzi09/2020
47618*10^112018-49112019Robert Price08/2019
47632^372108+74221112016Enzo Doria04/2016
4762(2^372109+2046)/2112016Stefano Morozzi09/2020
47648*10^112011-73112012Robert Price01/2022
4765(184*10^112007-1)/3112009Robert Price02/2020
47665*10^112003+81112004Robert Price03/2019
4767215^48018+48018^215112000Norbert Schneider10/2018
476825549^24148+24148^25549111979Hans Havermann02/2021
47692^371970-459491111975Enzo Doria05/2015
477041^69427-40^69427111971Robert Price07/2012
4771(2^371782+358)/2111918Stefano Morozzi01/2021
4772(34*10^111902-547)/9111903Robert Price03/2021
4773(10^111902+71)/9111902Serge Batalov07/2015
4774(2^371625+1610)/2111870Stefano Morozzi09/2020
477529080^7027+7027^29080111865Hans Havermann01/2021
477631307^3730+3730^31307111820Hans Havermann02/2021
47772^371440-112865111815Enzo Doria06/2014
47782^371426-459161111811Enzo Doria05/2015
477925768^21771+21771^25768111779Hans Havermann02/2021
478028022^9747+9747^28022111777Hans Havermann02/2021
4781(94*10^111770+11)/3111772Robert Price04/2020
47822^371276-461267111766Enzo Doria07/2015
47836*10^111760+43111761Robert Price07/2020
478498079!4-1024111747Robert Price11/2019
4785(2^371186+3162)/2111738Stefano Morozzi09/2020
47862^371098-113261111712Enzo Doria07/2014
4787(7*10^111706-61)/9111706Erik Branger01/2011
47882^371044+1869391111696Enzo Doria05/2016
478926310^17581+17581^26310111688Hans Havermann01/2021
479088^57416+87111645Norbert Schneider11/2015
47912^370829-109693111631Enzo Doria04/2014
479215^94906-2111619Lelio R Paula11/2013
479325835^20904+20904^25835111614Hans Havermann02/2021
4794(2^370726+1198)/2111600Stefano Morozzi09/2020
479527758^10479+10479^27758111597Hans Havermann02/2021
47962^370695-4627111591Yves Minet05/2019
47977*10^111579-87111580Robert Price06/2020
47992^370643-37111575Yves Minet01/2012
4798(2^370655-5)/2439111575Lelio R Paula03/2014
48002^370610-3911111565Yves Minet04/2017
4801(154*10^111549+17)/9111551Robert Price06/2022
480226200^18097+18097^26200111550Hans Havermann01/2021
4803286^45405+45405^286111532Norbert Schneider04/2015
48044*5^159563-9111531Lelio R Paula11/2014
48055*10^111528-21111529Robert Price12/2021
4806(4^185225+23)/3111517Robert Price10/2018
48072^370393-2797093111500Enzo Doria03/2016
4808(21*2^370382-1)/629111495Lelio R Paula03/2014
4809(2^370371+554)/2111493Stefano Morozzi09/2020
48106^143273-5111489Paul Bourdelais01/2021
48112^370292-2791979111469Enzo Doria03/2016
4812(14*10^111443-11)/3111444Robert Price08/2022
48132^370177-461551111435Enzo Doria07/2015
4814(2^370169+1706)/2111432Stefano Morozzi09/2020
4815109^54683-108111413Norbert Schneider02/2017
4816(83*10^111406-173)/9111407Robert Price04/2021
4817(2^370043+1010)/2111394Stefano Morozzi09/2020
481832961^2396+2396^32961111392Hans Havermann10/2020
4819numbpart(10^10+76282)111391Serge Batalov04/2015
4820(23*10^111380-29)/3111381Robert Price03/2022
48212^369974+733111374Lelio R Paula05/2013
4822121^53470+120111367Norbert Schneider10/2018
48232^369915-286267111356Enzo Doria07/2015
4824(62*10^111347-629)/9111348Robert Price07/2021
48252^369855-1615111338Lelio R Paula05/2017
48267*10^111325+3111326Robert Price08/2015
482751^65176+2111293Lelio R Paula08/2013
48282^369643-1865767111274Enzo Doria03/2016
48292^369603+885111262Lelio R Paula05/2017
483025555^22564+22564^25555111252Hans Havermann10/2020
4831L(532277)111240Renaud Lifchitz03/2004
4832105^55033-2111233Lelio R Paula10/2017
4833(35*10^111232-737)/9111233Robert Price07/2018
483426970^13307+13307^26970111227Hans Havermann10/2020
483525419^23716+23716^25419111210Hans Havermann10/2020
48369*10^111201-29111202Robert Price09/2019
48372^369392+29835111199Lelio R Paula05/2017
48383^233059+16111198Robert Price03/2020
48392^369354-3413111187Yves Minet12/2016
48402^369296-27111170Lelio R Paula02/2013
48412^369239-109837111153Enzo Doria05/2014
48422^369224-291839111148Enzo Doria07/2015
48432^369216+2798881111146Enzo Doria04/2016
484426842^13817+13817^26842111137Hans Havermann11/2020
4845(5*10^111119-191)/3111120Robert Price05/2021
4846(29*10^111112-23)/3111113Robert Price03/2022
484710^111111+163849111112Patrick De Geest03/2017
484810^111111-312911111111Patrick De Geest03/2017
48492^369092-216923111108Enzo Doria05/2014
48502^369081-55111105Lelio R Paula02/2013
4851(2^369047+3618)/2111094Stefano Morozzi09/2020
485288^57124-87111077Norbert Schneider11/2015
48532^368980+753111075Lelio R Paula05/2013
48542^368946-3623111064Yves Minet03/2017
48552^368929+29835111059Lelio R Paula05/2017
48564^184463-3^184463111058Jean-Louis Charton12/2004
4857111^54298+110111057Norbert Schneider04/2017
4858(4*10^111032-7)/3111033Ray Chandler04/2011
485935799^1262+1262^35799111015Hans Havermann10/2020
4860(298*10^111004+11)/3111006Robert Price11/2020
486127648^10349+10349^27648111004Hans Havermann11/2020
486228899^6932+6932^28899110997Hans Havermann11/2020
48632^368641-460303110972Enzo Doria06/2015
48642^368619-109087110966Enzo Doria04/2014
4865(74*10^110961+313)/9110962Robert Price06/2019
486625258^24711+24711^25258110956Hans Havermann11/2020
4867(2^368539+1290)/2110941Stefano Morozzi01/2021
48683*2^368489+7110927Lelio R Paula09/2014
4869(14*10^110922+61)/3110923Robert Price12/2018
487097411!4-2110913Robert Price07/2017
4871(301*10^110903+23)/9110905Robert Price06/2021
4872(9179*2^368330-1)/35110881Lelio R Paula05/2015
487325830^19619+19619^25830110880Hans Havermann10/2020
4874(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
487526022^18191+18191^26022110850Hans Havermann10/2020
4876(2^368211+2250)/2110843Stefano Morozzi01/2021
4877(37*10^110813+251)/9110814Robert Price09/2021
48782^368050-64875110795Lelio R Paula05/2017
48792^368048+25110794Lelio R Paula02/2013
4880(2^368017+2262)/2110784Stefano Morozzi02/2021
488169^60239-2110771Lelio R Paula10/2013
4882(23*2^367952+1)/15717110762Lelio R Paula03/2014
48832^367924-69110757Lelio R Paula02/2013
4884(23*10^110738+61)/3110739Robert Price01/2022
4885(2^367779+3750)/2110713Stefano Morozzi01/2021
48862^367709-109723110692Enzo Doria04/2014
4887(3*2^367644-1)/107110671Lelio R Paula03/2014
4888(2^367626+3514)/2110667Stefano Morozzi09/2020
4889(23*2^367398+1)/57963110595Lelio R Paula03/2014
4890140^51515-139110558Norbert Schneider04/2019
48912^367215+1879223110543Enzo Doria09/2016
489225782^19375+19375^25782110534Hans Havermann10/2020
489326117^17058+17058^26117110526Hans Havermann10/2020
48942^367141+41110521Lelio R Paula02/2013
48952^367126+29835110516Lelio R Paula05/2017
4896(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
4897(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
4898(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
4899(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
4900(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
4901(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
4902(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
4903(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
4904(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
4905(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
4906(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
49073*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
49083*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
49093*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
49103*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
49113*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
49123*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
49133*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
49147*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
49157*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
49167*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
49177*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
49187*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
49197*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
49207*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
49217*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
49227*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
49237*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
49247*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
49257*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
49267*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
49277*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
49287*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
4929(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
4930(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
4931(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
4932(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
4933(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
4934(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
4935(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
4936(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
4937(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
4938(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
4939(11*10^110496+49)/3110497Robert Price07/2018
494025447^21958+21958^25447110481Hans Havermann11/2020
4941(31*2^366976+1)/7110472Lelio R Paula03/2014
49427*10^110468-23110469Robert Price07/2019
49432^366853+5711110434Lelio R Paula05/2017
4944(21181*2^366833+1)/3110432Lelio R Paula07/2014
49452^366816+315110423Lelio R Paula05/2017
49462^366775-2787037110411Enzo Doria03/2016
4947(112*10^110405-1)/3110407Serge Batalov12/2014
49482^366751+2797553110404Enzo Doria03/2016
494925276^23331+23331^25276110404Hans Havermann10/2020
49502^366748+255110403Lelio R Paula05/2017
49512^366738-2985110400Yves Minet09/2014
4952(23*2^366739+1)/74575110396Lelio R Paula03/2014
4953(2^366722+1314)/2110395Stefano Morozzi02/2021
49542^366716+1871791110393Enzo Doria05/2016
49552^366649+1871687110373Enzo Doria05/2016
49562^366629-351205110367Enzo Doria06/2015
4957(31*10^110363+257)/9110364Robert Price12/2021
49592^366558+1874479110345Enzo Doria06/2016
495825132^24581+24581^25132110345Hans Havermann10/2020
4960(2^366539+770)/2110339Stefano Morozzi09/2020
496126368^15285+15285^26368110331Hans Havermann10/2020
4962(23*10^110290+19)/3110291Robert Price07/2019
496318^87853-4409110280Enzo Doria03/2013
496428490^7419+7419^28490110267Hans Havermann11/2020
49652^366218-23110243Lelio R Paula02/2013
4966(21*2^366193-1)/197110235Lelio R Paula03/2014
49672^366178-343991110231Enzo Doria07/2015
496825777^18798+18798^25777110174Hans Havermann10/2020
49692^365944+1871341110161Enzo Doria05/2016
49702^365838-461267110129Enzo Doria07/2015
497130152^4491+4491^30152110126Hans Havermann11/2020
497210^110111+464019110112Patrick De Geest05/2021
497310^110111-40001110111Robert Price01/2021
49742^365763-6555110106Lelio R Paula04/2017
4975(2^365689+2^182845+1)/511008311/2006
49762^365666-459161110077Enzo Doria05/2015
49773*10^110076-7110077Robert Price08/2015
497813^98785-72110041Lelio R Paula03/2017
4979(25^78707+1)/26110027Robert Price06/2013
4980(7*10^110027-277)/9110027Robert Price02/2022
4981(16*10^110014-73)/3110015Robert Price07/2020
4982(7*10^110006-151)/9110006Robert Price02/2018
49836^141361-7110001Lelio R Paula11/2014
498420^84536+81109984Lelio R Paula03/2017
49855*2^365347-9109982Lelio R Paula09/2014
49869*6^141303+7109957Lelio R Paula11/2014
498727635^9522+9522^27635109953Hans Havermann11/2020
498878^58099+77109929Norbert Schneider02/2015
49892*10^109928-7109929Robert Price10/2015
499030580^3933+3933^30580109927Hans Havermann11/2020
499126380^14689+14689^26380109926Hans Havermann11/2020
4992(2^365161+1130)/2109925Stefano Morozzi09/2020
4993(27*2^365137-1)/2021109916Lelio R Paula03/2014
4994(4441*29^75152-24)/7109905Curtis Bright05/2015
4995(2^365087+7)/6015109899Lelio R Paula01/2014
4996(2^365069+3774)/2109897Stefano Morozzi02/2021
499729652^5083+5083^29652109894Mark Rodenkirch10/2020
4998(2^365049+722)/2109891Stefano Morozzi09/2020
4999(35*10^109888-89)/9109889Robert Price02/2022
500018^87533-11109878Lelio R Paula04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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