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 ?
50012^364982-5109871Henri Lifchitz04/2006
50023*10^109861+59109862Robert Price08/2018
50035*10^109860-69109861Robert Price02/2021
50042^364936-1867979109857Enzo Doria04/2016
500527013^11652+11652^27013109846Hans Havermann10/2020
50062^364867-112087109836Enzo Doria06/2014
50074^182415-85061109825Mike Oakes06/2011
5008(2^364809+1034)/2109819Stefano Morozzi09/2020
5009(53*10^109809-287)/9109810Robert Price02/2022
5010(52*10^109807-133)/9109808Robert Price09/2021
501125708^18675+18675^25708109806Hans Havermann10/2020
5012(17^89227+16^89227)/33109788Robert Price08/2013
50132^364687-187109782Lelio R Paula01/2012
50142^364644+67109769Lelio R Paula01/2012
5015(9787*2^364625-1)/24947109763Lelio R Paula05/2015
5016(2^364616+5)/9109760Lelio R Paula01/2014
5017(55*10^109759+89)/9109760Robert Price03/2019
501812^101694+73109747Lelio R Paula03/2017
501913^98518-66109744Lelio R Paula03/2017
5020(8*10^109721-269)/9109721Robert Price09/2021
50212^364478-113261109719Enzo Doria07/2014
5022(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
5023(24737*2^364454+1)/3109716Lelio R Paula07/2014
502427814^8777+8777^27814109681Hans Havermann10/2020
5025(62*10^109673+1)/9109674Serge Batalov11/2010
50263^229824+340109654Lelio R Paula03/2017
5027(2*10^109645-71)/3109645Robert Price12/2017
50282^364169-112813109626Enzo Doria06/2014
502928822^6359+6359^28822109622Hans Havermann11/2020
503010^109615+21109616Lelio R Paula03/2017
503110^109615-456267109615Patrick De Geest03/2017
50322^364094-113109604Lelio R Paula01/2012
503325251^21898+21898^25251109600Hans Havermann11/2020
5034(4^182026+11)/3109591Robert Price02/2017
50352^364041-6883109588Lelio R Paula09/2011
503612^101545+11109586Lelio R Paula03/2017
503726536^13475+13475^26536109582Hans Havermann11/2020
50382^363842-2787101109528Enzo Doria03/2016
5039(2^363812+3570)/2109519Stefano Morozzi09/2020
5040(22699*2^363782+1)/763109511Lelio R Paula07/2014
50412^363769+5711109506Lelio R Paula04/2017
5042(31*2^363748+1)/49109499Lelio R Paula03/2014
5043(2^363670+100280245065)109476Paul Bourdelais05/2022
5044p(22245)#/2-8109462Robert Price01/2017
50452^363556+55109442Lelio R Paula01/2012
5046(509*10^109414+31)/9109416Robert Price08/2022
5047(2^363437+1682)/2109406Stefano Morozzi09/2020
5048(55459*2^363411+1)/81109401Lelio R Paula07/2014
50492^363406+1871569109397Enzo Doria05/2016
5050(2^363370+1338)/2109385Stefano Morozzi02/2021
5051(2^363349+7)/9109378Lelio R Paula01/2014
50523^229236+100109374Lelio R Paula03/2017
5053(2^363315+3258)/2109369Stefano Morozzi02/2021
50542^363268-58695109355Lelio R Paula04/2017
50552^363191-112321109332Enzo Doria06/2014
505626231^14718+14718^26231109327Hans Havermann10/2020
505725461^19672+19672^25461109326Hans Havermann10/2020
50584*10^109316-63109317Robert Price10/2018
50592^363120+3109311Donovan Johnson04/2006
5060(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
50612^363042-114641109287Enzo Doria04/2015
50622^363020-112793109280Enzo Doria06/2014
5063(85*10^109253+203)/9109254Robert Price09/2020
506424990^23431+23431^24990109202Hans Havermann10/2020
5065(2^362746+3738)/2109198Stefano Morozzi09/2020
5066(2^362716+1282)/2109189Stefano Morozzi01/2021
5067(67607*2^362695+1)/70499109183Lelio R Paula07/2014
506825060^22737+22737^25060109180Hans Havermann10/2020
5069(9*2^362644+1)/5109167Lelio R Paula03/2014
50705^156181+38109166Lelio R Paula02/2017
5071(2^362623+3618)/2109161Stefano Morozzi09/2020
507225138^21993+21993^25138109157Hans Havermann10/2020
50734*10^109142+91109143Robert Price08/2018
50743^228750+68109142Lelio R Paula03/2017
5075(2^362561+786)/2109142Stefano Morozzi09/2020
5076(23*10^109113+61)/3109114Robert Price01/2022
50772*10^109100-49109101Robert Price09/2020
5078(10223*2^362376+1)/9109090Lelio R Paula07/2014
507965^60167-64^60167109078Robert Price08/2013
50807*3^228589-2109066Lelio R Paula09/2014
508124874^24243+24243^24874109063Hans Havermann11/2020
5082(17*10^109059-161)/9109060Robert Price02/2021
508329158^5495+5495^29158109050Hans Havermann11/2020
5084(78557*2^362188+1)/189109033Lelio R Paula07/2014
50852*7^129008+9109025Lelio R Paula11/2014
508688*10^109022+7109024Robert Price03/2020
508728194^7337+7337^28194108985Hans Havermann10/2020
5088(5*10^108960+91)/3108961Robert Price04/2018
50892^361957+76367108960Enzo Doria05/2016
50902^361873-1411108935Yves Minet01/2013
5091(24737*2^361857+1)/35108933Lelio R Paula07/2014
5092115^52842-114108892Norbert Schneider07/2018
509313^97745-24108883Lelio R Paula03/2017
5094(2^361696+2562)/2108882Stefano Morozzi09/2020
509517^88475+8108864Lelio R Paula04/2017
50962^361567+51108843Lelio R Paula01/2012
50972^361563-109501108842Enzo Doria04/2014
509812^100852+83108838Lelio R Paula03/2017
50992^361497+767108822Lelio R Paula01/2012
510028019^7630+7630^28019108785Hans Havermann10/2020
510124723^24758-24758^24723108765Norbert Schneider11/2020
51022^361280-112349108757Enzo Doria06/2014
51032^361271-5955108754Lelio R Paula04/2017
510412^100757+19108736Lelio R Paula03/2017
510525368^19333+19333^25368108735Hans Havermann11/2020
5106(2^361195+3618)/2108731Stefano Morozzi09/2020
51072^361153-111546435108718Paul Bourdelais10/2021
510814^94849-61108710Lelio R Paula05/2017
510927267^9700+9700^27267108708Hans Havermann11/2020
5110(19^85009-5^85009)/14108705Robert Price07/2013
511124832^23853+23853^24832108704Hans Havermann11/2020
511227502^8963+8963^27502108701Hans Havermann11/2020
511325807^16278+16278^25807108689Hans Havermann11/2020
5114(11*2^361027+1)/40463108677Lelio R Paula03/2014
51152^360973+1299108664Lelio R Paula04/2017
51162^360959-109101108660Enzo Doria04/2014
51176*5^155454+7108659Lelio R Paula11/2014
511810^108656+79108657Lelio R Paula02/2017
511910^108656-50001108656Patrick De Geest03/2017
51202^360918-35108648Lelio R Paula01/2012
51214*10^108646-47108647Robert Price10/2021
5122(11*2^360886-1)/7108638Lelio R Paula03/2014
51233*10^108624-49108625Robert Price07/2018
5124(2^360831+666)/2108621Stefano Morozzi09/2020
5125(134*10^108610+7)/3108612Robert Price02/2020
51262*10^108609+29108610Robert Price02/2021
5127(10^108604+7)/71/191108600Alfred Reich06/2021
5128(2^360742+3222)/2108594Stefano Morozzi09/2020
51292^360706-458903108584Enzo Doria04/2015
513031112^3087+3087^31112108567Hans Havermann11/2020
51312^360641-113185108564Enzo Doria07/2014
5132(29*10^108559-71)/3108560Robert Price07/2021
51332^360618+75019108557Enzo Doria04/2016
51342^360607-216367108554Harrison Mesh06/2022
5135(14*10^108545-221)/9108546Robert Price04/2018
5136(44*10^108544-233)/9108545Robert Price01/2019
51373*5^155286+2108541Lelio R Paula11/2014
51387^128422+4108530Lelio R Paula11/2014
51397^128421-80108529Lelio R Paula03/2017
51402^360497+53807108521Yves Minet07/2010
51412^360468-4559108512Yves Minet03/2019
5142(2^360451+578)/2108507Stefano Morozzi09/2020
51432^360366+1459108481Lelio R Paula09/2011
51442^360364-1499108481Yves Minet05/2013
514525662^16871+16871^25662108477Hans Havermann10/2020
514625009^21748+21748^25009108475Hans Havermann10/2020
514714^94642-23108472Lelio R Paula05/2017
5148(197*10^108446-11)/3108448Robert Price03/2020
5149(2^360229+1290)/2108440Stefano Morozzi01/2021
51504*10^108412+9108413Robert Price05/2015
5151(259*10^108409-1)/3108411Robert Price12/2020
5152(2^360122+1194)/2108408Stefano Morozzi09/2020
5153133^51042-132108406Norbert Schneider02/2019
51542^360093-351103108399Enzo Doria06/2015
51552^360042+723108384Lelio R Paula01/2012
515685^56164-2108364Lelio R Paula10/2013
51572^359937-29323108352Enzo Doria07/2015
5158(2^359922+1762)/2108348Stefano Morozzi09/2020
5159(2^359903+758)/2108342Stefano Morozzi09/2020
51602^359898-19997108341Enzo Doria06/2013
5161(2^359886+2122)/2108337Stefano Morozzi09/2020
51622*5^154948-7108305Lelio R Paula11/2014
516310^108303+13108304Lelio R Paula02/2017
516410^108303-207959108303Patrick De Geest03/2017
51657*10^108300+69108301Robert Price07/2019
51662^359730+753108290Lelio R Paula12/2011
5167(8*10^108273+13)/3108274Robert Price06/2018
51682^359650-19797108266Enzo Doria06/2013
5169(47*10^108261+259)/9108262Robert Price03/2022
517091^55259-90^55259108255Robert Price07/2015
517110^108251+85749108252Patrick De Geest02/2021
517210^108251-50000000001108251Robert Price12/2020
517310^108251-252081108251Patrick De Geest02/2021
51744*10^108238-71108239Robert Price12/2018
51753^226845+68108233Lelio R Paula03/2017
517631836^2509+2509^31836108227Hans Havermann10/2020
51775^154822-12866108216Enzo Doria05/2014
5178(9*2^359480+1)/5108215Lelio R Paula03/2014
51792^359454-177108207Lelio R Paula12/2011
5180(19*10^108184+191)/3108185Robert Price05/2019
51816^139022-59108181Lelio R Paula02/2017
5182(19*10^108176-43)/3108177Robert Price05/2019
51832^359352-179108176Lelio R Paula12/2011
51842^359338-1858781108172Enzo Doria04/2016
518512^100230-97108167Lelio R Paula03/2017
518627028^10043+10043^27028108163Hans Havermann11/2020
5187(25*2^359297-1)/137108159Lelio R Paula03/2014
5188(2^359262-509203)/9108148Lelio R Paula12/2013
518926583^11702+11702^26583108147Hans Havermann11/2020
5190(3^226648-8)/352715633108131Lelio R Paula12/2013
51916^138956-59108129Lelio R Paula02/2017
51922^359184+30285108126Lelio R Paula04/2017
519313^97059+10108119Lelio R Paula03/2017
51942^359137-81108112Lelio R Paula12/2011
5196(15185*2^359105-1)/567108103Lelio R Paula05/2015
51952^359110-11655108103Lelio R Paula04/2017
51972^359069-933075108091Paul Bourdelais06/2021
519826227^13222+13222^26227108090Hans Havermann10/2020
51998*6^138875+5108067Lelio R Paula11/2014
52002^358987-216919108066Enzo Doria05/2014
5201(2^358977+2714)/2108063Stefano Morozzi09/2020
520239^67918-67918^39108062Norbert Schneider02/2017
520324^78283-1*78283^24108048Dylan Delgado12/2019
520425282^18767+18767^25282108040Hans Havermann11/2020
52052^358785-16933108006Enzo Doria05/2013
5206(2^358783+5)/33383108000Lelio R Paula12/2013
52076^138770-77107985Lelio R Paula02/2017
5208(2^358727-1017)/94178479107980Lelio R Paula12/2013
520910^107976+19107977Lelio R Paula02/2017
521010^107976-202103107976Patrick De Geest03/2017
52112^358684+75781107975Enzo Doria04/2016
521224928^21411+21411^24928107955Hans Havermann10/2020
521399^54094+2107952Lelio R Paula06/2013
5214(2^358583-9)/391107942Lelio R Paula12/2013
5215(2^358562+838)/2107938Stefano Morozzi02/2021
52162^358538+55107931Lelio R Paula12/2011
52172^358517-109009107925Enzo Doria03/2014
521826395^12258+12258^26395107914Hans Havermann10/2020
52193^226159+104107906Lelio R Paula03/2017
52202^358310-11655107863Lelio R Paula03/2017
5221(68*10^107852-329)/9107853Robert Price03/2021
52222^358275-112987107852Enzo Doria07/2014
52233^226038+4107848Tyler NeSmith01/2021
52242^358233-20005107839Enzo Doria06/2013
52252^358194+175107828Lelio R Paula12/2011
5226107^53125-106107812Norbert Schneider12/2016
5227(25*10^107804+161)/3107805Robert Price09/2019
52283^225922-2107793Lelio R Paula10/2013
522912^99874-95107783Lelio R Paula03/2017
5230(2^358042+3042)/2107782Stefano Morozzi09/2020
52312^358030-171107778Lelio R Paula12/2011
523211^103488-4170107772Enzo Doria12/2012
52332^357930-4547107748Yves Minet03/2019
52342^357911-20089107742Enzo Doria06/2013
52352^357885+12857107735Yves Minet07/2010
5236(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
52377^127473+40107728Lelio R Paula03/2017
52385*2^357850+9107725Lelio R Paula09/2014
52392^357786-291191107705Enzo Doria06/2015
524028907^5320+5320^28907107705Hans Havermann10/2020
524118^85798-23107700Lelio R Paula04/2017
52423*10^107697+61107698Robert Price09/2020
5243(14*10^107694-83)/3107695Robert Price12/2018
52442^357688-1854269107675Enzo Doria09/2015
52452^357671-112225107670Enzo Doria06/2014
524634323^1370+1370^34323107662Hans Havermann11/2020
52472^357618-21005107654Enzo Doria06/2013
52482^357615-17505107653Enzo Doria05/2013
524926350^12171+12171^26350107649Hans Havermann11/2020
5250(30^72871-1)/29107638Robert Price12/2011


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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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