PRP Records

Probable Primes Top 10000

(288949 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(2^363812+3570)/2109519Stefano Morozzi09/2020
4752(22699*2^363782+1)/763109511Lelio R Paula07/2014
47532^363769+5711109506Lelio R Paula04/2017
4754(31*2^363748+1)/49109499Lelio R Paula03/2014
4755p(22245)#/2-8109462Robert Price01/2017
47562^363556+55109442Lelio R Paula01/2012
4757(2^363437+1682)/2109406Stefano Morozzi09/2020
4758(55459*2^363411+1)/81109401Lelio R Paula07/2014
47592^363406+1871569109397Enzo Doria05/2016
4760(2^363370+1338)/2109385Stefano Morozzi02/2021
4761(2^363349+7)/9109378Lelio R Paula01/2014
47623^229236+100109374Lelio R Paula03/2017
4763(2^363315+3258)/2109369Stefano Morozzi02/2021
47642^363268-58695109355Lelio R Paula04/2017
47652^363191-112321109332Enzo Doria06/2014
476626231^14718+14718^26231109327Hans Havermann10/2020
476725461^19672+19672^25461109326Hans Havermann10/2020
47684*10^109316-63109317Robert Price10/2018
47692^363120+3109311Donovan Johnson04/2006
4770(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
47712^363042-114641109287Enzo Doria04/2015
47722^363020-112793109280Enzo Doria06/2014
4773(85*10^109253+203)/9109254Robert Price09/2020
477424990^23431+23431^24990109202Hans Havermann10/2020
4775(2^362746+3738)/2109198Stefano Morozzi09/2020
4776(2^362716+1282)/2109189Stefano Morozzi01/2021
4777(67607*2^362695+1)/70499109183Lelio R Paula07/2014
477825060^22737+22737^25060109180Hans Havermann10/2020
4779(9*2^362644+1)/5109167Lelio R Paula03/2014
47805^156181+38109166Lelio R Paula02/2017
4781(2^362623+3618)/2109161Stefano Morozzi09/2020
478225138^21993+21993^25138109157Hans Havermann10/2020
47834*10^109142+91109143Robert Price08/2018
47843^228750+68109142Lelio R Paula03/2017
4785(2^362561+786)/2109142Stefano Morozzi09/2020
4786(23*10^109113+61)/3109114Robert Price01/2022
47872*10^109100-49109101Robert Price09/2020
4788(10223*2^362376+1)/9109090Lelio R Paula07/2014
478965^60167-64^60167109078Robert Price08/2013
47907*3^228589-2109066Lelio R Paula09/2014
479124874^24243+24243^24874109063Hans Havermann11/2020
4792(17*10^109059-161)/9109060Robert Price02/2021
479329158^5495+5495^29158109050Hans Havermann11/2020
4794(78557*2^362188+1)/189109033Lelio R Paula07/2014
47952*7^129008+9109025Lelio R Paula11/2014
479688*10^109022+7109024Robert Price03/2020
479728194^7337+7337^28194108985Hans Havermann10/2020
4798(5*10^108960+91)/3108961Robert Price04/2018
47992^361957+76367108960Enzo Doria05/2016
48002^361873-1411108935Yves Minet01/2013
4801(24737*2^361857+1)/35108933Lelio R Paula07/2014
4802115^52842-114108892Norbert Schneider07/2018
480313^97745-24108883Lelio R Paula03/2017
4804(2^361696+2562)/2108882Stefano Morozzi09/2020
480517^88475+8108864Lelio R Paula04/2017
48062^361567+51108843Lelio R Paula01/2012
48072^361563-109501108842Enzo Doria04/2014
480812^100852+83108838Lelio R Paula03/2017
48092^361497+767108822Lelio R Paula01/2012
481028019^7630+7630^28019108785Hans Havermann10/2020
481124723^24758-24758^24723108765Norbert Schneider11/2020
48122^361280-112349108757Enzo Doria06/2014
48132^361271-5955108754Lelio R Paula04/2017
481412^100757+19108736Lelio R Paula03/2017
481525368^19333+19333^25368108735Hans Havermann11/2020
4816(2^361195+3618)/2108731Stefano Morozzi09/2020
48172^361153-111546435108718Paul Bourdelais10/2021
481814^94849-61108710Lelio R Paula05/2017
481927267^9700+9700^27267108708Hans Havermann11/2020
4820(19^85009-5^85009)/14108705Robert Price07/2013
482124832^23853+23853^24832108704Hans Havermann11/2020
482227502^8963+8963^27502108701Hans Havermann11/2020
482325807^16278+16278^25807108689Hans Havermann11/2020
4824(11*2^361027+1)/40463108677Lelio R Paula03/2014
48252^360973+1299108664Lelio R Paula04/2017
48262^360959-109101108660Enzo Doria04/2014
48276*5^155454+7108659Lelio R Paula11/2014
482810^108656+79108657Lelio R Paula02/2017
482910^108656-50001108656Patrick De Geest03/2017
48302^360918-35108648Lelio R Paula01/2012
48314*10^108646-47108647Robert Price10/2021
4832(11*2^360886-1)/7108638Lelio R Paula03/2014
48333*10^108624-49108625Robert Price07/2018
4834(2^360831+666)/2108621Stefano Morozzi09/2020
4835(134*10^108610+7)/3108612Robert Price02/2020
48362*10^108609+29108610Robert Price02/2021
4837(10^108604+7)/71/191108600Alfred Reich06/2021
4838(2^360742+3222)/2108594Stefano Morozzi09/2020
48392^360706-458903108584Enzo Doria04/2015
484031112^3087+3087^31112108567Hans Havermann11/2020
48412^360641-113185108564Enzo Doria07/2014
4842(29*10^108559-71)/3108560Robert Price07/2021
48432^360618+75019108557Enzo Doria04/2016
4844(14*10^108545-221)/9108546Robert Price04/2018
4845(44*10^108544-233)/9108545Robert Price01/2019
48463*5^155286+2108541Lelio R Paula11/2014
48477^128422+4108530Lelio R Paula11/2014
48487^128421-80108529Lelio R Paula03/2017
48492^360497+53807108521Yves Minet07/2010
48502^360468-4559108512Yves Minet03/2019
4851(2^360451+578)/2108507Stefano Morozzi09/2020
48522^360366+1459108481Lelio R Paula09/2011
48532^360364-1499108481Yves Minet05/2013
485425662^16871+16871^25662108477Hans Havermann10/2020
485525009^21748+21748^25009108475Hans Havermann10/2020
485614^94642-23108472Lelio R Paula05/2017
4857(197*10^108446-11)/3108448Robert Price03/2020
4858(2^360229+1290)/2108440Stefano Morozzi01/2021
48594*10^108412+9108413Robert Price05/2015
4860(259*10^108409-1)/3108411Robert Price12/2020
4861(2^360122+1194)/2108408Stefano Morozzi09/2020
4862133^51042-132108406Norbert Schneider02/2019
48632^360093-351103108399Enzo Doria06/2015
48642^360042+723108384Lelio R Paula01/2012
486585^56164-2108364Lelio R Paula10/2013
48662^359937-29323108352Enzo Doria07/2015
4867(2^359922+1762)/2108348Stefano Morozzi09/2020
4868(2^359903+758)/2108342Stefano Morozzi09/2020
48692^359898-19997108341Enzo Doria06/2013
4870(2^359886+2122)/2108337Stefano Morozzi09/2020
48712*5^154948-7108305Lelio R Paula11/2014
487210^108303+13108304Lelio R Paula02/2017
487310^108303-207959108303Patrick De Geest03/2017
48747*10^108300+69108301Robert Price07/2019
48752^359730+753108290Lelio R Paula12/2011
4876(8*10^108273+13)/3108274Robert Price06/2018
48772^359650-19797108266Enzo Doria06/2013
487891^55259-90^55259108255Robert Price07/2015
487910^108251+85749108252Patrick De Geest02/2021
488010^108251-50000000001108251Robert Price12/2020
488110^108251-252081108251Patrick De Geest02/2021
48824*10^108238-71108239Robert Price12/2018
48833^226845+68108233Lelio R Paula03/2017
488431836^2509+2509^31836108227Hans Havermann10/2020
48855^154822-12866108216Enzo Doria05/2014
4886(9*2^359480+1)/5108215Lelio R Paula03/2014
48872^359454-177108207Lelio R Paula12/2011
4888(19*10^108184+191)/3108185Robert Price05/2019
48896^139022-59108181Lelio R Paula02/2017
4890(19*10^108176-43)/3108177Robert Price05/2019
48912^359352-179108176Lelio R Paula12/2011
48922^359338-1858781108172Enzo Doria04/2016
489312^100230-97108167Lelio R Paula03/2017
489427028^10043+10043^27028108163Hans Havermann11/2020
4895(25*2^359297-1)/137108159Lelio R Paula03/2014
4896(2^359262-509203)/9108148Lelio R Paula12/2013
489726583^11702+11702^26583108147Hans Havermann11/2020
4898(3^226648-8)/352715633108131Lelio R Paula12/2013
48996^138956-59108129Lelio R Paula02/2017
49002^359184+30285108126Lelio R Paula04/2017
490113^97059+10108119Lelio R Paula03/2017
49022^359137-81108112Lelio R Paula12/2011
4904(15185*2^359105-1)/567108103Lelio R Paula05/2015
49032^359110-11655108103Lelio R Paula04/2017
49052^359069-933075108091Paul Bourdelais06/2021
490626227^13222+13222^26227108090Hans Havermann10/2020
49078*6^138875+5108067Lelio R Paula11/2014
49082^358987-216919108066Enzo Doria05/2014
4909(2^358977+2714)/2108063Stefano Morozzi09/2020
491039^67918-67918^39108062Norbert Schneider02/2017
491124^78283-1*78283^24108048Dylan Delgado12/2019
491225282^18767+18767^25282108040Hans Havermann11/2020
49132^358785-16933108006Enzo Doria05/2013
4914(2^358783+5)/33383108000Lelio R Paula12/2013
49156^138770-77107985Lelio R Paula02/2017
4916(2^358727-1017)/94178479107980Lelio R Paula12/2013
491710^107976+19107977Lelio R Paula02/2017
491810^107976-202103107976Patrick De Geest03/2017
49192^358684+75781107975Enzo Doria04/2016
492024928^21411+21411^24928107955Hans Havermann10/2020
492199^54094+2107952Lelio R Paula06/2013
4922(2^358583-9)/391107942Lelio R Paula12/2013
4923(2^358562+838)/2107938Stefano Morozzi02/2021
49242^358538+55107931Lelio R Paula12/2011
49252^358517-109009107925Enzo Doria03/2014
492626395^12258+12258^26395107914Hans Havermann10/2020
49273^226159+104107906Lelio R Paula03/2017
49282^358310-11655107863Lelio R Paula03/2017
4929(68*10^107852-329)/9107853Robert Price03/2021
49302^358275-112987107852Enzo Doria07/2014
49313^226038+4107848Tyler NeSmith01/2021
49322^358233-20005107839Enzo Doria06/2013
49332^358194+175107828Lelio R Paula12/2011
4934107^53125-106107812Norbert Schneider12/2016
4935(25*10^107804+161)/3107805Robert Price09/2019
49363^225922-2107793Lelio R Paula10/2013
493712^99874-95107783Lelio R Paula03/2017
4938(2^358042+3042)/2107782Stefano Morozzi09/2020
49392^358030-171107778Lelio R Paula12/2011
494011^103488-4170107772Enzo Doria12/2012
49412^357930-4547107748Yves Minet03/2019
49422^357911-20089107742Enzo Doria06/2013
49432^357885+12857107735Yves Minet07/2010
4944(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
49457^127473+40107728Lelio R Paula03/2017
49465*2^357850+9107725Lelio R Paula09/2014
49472^357786-291191107705Enzo Doria06/2015
494828907^5320+5320^28907107705Hans Havermann10/2020
494918^85798-23107700Lelio R Paula04/2017
49503*10^107697+61107698Robert Price09/2020
4951(14*10^107694-83)/3107695Robert Price12/2018
49522^357688-1854269107675Enzo Doria09/2015
49532^357671-112225107670Enzo Doria06/2014
495434323^1370+1370^34323107662Hans Havermann11/2020
49552^357618-21005107654Enzo Doria06/2013
49562^357615-17505107653Enzo Doria05/2013
495726350^12171+12171^26350107649Hans Havermann11/2020
4958(30^72871-1)/29107638Robert Price12/2011
495925021^20026+20026^25021107631Hans Havermann11/2020
49602^357521+1870217107625Enzo Doria05/2016
49612^357477-1203107612Lelio R Paula03/2017
496226008^13693+13693^26008107583Hans Havermann10/2020
496325432^16991+16991^25432107583Hans Havermann10/2020
4964(2^357371+3726)/2107580Stefano Morozzi09/2020
49655^153894-18107568Lelio R Paula02/2017
49662^357324-69059107566Enzo Doria11/2015
4967467^40296+40296^467107563Norbert Schneider03/2019
496829446^4495+4495^29446107559Hans Havermann10/2020
4969(8*10^107556-149)/3107557Robert Price12/2021
49702^357283-869688105107553Lelio R Paula01/2017
49712^357280-16805107552Enzo Doria05/2013
497210^107547+481719107548Patrick De Geest03/2017
497310^107547-47107547Lelio R Paula02/2017
497417^87396-32107537Lelio R Paula04/2017
4975(746*10^107505+1)/9107507Robert Price03/2020
4976(2^357125+1730)/2107506Stefano Morozzi09/2020
49772^357081+107107493Lelio R Paula12/2011
49782^357058-3911107486Yves Minet04/2017
49793^225274+64107484Lelio R Paula03/2017
49805*10^107482-57107483Robert Price03/2021
498118^85619-95107476Lelio R Paula04/2017
4982(2^357013+2526)/2107472Stefano Morozzi09/2020
49833^225248-130107471Lelio R Paula03/2017
4984(5*2^356961+1)/143107455Lelio R Paula03/2014
498527029^9448+9448^27029107450Hans Havermann11/2020
49862^356935-18085107449Enzo Doria05/2013
498755396^87+87^55396107442Hans Havermann10/2020
4988(14*10^107439-137)/3107440Robert Price04/2021
498910^107409+37107410Lelio R Paula02/2017
499010^107409-329633107409Patrick De Geest03/2017
4991(2^356799+3134)/2107407Stefano Morozzi09/2020
49922^356787-109027107404Enzo Doria04/2014
4993(2^356767+78557)/5107397Lelio R Paula12/2013
49943*10^107389+77107390Robert Price09/2018
49955^153622-42107378Lelio R Paula02/2017
49962^356699-97305107378Lelio R Paula03/2017
49972^356654+85107364Lelio R Paula11/2011
49982^356641-19921107360Enzo Doria06/2013
49995*10^107355+11107356Robert Price08/2019
50002^356623-465107355Lelio R Paula03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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