PRP Records

Probable Primes Top 10000

(295158 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 ?
450144235^878+878^44235130206Hans Havermann04/2021
450232160^11171+11171^32160130187Hans Havermann04/2021
450329489^25956+25956^29489130172Hans Havermann04/2021
4504(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
450533005^8766+8766^33005130133Hans Havermann04/2021
4506(35*10^130132-611)/9130133Robert Price02/2022
4507(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
45082^432217+41130111Lelio R Paula06/2017
4509(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
4510((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
451197^65480-2130094Lelio R Paula05/2017
451236007^4102+4102^36007130094Hans Havermann04/2021
45134*10^130088-89130089Robert Price11/2018
45142^432117-113215130081Enzo Doria07/2014
4515(4*10^130080+41)/9130080Serge Batalov11/2022
45162^431804+72511129986Enzo Doria04/2016
451727902^29237-29237^27902129978Frank Doornink03/2024
4518(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
4519(13*10^129896+137)/3129897Robert Price06/2021
4520(13*10^129890+71)/3129891Robert Price06/2021
452129048^29101-29101^29048129882Norbert Schneider03/2022
452237832^2709+2709^37832129871Hans Havermann04/2021
452331055^15184+15184^31055129853Hans Havermann04/2021
4524(3^272141-3^136071+1)/7129844Serge Batalov03/2014
452531385^13702+13702^31385129833Hans Havermann04/2021
4526(13*10^129826+41)/9129827Tyler Busby02/2023
452728901^29102-29102^28901129822Norbert Schneider03/2022
4528(47*10^129789-119)/9129790Robert Price05/2019
4529(9*2^431141+1)/17129787Lelio R Paula06/2015
453025999^29384-29384^25999129730Frank Doornink03/2024
453125771^29408-29408^25771129723Frank Doornink02/2024
4532(166*10^129712+17)/3129714Robert Price07/2022
4533(29*2^430881-1)/21129709Lelio R Paula06/2015
45342^430807+1869563129686Enzo Doria05/2016
45352^430721-21429129660Enzo Doria07/2013
4536(4*10^129618+89)/3129619Robert Price08/2021
4537(10^129587-7^129587)/3129587Jon Grantham07/2023
45382^430415-276271129568Enzo Doria07/2015
453932282^10311+10311^32282129558Hans Havermann04/2021
454029486^24741+24741^29486129545Hans Havermann04/2021
4541(29*10^129543+313)/9129544Robert Price04/2021
454237095^3104+3104^37095129533Hans Havermann04/2021
454331132^14459+14459^31132129514Hans Havermann04/2021
454432582^9435+9435^32582129506Hans Havermann03/2021
454530442^17953+17953^30442129505Hans Havermann03/2021
4546(199*10^129487-7)/3129489Robert Price05/2020
45472^430142-2791721129486Enzo Doria03/2016
4548(7*10^129472-13)/3129473Robert Price07/2018
4549(8*10^129469+79)/3129470Robert Price10/2020
455031678^12213+12213^31678129463Hans Havermann04/2021
455110620^32143-10619^32143129412Norbert Schneider08/2023
4552(772*10^129406-7)/9129408Robert Price06/2022
455331100^14439+14439^31100129362Hans Havermann04/2021
455433009^8288+8288^33009129345Hans Havermann04/2021
455525895^29306-29306^25895129334Frank Doornink03/2024
4556(44^78697+43^78697)/87129333Aurel Gibier11/2023
455729675^22804+22804^29675129324Hans Havermann04/2021
455829068^28099+28099^29068129315Hans Havermann04/2021
45592^429568-21017129313Enzo Doria07/2013
4560(10^129295+83)/3129295Robert Price08/2021
4561(853*10^129274-7)/9129276Robert Price07/2021
456230958^14961+14961^30958129249Hans Havermann04/2021
4563(11*10^129239-179)/3129240Robert Price09/2018
456428659^28988+28988^28659129208Norbert Schneider02/2021
456529423^24616+24616^29423129203Hans Havermann03/2021
45662^429194-112685129201Enzo Doria06/2014
45672^429145-2780449129186Enzo Doria04/2016
456832500^9427+9427^32500129168Hans Havermann04/2021
456933577^7014+7014^33577129136Hans Havermann03/2021
45702^428892-113453129110Enzo Doria07/2014
4571(11*2^428881-7)/15129106Renaud Lifchitz03/2011
45722^428727-113959129060Enzo Doria10/2014
4573(7*2^428725-1)/13129059Lelio R Paula05/2014
4574(10^129051-31)/3129051Serge Batalov12/2014
4575(134*10^129038+7)/3129040Robert Price02/2020
45762^428564+71161129011Enzo Doria04/2016
457728781^28930+28930^28781129002Norbert Schneider02/2021
457829065^27424+27424^29065128995Hans Havermann04/2021
45792^428502-113285128992Enzo Doria07/2014
45802^428421-21373128968Enzo Doria06/2013
4581L(616787)128901Henri Lifchitz09/2008
458220^99055-3128874Paul Bourdelais12/2020
458391^65772-2128851Lelio R Paula05/2017
45842^428022+43128848Lelio R Paula05/2017
45852^427999-459397128841Enzo Doria05/2015
45862^427993+76847128839Enzo Doria05/2016
458731059^14060+14060^31059128833Hans Havermann03/2021
458810^128805+152871128806Patrick De Geest05/2021
458910^128805-10001128805Robert Price02/2021
45902^427824-1851507128788Enzo Doria08/2015
45912^427807-21469128783Enzo Doria07/2013
459229082^26783+26783^29082128772Hans Havermann04/2021
459340055^1638+1638^40055128750Hans Havermann04/2021
459411^123594-240128710Enzo Doria09/2012
45952^427504-21503128692Enzo Doria07/2013
459637727^2574+2574^37727128673Hans Havermann04/2021
459729686^21591+21591^29686128668Hans Havermann04/2021
459810^128668-70000000001128668Robert Price08/2021
45992^427420+91128667Lelio R Paula05/2017
46008*10^128651-37128652Robert Price03/2022
4601(68*10^128645-257)/9128646Robert Price07/2019
46022^427269-113635128621Enzo Doria08/2014
46032^427130+1877569128579Enzo Doria08/2016
46042^427068+20011128561Enzo Doria06/2023
46052^427016-115349128545Enzo Doria07/2015
4606(4*10^128510+137)/3128511Robert Price03/2018
46072^426889-112879128507Enzo Doria06/2014
46082^426804+1869931128481Enzo Doria05/2016
46092^426750+77635128465Enzo Doria05/2016
461027708^28913-28913^27708128450Frank Doornink03/2024
461136988^2969+2969^36988128445Hans Havermann03/2021
461236664^3185+3185^36664128439Hans Havermann03/2021
461332618^8649+8649^32618128416Hans Havermann04/2021
461428883^27874+27874^28883128391Hans Havermann04/2021
46152^426425-91128367Lelio R Paula05/2017
4616(15*2^426398-1)/11128359Lelio R Paula05/2014
46172^426352+74971128345Enzo Doria04/2016
4618(199*10^128343-7)/3128345Robert Price05/2020
46194*10^128343-21128344Robert Price09/2018
4620(65*10^128338+493)/9128339Robert Price08/2021
462135632^3997+3997^35632128337Hans Havermann04/2021
46222^426300-1863689128330Enzo Doria03/2016
46232^426293+1881017128327Enzo Doria11/2016
4624(88*10^128324-637)/9128325Robert Price11/2020
4625(491*10^128285+31)/9128287Robert Price04/2022
462639103^1908+1908^39103128281Hans Havermann04/2021
46272^426043+35128252Robert Price11/2015
4628(4*10^128244-19)/3128245Robert Price03/2018
462926220^29021-29021^26220128234Frank Doornink03/2024
463035489^4102+4102^35489128222Hans Havermann04/2021
463134721^4926+4926^34721128208Hans Havermann04/2021
4632(305*10^128198+1)/9128200Robert Price02/2020
46332^425808-459959128181Enzo Doria06/2015
463430632^15291+15291^30632128178Hans Havermann04/2021
463535981^3648+3648^35981128167Hans Havermann04/2021
46362^425627-113605128127Enzo Doria08/2014
4637(4*10^128109+119)/3128110Robert Price12/2021
4638(22*10^128094+53)/3128095Robert Price07/2019
4639(86*10^128086-221)/9128087Robert Price09/2019
464018565^30002-30002^18565128070Norbert Schneider01/2015
4641(2^425287-9)/2737128021Lelio R Paula05/2015
4642(3*2^425233-1)/25128007Lelio R Paula05/2014
4643Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
46442^425205+4911128000Marek Hubal02/2017
464529241^23836+23836^29241127995Hans Havermann04/2021
46462^425118-113663127974Enzo Doria08/2014
4647(86*10^127967-329)/9127968Robert Price01/2020
46482^425061+1869761127957Enzo Doria05/2016
4649746^44541+44541^746127955Norbert Schneider07/2019
465030236^17043+17043^30236127946Hans Havermann03/2021
46512^424938+212419127920Enzo Doria08/2023
46522^424918-21141127914Enzo Doria07/2013
4653(62*10^127903+91)/9127904Robert Price07/2021
46542^424864-29489127897Enzo Doria08/2015
465530438^15893+15893^30438127877Hans Havermann02/2021
4656(97*10^127858-1)/3127860Serge Batalov12/2014
465728929^26258+26258^28929127845Hans Havermann03/2021
465830563^15220+15220^30563127828Hans Havermann03/2021
46592^424632-2786639127827Enzo Doria03/2016
466010^127821-700001127821Robert Price08/2021
46612^424577-113755127811Enzo Doria09/2014
4662(7*2^424512-1)/3127792Lelio R Paula05/2014
4663(56*10^127752+691)/9127753Robert Price05/2019
466411^122629-720127705Enzo Doria11/2012
466522*10^127645+3127647Robert Price01/2020
466628715^27844+27844^28715127631Hans Havermann03/2021
4667(56*10^127612+187)/9127613Robert Price10/2021
4668(5*36^81995+821)/7127609Eric Chen01/2021
46694*10^127562-39127563Robert Price09/2020
467032595^8186+8186^32595127547Hans Havermann03/2021
46712^423696-21429127546Enzo Doria07/2013
46722^423664-1864559127536Enzo Doria03/2016
467337889^2322+2322^37889127530Hans Havermann03/2021
467437668^2429+2429^37668127523Hans Havermann03/2021
46753^267267-4127519Henri Lifchitz10/2014
4676fibonacci(610144)-2127513Jon Grantham08/2023
467726253^28852-28852^26253127503Frank Doornink03/2024
4678(103*10^127491+17)/3127493Robert Price08/2020
467929376^21869+21869^29376127487Hans Havermann03/2021
468031186^12241+12241^31186127483Hans Havermann02/2021
4681(19^99689+5^99689)/24127477Robert Price09/2013
468227069^28754-28754^27069127452Frank Doornink01/2024
4683(21*2^423372+1)/101127447Lelio R Paula05/2014
468430594^14645+14645^30594127446Hans Havermann03/2021
46852^423328-21537127435Enzo Doria07/2013
4686(67*10^127413-7)/3127415Robert Price01/2020
4687(5*34^83193+700233)/11127408Eric Chen08/2023
4688(2*10^127407+73)/3127407Robert Price09/2020
4689(2^423165-7)/25127384Lelio R Paula05/2015
4690(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
4691(4*10^127349+17)/3127350Tyler Busby01/2023
469229512^20647+20647^29512127341Hans Havermann03/2021
46932^422987-3001935127332Paul Bourdelais07/2023
4694(112*10^127324+17)/3127326Robert Price03/2020
469529565^20252+20252^29565127321Hans Havermann03/2021
4696fibonacci(609165)-3127308Jon Grantham08/2023
4698(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
4697(5^182099-3^182099)/2127282Kellen Shenton05/2022
4699(16*10^127259+197)/3127260Robert Price04/2019
4700(26*10^127240+61)/3127241Robert Price10/2019
4701(234483*27^88884-145)/26127230Curtis Bright05/2015
47022^422515-114997127190Enzo Doria06/2015
47035*10^127179-3127180Robert Price07/2015
470431678^10343+10343^31678127176Hans Havermann03/2021
4705(44*10^127169-233)/9127170Robert Price01/2019
470634947^4352+4352^34947127162Hans Havermann03/2021
47076*10^127158+19127159Robert Price11/2021
470830469^14902+14902^30469127155Hans Havermann03/2021
47095*10^127153+77127154Robert Price12/2018
471029941^17620+17620^29941127130Hans Havermann02/2021
471131607^10516+10516^31607127119Hans Havermann03/2021
4712(19*10^127118-97)/3127119Robert Price10/2021
4713(29*10^127111+691)/9127112Robert Price08/2021
4714736^44335+44335^736127104Norbert Schneider07/2019
471533040^7023+7023^33040127090Hans Havermann03/2021
4716(4*10^127081+167)/9127081Robert Price03/2022
471729748^18661+18661^29748127052Hans Havermann03/2021
471827905^28578-28578^27905127049Frank Doornink03/2024
4719-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
4720(78^67141-1)/77127036Paul Bourdelais09/2017
4721(14*10^127014-137)/3127015Robert Price04/2021
472231436^10965+10965^31436127002Hans Havermann03/2021
472328905^24758+24758^28905127001Hans Havermann03/2021
47242^421860-113285126993Enzo Doria07/2014
4725(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
4726(2^421827-7)/11126982Lelio R Paula05/2015
472726268^28729-28729^26268126966Frank Doornink03/2024
472811^121910-840126957Enzo Doria12/2012
4729(56*10^126935+187)/9126936Robert Price10/2021
473028915^24538+24538^28915126933Hans Havermann03/2021
4731(29*10^126928-77)/3126929Robert Price02/2020
4732(259*10^126919-1)/3126921Robert Price12/2020
473310^126919+204567126920Patrick De Geest05/2021
4734(2^421617+100280245065)126920Paul Bourdelais05/2022
473510^126919-100001126919Robert Price07/2020
473628340^28503+28503^28340126907Norbert Schneider02/2021
47372^421534-3001935126895Paul Bourdelais07/2023
4738(71^68539+1)/72126882Paul Bourdelais09/2017
4739(5*10^126871-119)/3126872Robert Price03/2018
4740331^50339-10004126846Enzo Doria07/2012
47412^421363-2790757126843Enzo Doria03/2016
4742(106*10^126839-1)/3126841Serge Batalov12/2014
474337938^2203+2203^37938126828Hans Havermann03/2021
4744(13*10^126819+77)/9126820Robert Price07/2022
4745(7*2^421243+1)/39126807Lelio R Paula05/2014
4747(14*10^126784-83)/3126785Robert Price12/2018
47462^421169-3001935126785Paul Bourdelais07/2023
47482^421161-286183126783Enzo Doria06/2015
474926733^28628-28628^26733126738Frank Doornink03/2024
4750(106*10^126726+17)/3126728Robert Price04/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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