PRP Records

Probable Primes Top 10000

(295461 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 ?
956310^100000+15136771100001Robert Price09/2019
956410^100000+15219873100001Robert Price10/2019
956510^100000+15274039100001Robert Price10/2019
956610^100000+15394069100001Robert Price10/2019
956710^100000+15547119100001Robert Price10/2019
956810^100000+15932923100001Robert Price11/2019
956910^100000+16345467100001Robert Price12/2019
957010^100000+16672143100001Robert Price01/2020
957110^100000+16731939100001Robert Price02/2020
957210^100000+16907049100001Robert Price03/2020
957310^100000+17652523100001Robert Price05/2020
957410^100000+18047167100001Robert Price05/2020
957510^100000+18471819100001Robert Price06/2020
957610^100000+18494793100001Robert Price07/2020
957710^100000+18762609100001Robert Price07/2020
957810^100000+19204141100001Robert Price08/2020
957910^100000+19349793100001Robert Price08/2020
958010^100000+19495699100001Robert Price09/2020
958110^100000+19668927100001Robert Price09/2020
958210^100000+19704313100001Robert Price09/2020
953210^100000+19956229100001Robert Price09/2020
953310^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
953410^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
953510^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
953610^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
953710^100000+20234607100001Robert Price10/2020
953810^100000+20752303100001Robert Price11/2020
953910^100000+20774041100001Robert Price11/2020
954010^100000+20854741100001Robert Price11/2020
954110^100000+20908917100001Robert Price11/2020
954210^100000+20994793100001Robert Price11/2020
954310^100000+21354249100001Robert Price12/2020
954410^100000+21455559100001Robert Price12/2020
954510^100000+21538873100001Robert Price12/2020
954610^100000+21830901100001Robert Price01/2021
954710^100000+21842629100001Robert Price01/2021
954810^100000+21930861100001Robert Price01/2021
954910^100000+22092943100001Robert Price03/2021
955010^100000+22278417100001Robert Price03/2021
955110^100000+22388581100001Robert Price03/2021
955210^100000+22390933100001Robert Price03/2021
955310^100000+22436169100001Robert Price03/2021
955410^100000+22714557100001Robert Price04/2021
955510^100000+22847671100001Robert Price04/2021
955610^100000+23178567100001Robert Price05/2021
955710^100000+23332003100001Robert Price05/2021
955810^100000+23414571100001Robert Price05/2021
955910^100000+23529979100001Robert Price05/2021
956010^100000+23749243100001Robert Price06/2021
956110^100000+23821771100001Robert Price06/2021
956210^100000+24179307100001Robert Price07/2021
950110^100000+64067989100001Robert Price07/2024
950210^100000+64537969100001Robert Price07/2024
950310^100000+64684401100001Robert Price07/2024
950410^100000+65078241100001Robert Price07/2024
950510^100000+65108589100001Robert Price07/2024
950610^100000+65321659100001Robert Price07/2024
950710^100000+65530773100001Robert Price07/2024
950810^100000+60000000+2860971100001Robert Price07/2024
950910^100000+60000000+2993517100001Robert Price07/2024
951010^100000+60000000+3372931100001Robert Price07/2024
951110^100000+60000000+3571039100001Robert Price07/2024
951210^100000+60000000+3701257100001Robert Price07/2024
951310^100000+60000000+3765727100001Robert Price07/2024
951410^100000+40000000+8024501100001Robert Price07/2024
951510^100000+40000000+8234057100001Robert Price07/2024
951610^100000+40000000+8313399100001Robert Price07/2024
951710^100000+40000000+8831817100001Robert Price07/2024
951810^100000+40000000+9154433100001Robert Price07/2024
951910^100000+40000000+9457031100001Robert Price07/2024
952010^100000+40000000+9741063100001Robert Price07/2024
952110^100000+46334983100001Robert Price07/2024
952210^100000+46408929100001Robert Price07/2024
952310^100000+46477587100001Robert Price07/2024
952410^100000+46484211100001Robert Price07/2024
952510^100000+46496169100001Robert Price07/2024
952610^100000+46629949100001Robert Price07/2024
952710^100000+46655869100001Robert Price07/2024
952810^100000+47167941100001Robert Price07/2024
952910^100000+47225599100001Robert Price07/2024
953010^100000+47784519100001Robert Price07/2024
953110^100000+47831149100001Robert Price07/2024
958510^99999+309403100000Daniel Heuer01/2004
958610^100000-260199100000Patrick De Geest01/2010
95832^332192+10192681100000Sujan Das06/2022
95841610172603059^8192+1610172602878^8192100000Youcef Lemsafer01/2023
958710^99999-5951199999Patrick De Geest07/2009
958810^99998+23543799999Patrick De Geest02/2020
958910^99998-28658799998Patrick De Geest02/2020
959010^99997+7229799998Patrick De Geest02/2020
959110^99997-40262799997Patrick De Geest02/2020
959210^99996+27985399997Patrick De Geest02/2020
959310^99997-50000000199997Robert Price12/2020
959410^99996-9496199996Patrick De Geest02/2020
959510^99995+5463399996Patrick De Geest02/2020
959610^99995-10142999995Patrick De Geest02/2020
959710^99994+11727199995Patrick De Geest02/2020
959810^99994-45228999994Patrick De Geest02/2020
959910^99993+37131199994Patrick De Geest02/2020
960010^99993-18649199993Patrick De Geest02/2020
960110^99992+1743199993Patrick De Geest02/2020
960210^99992-2860799992Patrick De Geest02/2020
960310^99991+12539199992Patrick De Geest02/2020
960410^99991-20457399991Patrick De Geest02/2020
960510^99990+1389999991Patrick De Geest02/2020
960610^99990-811199990Patrick De Geest02/2020
96072^332141-11307399985Enzo Doria07/2014
9608(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
96096*10^99979-7999980Robert Price03/2022
9611(3^209561+2)/72810125599978Lelio R Paula09/2013
961023827^15702+15702^2382799978Hans Havermann04/2018
96122^332085+186589799968Enzo Doria03/2016
9613(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
96142^332023+19199949Lelio R Paula02/2011
9615(6271^26321-1)/627099946Serge Batalov06/2022
96167*10^99944+2799945Robert Price11/2020
96173188^28523-28523^318899931Norbert Schneider06/2023
96182^331938+7114999924Enzo Doria04/2016
96192^331932-7879599922Lelio R Paula09/2016
96202^331921+77199919Lelio R Paula01/2013
96217947^25618-25618^794799916Norbert Schneider08/2023
9622(3^209419-2)/513275599912Lelio R Paula09/2013
962321657^23042-23042^2165799901Norbert Schneider04/2024
96242^331860-11498999900Enzo Doria05/2015
962523*31^66974+297099884Eric Chen04/2024
96262^331746-1165599866Lelio R Paula09/2016
962711^95891-2899861Lelio R Paula08/2016
9628(2^331694-5)/1199849Lelio R Paula10/2013
9629(3^209246+7)/6499834Lelio R Paula09/2013
963025062^9617+9617^2506299823Hans Havermann04/2018
963115^84866-5299811Lelio R Paula08/2016
963213^89600+3099810Lelio R Paula08/2016
96332^331527+10028024506599800Paul Bourdelais10/2021
963422950^22309+22309^2295099798Hans Havermann03/2018
96355^142772-3899794Lelio R Paula08/2016
9636(7482^25759-1)/748199787Serge Batalov06/2022
9637(23*2^331459+1)/47599778Lelio R Paula11/2013
96382^331416-331416+199767Robert Price10/2014
96392^331256-5799718Lelio R Paula12/2012
964028192^3443+3443^2819299714Hans Havermann03/2018
96412^331185+73799697Lelio R Paula01/2013
9642(4*10^99693+149)/999693Robert Price03/2017
96432^331154+188052799688Enzo Doria10/2016
9645(19^77951+1)/2099679Paul Bourdelais03/2010
964424354^12385+12385^2435499679Hans Havermann03/2018
96462^331110+187045999675Enzo Doria05/2016
96475*2^331075+799665Lelio R Paula08/2014
964825776^7351+7351^2577699659Hans Havermann02/2018
9649(16*10^99656-31)/399657Robert Price03/2016
9650(6059^26347-1)/605899652Serge Batalov06/2022
9651(15544^23773-1)/1554399642Serge Batalov06/2022
96532^330968+34599632Lelio R Paula09/2016
9652(2^330969+690)/299632Stefano Morozzi09/2020
96552*5^142528-799624Lelio R Paula11/2014
96542^330942+7732999624Enzo Doria05/2016
965614^86914-9999615Lelio R Paula08/2016
9657(19*2^330902+1)/7799611Lelio R Paula11/2013
965822971^21692+21692^2297199610Hans Havermann03/2018
96592^330845+7168799595Enzo Doria04/2016
9660(26667^22501-1)/2666699585Serge Batalov06/2022
9661(23*2^330770+1)/399573Lelio R Paula11/2013
966224494^11613+11613^2449499567Hans Havermann03/2018
96632^330735+841599562Lelio R Paula09/2016
96642^330720+7407199557Enzo Doria04/2016
9665(10405^24781-1)/1040499548Serge Batalov06/2022
966731^66738-299531Lelio R Paula09/2013
9666(9002^25171-1)/900199531Serge Batalov06/2022
9668(5023^26893-1)/502299527Serge Batalov06/2022
96697*3^208567+499513Lelio R Paula08/2014
9670(15881^23689-1)/1588099511Serge Batalov06/2022
9671(13*10^99508+47)/399509Robert Price01/2017
96722^330553+77999507Lelio R Paula01/2013
967315^84606-9499505Lelio R Paula08/2016
9674(10^99497+173)/399497Robert Price05/2021
96759*10^99493-4399494Robert Price09/2021
96766^127858+4799493Lelio R Paula08/2016
96775^142337+4899490Lelio R Paula08/2016
96787^117724-2099489Lelio R Paula08/2016
9679(559^36209-1)/55899479Serge Batalov06/2022
9680(13470^24091-1)/1346999477Serge Batalov06/2022
9681(29*10^99474-17)/399475Erik Branger09/2014
9682(185*10^99466-11)/399468Robert Price10/2020
9683(2^330410+2038)/299464Stefano Morozzi09/2020
9684(9*2^330407-1)/799463Lelio R Paula03/2014
9685(516*32^66077-175)/3199458Eric Chen04/2023
9686(2863^28771-1)/286299453Serge Batalov06/2022
9687(2^330373+2114)/299452Stefano Morozzi09/2020
9688(68*10^99441+7)/399443Robert Price03/2016
968910^99434+15557199435Patrick De Geest04/2020
969010^99434-12345678999434Robert Price02/2020
969110^99434-19123799434Patrick De Geest04/2020
969246^59791-45^5979199418Jean-Louis Charton01/2013
969323839^14802+14802^2383999417Hans Havermann02/2018
9694(2*10^99408+529)/999408Robert Price01/2017
9695(2^330216+3510)/299405Stefano Morozzi09/2020
969653^57646-299398Lelio R Paula09/2013
96972^330165+187002599390Enzo Doria05/2016
96987*10^99383+9799384Robert Price09/2021
96992^330142-15599383Lelio R Paula12/2012
97002^330088-11525999367Enzo Doria06/2015
970124216^12671+12671^2421699354Hans Havermann01/2018
9702Phi(200548,10)/320876999354Makoto Kamada04/2019
9703(746*10^99303+1)/999305Robert Price02/2017
97043^208107+4099293Lelio R Paula08/2016
97052^329843+21134399293Enzo Doria08/2023
9706(3939^27617-1)/393899291Serge Batalov06/2022
9707(5*2^329833-1)/36999288Lelio R Paula02/2014
97088*3^208093+599287Lelio R Paula08/2014
97095^142043+5699284Lelio R Paula08/2016
9710(13*10^99282-157)/999283Robert Price05/2021
9711(10^99284+7)/53/6799281Alfred Reich06/2021
971222*10^99275+799277Robert Price04/2016
97132^329778+187618999274Enzo Doria07/2016
9714(149557^19321-1)/(149557^139-1)99264Ryan Propper11/2023
9715(6580^25997-1)/657999259Serge Batalov06/2022
9716(2249^29611-1)/224899253Serge Batalov06/2022
9717(10^99239-13)/399239Robert Price02/2017
9718(1199^32233-1)/119899237Serge Batalov06/2022
97203^207987+6299236Lelio R Paula08/2016
9719(62*10^99235+91)/999236Robert Price07/2021
97212^329638+4999231Lelio R Paula12/2012
97227^117413-1899226Lelio R Paula08/2016
97232^329586-45890399216Enzo Doria04/2015
9724(6290^26119-1)/628999214Serge Batalov06/2022
97262^329553+10199206Lelio R Paula12/2012
9725(21297^22921-1)/2129699206Serge Batalov06/2022
97272^329551-11289799205Enzo Doria06/2014
9728(3^207925+7)/5099204Lelio R Paula09/2013
97296^127458-1799399182Enzo Doria03/2013
973027197^4428+4428^2719799166Hans Havermann10/2017
9731(46*10^99143-1)/999144Robert Price12/2014
9732(64*10^99135+161)/999136Robert Price08/2022
97337*10^99133+6999134Robert Price10/2017
9734(21701^22861-1)/2170099132Serge Batalov06/2022
973518^78968-306599127Enzo Doria03/2013
973625927^6654+6654^2592799122Hans Havermann10/2017
973787915!4+1699122Robert Price09/2019
97382^329259+18999117Lelio R Paula12/2012
97398*10^99113+3999114Robert Price01/2017
97406^127364+7799109Lelio R Paula08/2016
9741(82*10^99103+143)/999104Robert Price06/2021
9742(11414^24421-1)/1141399083Serge Batalov06/2022
9743(2^329135+1110)/299080Stefano Morozzi09/2020
9744(22089^22807-1)/2208899074Serge Batalov06/2022
9745(59*10^99069+391)/999070Robert Price03/2021
9746(797*10^99061-41)/999063Robert Price04/2022
97472^329058-28768199057Harrison Mesh06/2022
97486^127285+1399047Lelio R Paula08/2016
9749(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
97502^329007+7328399041Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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