PRP Records

Probable Primes Top 10000

(301901 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 ?
350121^128327-20^128327169677Jean-Louis Charton11/2014
35022^563583+89169656Stefano Morozzi04/2021
35032^563311+215813169574Enzo Doria11/2023
3504(4*10^169559+83)/3169560Robert Price02/2018
3505(194*10^169461-17)/3169463Robert Price09/2020
35062^562749+2793047169405Enzo Doria02/2016
3507(154*10^169337-1)/9169339Serge Batalov12/2014
3508(109*10^169337+11)/3169339Robert Price06/2022
3509(56*10^169311+691)/9169312Robert Price05/2019
35102^562369-29503169290Enzo Doria08/2015
3511(17*10^169283+19)/9169284Robert Price03/2021
3512390151#-2322911169082Hayden Chesnut07/2024
351310^169074-5000000001169074Robert Price09/2022
35148*10^169071+59169072Robert Price11/2021
3515(10^169044+173)/3169044Robert Price05/2021
3516(22*10^169019+383)/9169020Robert Price05/2018
3517(64*10^168935+143)/9168936Robert Price05/2021
3518(22*10^168906+47)/3168907Robert Price06/2021
35195*10^168807+87168808Robert Price02/2019
3520(77*10^168803-149)/9168804Robert Price03/2022
35214*10^168788-47168789Robert Price10/2021
3522(154*10^168781+17)/9168783Robert Price06/2022
3523(418*10^168751-31)/9168753Robert Price05/2022
3524(29*10^168711+691)/9168712Robert Price08/2021
35252^560405-39943168699Enzo Doria09/2015
3526(397*10^168634+17)/9168636Robert Price03/2022
35272^560189+36587168634Enzo Doria09/2024
352889*10^168614-7168616Robert Price04/2020
3529(23*10^168608-83)/3168609Robert Price08/2019
3530(94*10^168541+11)/3168543Robert Price04/2020
35312^559686-350471168483Enzo Doria06/2015
35322^559672-1855889168479Enzo Doria09/2015
3533(5*10^168379-473)/9168379Robert Price01/2018
35342024^50920+3168353Martin Hopf01/2024
35352^559000-59939168276Enzo Doria11/2015
35362^558830+25009168225Enzo Doria11/2023
3537(16*10^168181+41)/3168182Robert Price03/2019
3538(19*10^168173+77)/3168174Robert Price05/2019
3539(74*10^168170+529)/9168171Robert Price02/2022
35402^558640-114149168168Enzo Doria12/2014
35412^558498-1849277168125Enzo Doria08/2015
35422^558476-1850249168119Enzo Doria08/2015
3543(7*10^168067+71)/3168068Robert Price05/2018
35442^558150-1852211168020Enzo Doria08/2015
35452^558125-113661168013Enzo Doria09/2014
3546393^64747-392^64747167980Jean-Louis Charton08/2012
3547(8*10^167965-11)/3167966Robert Price07/2023
35482^557916+216151167950Enzo Doria12/2023
3549(13*10^167911+179)/3167912Robert Price11/2018
3550(26*10^167861-167)/3167862Robert Price10/2019
355136^107827-107827167812Kellen Shenton06/2023
355232027^37242-37242^32027167795Frank Doornink01/2024
355339^105456+2167788Robert Price04/2015
35542^557322+217519167771Enzo Doria01/2024
3555(28^115877-1)/27167691Paul Bourdelais12/2017
35566*10^167662-13167663Robert Price07/2022
355710^167639+121911167640Patrick De Geest07/2018
355810^167639-8001167639Robert Price03/2018
35592^556504-462059167525Enzo Doria07/2015
3560(88*10^167522-637)/9167523Robert Price11/2020
35615*10^167510+9167511Robert Price08/2015
35627*10^167437-93167438Robert Price08/2020
3563(43^102451-1)/7138097213378082167335Paul Vanderveen05/2025
356425455^37978-37978^25455167323Frank Doornink01/2024
356511^160663+6167314Paul Bourdelais02/2021
3566(7*10^167308-493)/9167308Robert Price04/2021
35672^555759+74333167301Enzo Doria07/2023
356826084^37871-37871^26084167253Frank Doornink03/2024
35692^555343+1874333167175Enzo Doria06/2016
35702^555210-461261167135Enzo Doria07/2015
35719*10^166996+59166997Robert Price01/2020
3572(68*10^166976-329)/9166977Robert Price03/2021
3573(64*10^166901+683)/9166902Robert Price06/2022
35742^554372+1880527166883Enzo Doria11/2016
35752^554299+72173166861Enzo Doria04/2016
3576(185*10^166837+7)/3166839Robert Price03/2020
3577(14*10^166813+139)/9166814Robert Price11/2021
357826084^37767-37767^26084166794Frank Doornink03/2024
35792^554037-2797063166782Enzo Doria03/2016
358031861^37028-37028^31861166747Frank Doornink01/2024
3581(49*10^166721-139)/9166722Robert Price03/2019
35822*10^166646+69166647Robert Price06/2020
35832^553484-29819166616Enzo Doria08/2015
3584(188*10^166611+7)/3166613Robert Price03/2020
35852^553383-2784217166585Enzo Doria10/2015
35862^553069+76427166491Enzo Doria05/2016
358725218^37819-37819^25218166469Frank Doornink12/2023
35882*10^166458+51166459Robert Price05/2018
3589589^60089-588^60089166454Jean-Louis Charton09/2012
359025214^37799-37799^25214166378Frank Doornink11/2023
359111^159756-2424166369Mike Oakes06/2010
35922^552649-361275166364Enzo Doria05/2014
35932^552628-113669166358Enzo Doria09/2014
3594(19*10^166325+137)/3166326Robert Price03/2022
359510^166324+550603166325Patrick De Geest07/2018
359610^166324-801166324Robert Price02/2018
3597(85*10^166297-1)/3166299Robert Price02/2020
3598(19*10^166280-7)/3166281Robert Price12/2023
359925533^37726-37726^25533166263Frank Doornink02/2024
36008*10^166227+87166228Robert Price10/2019
36012^552137+1879397166210Enzo Doria09/2016
3602262273205671539190984629()252475512364409752762433166141Anonymous01/2025
3603490079063773165613318095()218182139934160868002603166141Anonymous01/2025
3604140717254840416411192803()712689271538459396766869166140Anonymous01/2025
3605122398296040696255481419()271117913237372866926417166140Anonymous01/2025
3606(103*10^166126+11)/3166128Robert Price01/2021
3607(22*10^166077+179)/3166078Robert Price02/2022
3608(23^121949-1)/22166061Paul Bourdelais10/2017
36092^551576+236221166041Enzo Doria05/2025
36102^551542+19249166031Payam Samidoost08/2002
36112^551535-23821166029Enzo Doria08/2013
36122^551507-23557166021Enzo Doria08/2013
361332030^36841-36841^32030165990Frank Doornink01/2024
361410^165947-7000000001165947Robert Price12/2021
36154*10^165938-47165939Robert Price10/2021
36167*10^165916-3165917Robert Price08/2015
3617(29*10^165796+67)/3165797Robert Price12/2019
361881^86837-80^86837165728Robert Price01/2015
3619(71*10^165716-17)/9165717Serge Batalov01/2023
3620fibonacci(792909)+3165708Jon Grantham08/2023
3621(71*10^165663-539)/9165664Robert Price07/2019
362225682^37567-37567^25682165657Frank Doornink02/2024
36232^550270-69551165648Enzo Doria12/2015
36242^550250+29329165642Enzo Doria03/2024
3625(202*10^165569-13)/9165571Robert Price01/2020
36262^550000-23625165567Enzo Doria08/2013
362731688^36783-36783^31688165557Frank Doornink01/2024
36282^549675-1852057165469Enzo Doria08/2015
36292^549663+212543165466Enzo Doria08/2023
3630(3^549633)%(2^549633)165456Henri Lifchitz06/2025
3631(529*10^165394-7)/9165396Robert Price08/2021
363226253^37424-37424^26253165384Frank Doornink03/2024
3633-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
3634(28*10^165358-1)/9165359Serge Batalov10/2014
36352^549278+1879669165350Enzo Doria09/2016
3636(7*10^165350-439)/9165350Robert Price02/2018
36372^549252-351269165342Enzo Doria06/2015
36382^549221+335931165332Enzo Doria09/2024
363967*10^165327-9165329Robert Price03/2021
3640(14*10^165282+73)/3165283Robert Price12/2018
3641(8*10^165283-629)/9165283Robert Price01/2022
36422^549049+2797607165281Enzo Doria04/2016
3643(218*10^165258+7)/9165260Robert Price06/2022
3644(7*10^165239+107)/3165240Robert Price02/2018
36452^548880+23961165230Enzo Doria10/2023
36465*2^548778+3165200Jon Grantham07/2023
3647(44^100511-1)/43165184Paul Bourdelais11/2017
3648(7*10^165134+107)/3165135Robert Price02/2018
3649(301*10^165082+23)/9165084Robert Price06/2021
3650(23*10^165060-83)/3165061Robert Price08/2019
36517*10^165023-27165024Robert Price11/2022
3652(76*10^164984+77)/9164985Robert Price10/2019
365331058^36715-36715^31058164931Frank Doornink01/2024
3654(4*10^164929-211)/9164929Robert Price03/2022
365510^164878-500001164878Robert Price03/2022
36569*10^164791-89164792Robert Price04/2020
3657(2^788414)%F(788414)164769Henri Lifchitz05/2025
36582^547178-1856501164717Enzo Doria10/2015
365911^158160-60164707Enzo Doria07/2012
3660(26*10^164643-167)/3164644Robert Price10/2019
3661(10^164643+83)/3164643Robert Price08/2021
36622^546398-59201164483Enzo Doria10/2015
36632^546332-114893164463Enzo Doria05/2015
366436087^36087-36080^36080164462Henri Lifchitz08/2024
366532003^36504-36504^32003164458Frank Doornink01/2024
3666(65*10^164427+277)/9164428Robert Price08/2021
36672^545958+1876189164350Enzo Doria07/2016
36682^545878-49841164326Enzo Doria10/2015
3669(10^164284+77)/3164284Robert Price01/2018
36702^545668-4019164263Yves Minet04/2017
367110^164216+780639164217Patrick De Geest08/2021
367310^164216-50000000001164216Robert Price12/2020
367210^164216-891051164216Patrick De Geest08/2021
3674(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
3675(16*10^164122+197)/3164123Robert Price04/2019
36762^545185+76757164118Enzo Doria05/2016
36772^545076-114329164085Enzo Doria01/2015
3678(2*10^164043-143)/3164043Robert Price03/2018
3679(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
3680(29^112153+1)/30164011Lelio R Paula03/2017
36812^544757+1874777163989Enzo Doria06/2016
36822^544723+211193163978Enzo Doria08/2023
36832^544444-457199163894Enzo Doria01/2015
3684(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
36852^544264-343529163840Enzo Doria07/2015
36867*10^163780+9163781Robert Price09/2015
3687(2^783598)%L(783598)163761Henri Lifchitz05/2025
36882^543989+2793047163758Enzo Doria02/2016
3689(28*10^163709+113)/3163710Robert Price03/2020
3690(2^543398)/(543398^2)163568Henri Lifchitz05/2025
3691(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
3692L(2*543272)%(2^543272)163541Henri Lifchitz07/2025
3693(23*10^163523+301)/9163524Robert Price06/2021
3694(68*10^163521-329)/9163522Robert Price03/2021
369535820^35899+35899^35820163489Norbert Schneider11/2021
36962^542870-69551163421Enzo Doria12/2015
36972^542502+24799163310Enzo Doria10/2023
36982^542395+72533163278Enzo Doria04/2016
36992^542258+216949163236Enzo Doria12/2023
37002^542072-3683163180Yves Minet03/2017
3701fibonacci(780566)-4163129Jon Grantham08/2023
3702(682*10^163106-7)/9163108Robert Price08/2021
37032^541779-1867357163092Enzo Doria04/2016
3704(29*10^163056+313)/9163057Robert Price04/2021
37052^541476+214743163001Enzo Doria11/2023
370613^142159+14^142159-2162933Harsh Aggarwal05/2024
37078*10^162924+9162925Robert Price12/2015
37082^540905+81557162829Enzo Doria08/2016
37092^540628-2939162746Yves Minet09/2014
3710919^54919-918^54919162743Jean-Louis Charton01/2013
3711(203*10^162689+1)/3162691Robert Price03/2020
37123*10^162620-59162621Robert Price09/2018
37132^540180+26791162611Enzo Doria12/2023
37143^340694-112960162553Enzo Doria07/2014
37152^539925+81162534Henri Lifchitz11/2024
37162^539807-114081162499Enzo Doria12/2014
3717414^62093+62093^414162498Norbert Schneider03/2022
37182^539654-114893162453Enzo Doria05/2015
37199*10^162449-71162450Robert Price11/2020
37202^539617-1851583162441Enzo Doria08/2015
3721(509*10^162422+31)/9162424Robert Price08/2022
3722(91*10^162410+11)/3162412Robert Price02/2020
37232^539346+81049162360Enzo Doria07/2016
37242^539220-115499162322Enzo Doria07/2015
37252^539217-113713162321Enzo Doria09/2014
37269^170099-8^170099162316Jean-Louis Charton05/2005
37274*10^162263-39162264Robert Price09/2020
372831243^36098-36098^31243162252Frank Doornink01/2024
372931987^36000-36000^31987162180Frank Doornink01/2024
3730(115*10^162153-1)/3162155Serge Batalov12/2014
3731(10^162138+11)/3162138Serge Batalov07/2015
3732(61*10^162100-403)/9162101Robert Price10/2021
37332^538473-112723162097Enzo Doria06/2014
37342^538157+79337162002Enzo Doria06/2016
37352^538136-114749161996Enzo Doria05/2015
37362^538104+1531161986Lelio R Paula01/2013
3737(9*29^110727-1199)/14161927Curtis Bright05/2015
3738((2^179294-1)^3+2)/11161918Serge Batalov03/2023
373931198^36027-36027^31198161910Frank Doornink01/2024
37402^537815-22737161899Enzo Doria07/2013
37412^537804-39839161896Enzo Doria09/2015
3742(754*10^161816-7)/9161818Robert Price05/2020
37432^537461+29867161792Enzo Doria03/2024
37442^537458-59201161791Enzo Doria10/2015
37452*10^161766+51161767Robert Price05/2018
3746(7*10^161760+131)/3161761Robert Price06/2020
37472^537209-49849161717Enzo Doria10/2015
3748(58*10^161691+329)/9161692Robert Price05/2019
374923*10^161668-3161670Robert Price10/2021
37502^536937+1879397161635Enzo Doria09/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2025 16:29 (Time in France)

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