PRP Records

Probable Primes Top 10000

(301421 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 ?
3251(23*10^168608-83)/3168609Robert Price08/2019
3252(94*10^168541+11)/3168543Robert Price04/2020
32532^559686-350471168483Enzo Doria06/2015
32542^559672-1855889168479Enzo Doria09/2015
3255(5*10^168379-473)/9168379Robert Price01/2018
32562024^50920+3168353Martin Hopf01/2024
32572^559000-59939168276Enzo Doria11/2015
32582^558830+25009168225Enzo Doria11/2023
3259(16*10^168181+41)/3168182Robert Price03/2019
3260(19*10^168173+77)/3168174Robert Price05/2019
3261(74*10^168170+529)/9168171Robert Price02/2022
32622^558640-114149168168Enzo Doria12/2014
32632^558498-1849277168125Enzo Doria08/2015
32642^558476-1850249168119Enzo Doria08/2015
3265(7*10^168067+71)/3168068Robert Price05/2018
32662^558150-1852211168020Enzo Doria08/2015
32672^558125-113661168013Enzo Doria09/2014
3268393^64747-392^64747167980Jean-Louis Charton08/2012
3269(8*10^167965-11)/3167966Robert Price07/2023
32702^557916+216151167950Enzo Doria12/2023
3271(13*10^167911+179)/3167912Robert Price11/2018
3272(26*10^167861-167)/3167862Robert Price10/2019
327336^107827-107827167812Kellen Shenton06/2023
327432027^37242-37242^32027167795Frank Doornink01/2024
327539^105456+2167788Robert Price04/2015
32762^557322+217519167771Enzo Doria01/2024
3277(28^115877-1)/27167691Paul Bourdelais12/2017
32786*10^167662-13167663Robert Price07/2022
327910^167639+121911167640Patrick De Geest07/2018
328010^167639-8001167639Robert Price03/2018
32812^556504-462059167525Enzo Doria07/2015
3282(88*10^167522-637)/9167523Robert Price11/2020
32835*10^167510+9167511Robert Price08/2015
32847*10^167437-93167438Robert Price08/2020
328525455^37978-37978^25455167323Frank Doornink01/2024
328611^160663+6167314Paul Bourdelais02/2021
3287(7*10^167308-493)/9167308Robert Price04/2021
32882^555759+74333167301Enzo Doria07/2023
328926084^37871-37871^26084167253Frank Doornink03/2024
32902^555343+1874333167175Enzo Doria06/2016
32912^555210-461261167135Enzo Doria07/2015
32929*10^166996+59166997Robert Price01/2020
3293(68*10^166976-329)/9166977Robert Price03/2021
3294(64*10^166901+683)/9166902Robert Price06/2022
32952^554372+1880527166883Enzo Doria11/2016
32962^554299+72173166861Enzo Doria04/2016
3297(185*10^166837+7)/3166839Robert Price03/2020
3298(14*10^166813+139)/9166814Robert Price11/2021
329926084^37767-37767^26084166794Frank Doornink03/2024
33002^554037-2797063166782Enzo Doria03/2016
330131861^37028-37028^31861166747Frank Doornink01/2024
3302(49*10^166721-139)/9166722Robert Price03/2019
33032*10^166646+69166647Robert Price06/2020
33042^553484-29819166616Enzo Doria08/2015
3305(188*10^166611+7)/3166613Robert Price03/2020
33062^553383-2784217166585Enzo Doria10/2015
33072^553069+76427166491Enzo Doria05/2016
330825218^37819-37819^25218166469Frank Doornink12/2023
33092*10^166458+51166459Robert Price05/2018
3310589^60089-588^60089166454Jean-Louis Charton09/2012
331125214^37799-37799^25214166378Frank Doornink11/2023
331211^159756-2424166369Mike Oakes06/2010
33132^552649-361275166364Enzo Doria05/2014
33142^552628-113669166358Enzo Doria09/2014
3315(19*10^166325+137)/3166326Robert Price03/2022
331610^166324+550603166325Patrick De Geest07/2018
331710^166324-801166324Robert Price02/2018
3318(85*10^166297-1)/3166299Robert Price02/2020
3319(19*10^166280-7)/3166281Robert Price12/2023
332025533^37726-37726^25533166263Frank Doornink02/2024
33218*10^166227+87166228Robert Price10/2019
33222^552137+1879397166210Enzo Doria09/2016
3323262273205671539190984629()252475512364409752762433166141Anonymous01/2025
3324490079063773165613318095()218182139934160868002603166141Anonymous01/2025
3325140717254840416411192803()712689271538459396766869166140Anonymous01/2025
3326122398296040696255481419()271117913237372866926417166140Anonymous01/2025
3327(103*10^166126+11)/3166128Robert Price01/2021
3328(22*10^166077+179)/3166078Robert Price02/2022
3329(23^121949-1)/22166061Paul Bourdelais10/2017
33302^551576+236221166041Enzo Doria05/2025
33312^551542+19249166031Payam Samidoost08/2002
33322^551535-23821166029Enzo Doria08/2013
33332^551507-23557166021Enzo Doria08/2013
333432030^36841-36841^32030165990Frank Doornink01/2024
333510^165947-7000000001165947Robert Price12/2021
33364*10^165938-47165939Robert Price10/2021
33377*10^165916-3165917Robert Price08/2015
3338(29*10^165796+67)/3165797Robert Price12/2019
333981^86837-80^86837165728Robert Price01/2015
3340(71*10^165716-17)/9165717Serge Batalov01/2023
3341fibonacci(792909)+3165708Jon Grantham08/2023
3342(71*10^165663-539)/9165664Robert Price07/2019
334325682^37567-37567^25682165657Frank Doornink02/2024
33442^550270-69551165648Enzo Doria12/2015
33452^550250+29329165642Enzo Doria03/2024
3346(202*10^165569-13)/9165571Robert Price01/2020
33472^550000-23625165567Enzo Doria08/2013
334831688^36783-36783^31688165557Frank Doornink01/2024
33492^549675-1852057165469Enzo Doria08/2015
33502^549663+212543165466Enzo Doria08/2023
3351(529*10^165394-7)/9165396Robert Price08/2021
335226253^37424-37424^26253165384Frank Doornink03/2024
3353-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
3354(28*10^165358-1)/9165359Serge Batalov10/2014
33552^549278+1879669165350Enzo Doria09/2016
3356(7*10^165350-439)/9165350Robert Price02/2018
33572^549252-351269165342Enzo Doria06/2015
33582^549221+335931165332Enzo Doria09/2024
335967*10^165327-9165329Robert Price03/2021
3360(14*10^165282+73)/3165283Robert Price12/2018
3361(8*10^165283-629)/9165283Robert Price01/2022
33622^549049+2797607165281Enzo Doria04/2016
3363(218*10^165258+7)/9165260Robert Price06/2022
3364(7*10^165239+107)/3165240Robert Price02/2018
33652^548880+23961165230Enzo Doria10/2023
33665*2^548778+3165200Jon Grantham07/2023
3367(44^100511-1)/43165184Paul Bourdelais11/2017
3368(7*10^165134+107)/3165135Robert Price02/2018
3369(301*10^165082+23)/9165084Robert Price06/2021
3370(23*10^165060-83)/3165061Robert Price08/2019
33717*10^165023-27165024Robert Price11/2022
3372(76*10^164984+77)/9164985Robert Price10/2019
337331058^36715-36715^31058164931Frank Doornink01/2024
3374(4*10^164929-211)/9164929Robert Price03/2022
337510^164878-500001164878Robert Price03/2022
33769*10^164791-89164792Robert Price04/2020
33772^547178-1856501164717Enzo Doria10/2015
337811^158160-60164707Enzo Doria07/2012
3379(26*10^164643-167)/3164644Robert Price10/2019
3380(10^164643+83)/3164643Robert Price08/2021
33812^546398-59201164483Enzo Doria10/2015
33822^546332-114893164463Enzo Doria05/2015
338336087^36087-36080^36080164462Henri Lifchitz08/2024
338432003^36504-36504^32003164458Frank Doornink01/2024
3385(65*10^164427+277)/9164428Robert Price08/2021
33862^545958+1876189164350Enzo Doria07/2016
33872^545878-49841164326Enzo Doria10/2015
3388(10^164284+77)/3164284Robert Price01/2018
33892^545668-4019164263Yves Minet04/2017
339010^164216+780639164217Patrick De Geest08/2021
339210^164216-50000000001164216Robert Price12/2020
339110^164216-891051164216Patrick De Geest08/2021
3393(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
3394(16*10^164122+197)/3164123Robert Price04/2019
33952^545185+76757164118Enzo Doria05/2016
33962^545076-114329164085Enzo Doria01/2015
3397(2*10^164043-143)/3164043Robert Price03/2018
3398(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
3399(29^112153+1)/30164011Lelio R Paula03/2017
34002^544757+1874777163989Enzo Doria06/2016
34012^544723+211193163978Enzo Doria08/2023
34022^544444-457199163894Enzo Doria01/2015
3403(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
34042^544264-343529163840Enzo Doria07/2015
34057*10^163780+9163781Robert Price09/2015
34062^543989+2793047163758Enzo Doria02/2016
3407(28*10^163709+113)/3163710Robert Price03/2020
3408(2^543398)/(543398^2)163568Henri Lifchitz05/2025
3409(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
3410(23*10^163523+301)/9163524Robert Price06/2021
3411(68*10^163521-329)/9163522Robert Price03/2021
341235820^35899+35899^35820163489Norbert Schneider11/2021
34132^542870-69551163421Enzo Doria12/2015
34142^542502+24799163310Enzo Doria10/2023
34152^542395+72533163278Enzo Doria04/2016
34162^542258+216949163236Enzo Doria12/2023
34172^542072-3683163180Yves Minet03/2017
3418fibonacci(780566)-4163129Jon Grantham08/2023
3419(682*10^163106-7)/9163108Robert Price08/2021
34202^541779-1867357163092Enzo Doria04/2016
3421(29*10^163056+313)/9163057Robert Price04/2021
34222^541476+214743163001Enzo Doria11/2023
342313^142159+14^142159-2162933Harsh Aggarwal05/2024
34248*10^162924+9162925Robert Price12/2015
34252^540905+81557162829Enzo Doria08/2016
34262^540628-2939162746Yves Minet09/2014
3427919^54919-918^54919162743Jean-Louis Charton01/2013
3428(203*10^162689+1)/3162691Robert Price03/2020
34293*10^162620-59162621Robert Price09/2018
34302^540180+26791162611Enzo Doria12/2023
34313^340694-112960162553Enzo Doria07/2014
34322^539925+81162534Henri Lifchitz11/2024
34332^539807-114081162499Enzo Doria12/2014
3434414^62093+62093^414162498Norbert Schneider03/2022
34352^539654-114893162453Enzo Doria05/2015
34369*10^162449-71162450Robert Price11/2020
34372^539617-1851583162441Enzo Doria08/2015
3438(509*10^162422+31)/9162424Robert Price08/2022
3439(91*10^162410+11)/3162412Robert Price02/2020
34402^539346+81049162360Enzo Doria07/2016
34412^539220-115499162322Enzo Doria07/2015
34422^539217-113713162321Enzo Doria09/2014
34439^170099-8^170099162316Jean-Louis Charton05/2005
34444*10^162263-39162264Robert Price09/2020
344531243^36098-36098^31243162252Frank Doornink01/2024
344631987^36000-36000^31987162180Frank Doornink01/2024
3447(115*10^162153-1)/3162155Serge Batalov12/2014
3448(10^162138+11)/3162138Serge Batalov07/2015
3449(61*10^162100-403)/9162101Robert Price10/2021
34502^538473-112723162097Enzo Doria06/2014
34512^538157+79337162002Enzo Doria06/2016
34522^538136-114749161996Enzo Doria05/2015
34532^538104+1531161986Lelio R Paula01/2013
3454(9*29^110727-1199)/14161927Curtis Bright05/2015
3455((2^179294-1)^3+2)/11161918Serge Batalov03/2023
345631198^36027-36027^31198161910Frank Doornink01/2024
34572^537815-22737161899Enzo Doria07/2013
34582^537804-39839161896Enzo Doria09/2015
3459(754*10^161816-7)/9161818Robert Price05/2020
34602^537461+29867161792Enzo Doria03/2024
34612^537458-59201161791Enzo Doria10/2015
34622*10^161766+51161767Robert Price05/2018
3463(7*10^161760+131)/3161761Robert Price06/2020
34642^537209-49849161717Enzo Doria10/2015
3465(58*10^161691+329)/9161692Robert Price05/2019
346623*10^161668-3161670Robert Price10/2021
34672^536937+1879397161635Enzo Doria09/2016
34683*2^536868-5161614Jon Grantham07/2023
346934*10^161593-9161595Robert Price06/2020
3470(31*10^161582-1)/3161584Robert Price02/2020
347124494^36813+36813^24494161575Norbert Schneider11/2023
34722^536569-22881161524Enzo Doria07/2013
3473(46*10^161505+593)/9161506Robert Price04/2022
347410^161253+573493161254Patrick De Geest07/2018
347510^161253-8001161253Robert Price03/2018
347697*10^161247-3161249Robert Price05/2020
34777*10^161192-9161193Robert Price10/2015
34782^535415-19161176Stefano Morozzi07/2022
34792^535269-113803161133Enzo Doria09/2014
34802^535205-23295161113Enzo Doria08/2013
3481(49*10^161105+437)/9161106Robert Price09/2021
34822^534961+6561161040Henri Lifchitz11/2024
3483(89^82609+1)/90161036Paul Bourdelais10/2017
348435385^35385-17692^17692160960Henri Lifchitz10/2024
34852^534429-19160880Stefano Morozzi07/2022
34862^534359-23229160859Enzo Doria08/2013
348710^160836-1001160836Robert Price10/2022
3488457^60454+60454^457160803Norbert Schneider07/2021
34898*10^160782+53160783Robert Price08/2020
349067^88037-66^88037160763Robert Price10/2013
3491(88*10^160761-637)/9160762Robert Price11/2020
34922^533981+81160745Henri Lifchitz11/2024
34932^533948-1852559160735Enzo Doria08/2015
34942^533665-23335160650Enzo Doria08/2013
34952^533600+217981160630Enzo Doria01/2024
3496(19*10^160619+77)/3160620Robert Price05/2019
34972^533350-5160555Stefano Morozzi07/2022
3498(38*10^160508+151)/9160509Robert Price03/2022
34993^336353-2^336353160482Mike Oakes10/2007
350026134^36315-36315^26134160411Frank Doornink03/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 19 2025 12:52 (Time in France)

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