PRP Records

Probable Primes Top 10000

(300935 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 ?
3001(36^110503+1)/37171975Lelio R Paula04/2017
30028*10^171934+71171935Robert Price05/2022
3003(11*10^171933+601)/9171934Robert Price02/2022
3004(22*10^171929-73)/3171930Robert Price04/2019
3005(49*10^171892-319)/9171893Robert Price10/2021
30064*10^171891-63171892Robert Price10/2018
300767*10^171882-9171884Robert Price03/2021
30082^570980-2782289171883Enzo Doria09/2015
3009(25*10^171849-37)/3171850Robert Price10/2019
301010^171832+387909171833Patrick De Geest08/2021
301110^171832-10001171832Robert Price02/2021
3013(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
3012(2^570769-9)/7171818Stefano Morozzi08/2022
30142^570545+11025171752Henri Lifchitz01/2025
301524^124375-124375^24171664Henri Lifchitz08/2024
3016(74*10^171651-29)/9171652Robert Price06/2022
3017(536*10^171601-23)/9171603Robert Price02/2020
30187*10^171535-99171536Robert Price06/2019
3019(28*10^171534+101)/3171535Robert Price09/2020
30202^569563-1854607171456Enzo Doria09/2015
302132133^38042-38042^32133171454Frank Doornink02/2024
30223*10^171391+59171392Robert Price08/2018
3023(13*10^171306-37)/3171307Robert Price01/2019
30248*10^171296+87171297Robert Price10/2019
3025(55^98419-1)/54171284Paul Bourdelais12/2017
3026(29*10^171275+67)/3171276Robert Price12/2019
3027(457*10^171248-7)/9171250Robert Price09/2022
3028(194*10^171193+1)/3171195Robert Price01/2022
30292^568642+1876129171179Enzo Doria07/2016
30304*10^171146-47171147Robert Price10/2021
3031(19*10^170970+131)/3170971Robert Price06/2020
3032(46*10^170932+143)/9170933Robert Price01/2019
3033(79*10^170901-1)/3170903Robert Price02/2020
3034(58*10^170842+221)/9170843Robert Price02/2017
3035(29*10^170830+583)/9170831Robert Price06/2021
30363*10^170800+73170801Robert Price08/2018
3037(29*10^170799-119)/9170800Robert Price12/2021
303811^164009-270170798Enzo Doria10/2012
30392*10^170767+41170768Robert Price05/2018
30403^357706-112358170670Enzo Doria07/2014
3041TheodorusPrime(170657)170657Eric W. Weisstein08/2013
30422^566871+1876163170646Enzo Doria07/2016
3043(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
30442^566496+7170533Donovan Johnson07/2006
3045(7^201653+1)/8170416Paul Bourdelais02/2010
304632150^37807-37807^32150170403Frank Doornink02/2024
30477*10^170348+33170349Robert Price06/2020
30482^565799+216011170323Enzo Doria12/2023
30492^565183-352021170138Enzo Doria07/2015
30502^565143-114457170125Enzo Doria02/2015
30513*2^565024-5170090Jon Grantham07/2023
30522^564976-49869170075Enzo Doria10/2015
30532^564561+225169950Henri Lifchitz11/2024
3054(7*10^169944+23)/3169945Robert Price06/2020
3055(37*10^169943+251)/9169944Robert Price09/2021
30562^564526-351401169940Enzo Doria07/2015
30573^355902+4169809Aurel Gibier10/2024
30584*10^169759+19169760Robert Price10/2018
3059(2^563903-13)/5169752Stefano Morozzi08/2022
306021^128327-20^128327169677Jean-Louis Charton11/2014
30612^563583+89169656Stefano Morozzi04/2021
30622^563311+215813169574Enzo Doria11/2023
3063(4*10^169559+83)/3169560Robert Price02/2018
3064(194*10^169461-17)/3169463Robert Price09/2020
30652^562749+2793047169405Enzo Doria02/2016
3066(154*10^169337-1)/9169339Serge Batalov12/2014
3067(109*10^169337+11)/3169339Robert Price06/2022
3068(56*10^169311+691)/9169312Robert Price05/2019
30692^562369-29503169290Enzo Doria08/2015
3070(17*10^169283+19)/9169284Robert Price03/2021
3071390151#-2322911169082Hayden Chesnut07/2024
307210^169074-5000000001169074Robert Price09/2022
30738*10^169071+59169072Robert Price11/2021
3074(10^169044+173)/3169044Robert Price05/2021
3075(22*10^169019+383)/9169020Robert Price05/2018
3076(64*10^168935+143)/9168936Robert Price05/2021
3077(22*10^168906+47)/3168907Robert Price06/2021
30785*10^168807+87168808Robert Price02/2019
3079(77*10^168803-149)/9168804Robert Price03/2022
30804*10^168788-47168789Robert Price10/2021
3081(154*10^168781+17)/9168783Robert Price06/2022
3082(418*10^168751-31)/9168753Robert Price05/2022
3083(29*10^168711+691)/9168712Robert Price08/2021
30842^560405-39943168699Enzo Doria09/2015
3085(397*10^168634+17)/9168636Robert Price03/2022
30862^560189+36587168634Enzo Doria09/2024
308789*10^168614-7168616Robert Price04/2020
3088(23*10^168608-83)/3168609Robert Price08/2019
3089(94*10^168541+11)/3168543Robert Price04/2020
30902^559686-350471168483Enzo Doria06/2015
30912^559672-1855889168479Enzo Doria09/2015
3092(5*10^168379-473)/9168379Robert Price01/2018
30932024^50920+3168353Martin Hopf01/2024
30942^559000-59939168276Enzo Doria11/2015
30952^558830+25009168225Enzo Doria11/2023
3096(16*10^168181+41)/3168182Robert Price03/2019
3097(19*10^168173+77)/3168174Robert Price05/2019
3098(74*10^168170+529)/9168171Robert Price02/2022
30992^558640-114149168168Enzo Doria12/2014
31002^558498-1849277168125Enzo Doria08/2015
31012^558476-1850249168119Enzo Doria08/2015
3102(7*10^168067+71)/3168068Robert Price05/2018
31032^558150-1852211168020Enzo Doria08/2015
31042^558125-113661168013Enzo Doria09/2014
3105393^64747-392^64747167980Jean-Louis Charton08/2012
3106(8*10^167965-11)/3167966Robert Price07/2023
31072^557916+216151167950Enzo Doria12/2023
3108(13*10^167911+179)/3167912Robert Price11/2018
3109(26*10^167861-167)/3167862Robert Price10/2019
311036^107827-107827167812Kellen Shenton06/2023
311132027^37242-37242^32027167795Frank Doornink01/2024
311239^105456+2167788Robert Price04/2015
31132^557322+217519167771Enzo Doria01/2024
3114(28^115877-1)/27167691Paul Bourdelais12/2017
31156*10^167662-13167663Robert Price07/2022
311610^167639+121911167640Patrick De Geest07/2018
311710^167639-8001167639Robert Price03/2018
31182^556504-462059167525Enzo Doria07/2015
3119(88*10^167522-637)/9167523Robert Price11/2020
31205*10^167510+9167511Robert Price08/2015
31217*10^167437-93167438Robert Price08/2020
312225455^37978-37978^25455167323Frank Doornink01/2024
312311^160663+6167314Paul Bourdelais02/2021
3124(7*10^167308-493)/9167308Robert Price04/2021
31252^555759+74333167301Enzo Doria07/2023
312626084^37871-37871^26084167253Frank Doornink03/2024
31272^555343+1874333167175Enzo Doria06/2016
31282^555210-461261167135Enzo Doria07/2015
31299*10^166996+59166997Robert Price01/2020
3130(68*10^166976-329)/9166977Robert Price03/2021
3131(64*10^166901+683)/9166902Robert Price06/2022
31322^554372+1880527166883Enzo Doria11/2016
31332^554299+72173166861Enzo Doria04/2016
3134(185*10^166837+7)/3166839Robert Price03/2020
3135(14*10^166813+139)/9166814Robert Price11/2021
313626084^37767-37767^26084166794Frank Doornink03/2024
31372^554037-2797063166782Enzo Doria03/2016
313831861^37028-37028^31861166747Frank Doornink01/2024
3139(49*10^166721-139)/9166722Robert Price03/2019
31402*10^166646+69166647Robert Price06/2020
31412^553484-29819166616Enzo Doria08/2015
3142(188*10^166611+7)/3166613Robert Price03/2020
31432^553383-2784217166585Enzo Doria10/2015
31442^553069+76427166491Enzo Doria05/2016
314525218^37819-37819^25218166469Frank Doornink12/2023
31462*10^166458+51166459Robert Price05/2018
3147589^60089-588^60089166454Jean-Louis Charton09/2012
314825214^37799-37799^25214166378Frank Doornink11/2023
314911^159756-2424166369Mike Oakes06/2010
31502^552649-361275166364Enzo Doria05/2014
31512^552628-113669166358Enzo Doria09/2014
3152(19*10^166325+137)/3166326Robert Price03/2022
315310^166324+550603166325Patrick De Geest07/2018
315410^166324-801166324Robert Price02/2018
3155(85*10^166297-1)/3166299Robert Price02/2020
3156(19*10^166280-7)/3166281Robert Price12/2023
315725533^37726-37726^25533166263Frank Doornink02/2024
31588*10^166227+87166228Robert Price10/2019
31592^552137+1879397166210Enzo Doria09/2016
3160262273205671539190984629()252475512364409752762433166141Anonymous01/2025
3161490079063773165613318095()218182139934160868002603166141Anonymous01/2025
3162140717254840416411192803()712689271538459396766869166140Anonymous01/2025
3163122398296040696255481419()271117913237372866926417166140Anonymous01/2025
3164(103*10^166126+11)/3166128Robert Price01/2021
3165(22*10^166077+179)/3166078Robert Price02/2022
3166(23^121949-1)/22166061Paul Bourdelais10/2017
31672^551542+19249166031Payam Samidoost08/2002
31682^551535-23821166029Enzo Doria08/2013
31692^551507-23557166021Enzo Doria08/2013
317032030^36841-36841^32030165990Frank Doornink01/2024
317110^165947-7000000001165947Robert Price12/2021
31724*10^165938-47165939Robert Price10/2021
31737*10^165916-3165917Robert Price08/2015
3174(29*10^165796+67)/3165797Robert Price12/2019
317581^86837-80^86837165728Robert Price01/2015
3176(71*10^165716-17)/9165717Serge Batalov01/2023
3177fibonacci(792909)+3165708Jon Grantham08/2023
3178(71*10^165663-539)/9165664Robert Price07/2019
317925682^37567-37567^25682165657Frank Doornink02/2024
31802^550270-69551165648Enzo Doria12/2015
31812^550250+29329165642Enzo Doria03/2024
3182(202*10^165569-13)/9165571Robert Price01/2020
31832^550000-23625165567Enzo Doria08/2013
318431688^36783-36783^31688165557Frank Doornink01/2024
31852^549675-1852057165469Enzo Doria08/2015
31862^549663+212543165466Enzo Doria08/2023
3187(529*10^165394-7)/9165396Robert Price08/2021
318826253^37424-37424^26253165384Frank Doornink03/2024
3189-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
3190(28*10^165358-1)/9165359Serge Batalov10/2014
31912^549278+1879669165350Enzo Doria09/2016
3192(7*10^165350-439)/9165350Robert Price02/2018
31932^549252-351269165342Enzo Doria06/2015
31942^549221+335931165332Enzo Doria09/2024
319567*10^165327-9165329Robert Price03/2021
3197(14*10^165282+73)/3165283Robert Price12/2018
3196(8*10^165283-629)/9165283Robert Price01/2022
31982^549049+2797607165281Enzo Doria04/2016
3199(218*10^165258+7)/9165260Robert Price06/2022
3200(7*10^165239+107)/3165240Robert Price02/2018
32012^548880+23961165230Enzo Doria10/2023
32025*2^548778+3165200Jon Grantham07/2023
3203(44^100511-1)/43165184Paul Bourdelais11/2017
3204(7*10^165134+107)/3165135Robert Price02/2018
3205(301*10^165082+23)/9165084Robert Price06/2021
3206(23*10^165060-83)/3165061Robert Price08/2019
32077*10^165023-27165024Robert Price11/2022
3208(76*10^164984+77)/9164985Robert Price10/2019
320931058^36715-36715^31058164931Frank Doornink01/2024
3210(4*10^164929-211)/9164929Robert Price03/2022
321110^164878-500001164878Robert Price03/2022
32129*10^164791-89164792Robert Price04/2020
32132^547178-1856501164717Enzo Doria10/2015
321411^158160-60164707Enzo Doria07/2012
3215(26*10^164643-167)/3164644Robert Price10/2019
3216(10^164643+83)/3164643Robert Price08/2021
32172^546398-59201164483Enzo Doria10/2015
32182^546332-114893164463Enzo Doria05/2015
321936087^36087-36080^36080164462Henri Lifchitz08/2024
322032003^36504-36504^32003164458Frank Doornink01/2024
3221(65*10^164427+277)/9164428Robert Price08/2021
32222^545958+1876189164350Enzo Doria07/2016
32232^545878-49841164326Enzo Doria10/2015
3224(10^164284+77)/3164284Robert Price01/2018
32252^545668-4019164263Yves Minet04/2017
322610^164216+780639164217Patrick De Geest08/2021
322810^164216-50000000001164216Robert Price12/2020
322710^164216-891051164216Patrick De Geest08/2021
3229(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
3230(16*10^164122+197)/3164123Robert Price04/2019
32312^545185+76757164118Enzo Doria05/2016
32322^545076-114329164085Enzo Doria01/2015
3233(2*10^164043-143)/3164043Robert Price03/2018
3234(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
3235(29^112153+1)/30164011Lelio R Paula03/2017
32362^544757+1874777163989Enzo Doria06/2016
32372^544723+211193163978Enzo Doria08/2023
32382^544444-457199163894Enzo Doria01/2015
3239(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
32402^544264-343529163840Enzo Doria07/2015
32417*10^163780+9163781Robert Price09/2015
32422^543989+2793047163758Enzo Doria02/2016
3243(28*10^163709+113)/3163710Robert Price03/2020
3244(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
3245(23*10^163523+301)/9163524Robert Price06/2021
3246(68*10^163521-329)/9163522Robert Price03/2021
324735820^35899+35899^35820163489Norbert Schneider11/2021
32482^542870-69551163421Enzo Doria12/2015
32492^542502+24799163310Enzo Doria10/2023
32502^542395+72533163278Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 07 2025 10:37 (Time in France)

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