PRP Records

Probable Primes Top 10000

(294613 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 ?
25012^576889+49727173661Enzo Doria09/2016
2502(167*10^173571-17)/3173573Robert Price03/2020
250337803^37916+37916^37803173562Norbert Schneider06/2022
25045*10^173534+29173535Robert Price12/2020
2505(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
25064*10^173509+99173510Robert Price12/2020
2507(13*10^173467-37)/3173468Robert Price01/2019
25082^576016-113919173399Enzo Doria11/2014
25092^575911-1849387173367Enzo Doria08/2015
25102^575879+215843173357Enzo Doria11/2023
25112^575871+28733173355Enzo Doria01/2024
2512515^63898+63898^515173280Norbert Schneider12/2022
25132^575614+9173278Stefano Morozzi04/2021
25142^575606-219533173275Enzo Doria03/2024
2515(16*10^173251+107)/3173252Robert Price03/2019
25162^575196-114053173152Enzo Doria11/2014
25177*10^173135-53173136Robert Price06/2020
2518(301*10^173047+23)/9173049Robert Price06/2021
25192^574591-115387172970Enzo Doria07/2015
252025210^39297-39297^25210172969Frank Doornink12/2023
2521(202*10^172940-13)/9172942Robert Price01/2020
252245^104608+104608^45172940Norbert Schneider06/2021
25232^574328+81121172890Enzo Doria07/2016
2524(115*10^172862-1)/3172864Serge Batalov12/2014
25253*10^172812+13172813Robert Price07/2018
25264*5^247217-9172798Lelio R Paula10/2015
25276*10^172772-31172773Robert Price07/2020
252869061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
2529(34*10^172693-547)/9172694Robert Price03/2021
25305*10^172692+57172693Robert Price12/2018
25312^573668-2782319172692Enzo Doria09/2015
25322^573444-1855109172624Enzo Doria09/2015
253325500^39173-39173^25500172618Frank Doornink02/2024
253427180^38917-38917^27180172568Frank Doornink01/2024
2535(14*10^172532-29)/3172533Robert Price09/2021
25363^361608+2172531Robert Price08/2014
2537(54^99563+1)/55172481Paul Bourdelais11/2017
25382^572592-114893172368Enzo Doria05/2015
25394*10^172354-39172355Robert Price09/2020
254037535^37674+37674^37535172338Norbert Schneider05/2022
2541(11*10^172322-119)/9172323Robert Price11/2021
25425^246497-4^246497172295Jean-Louis Charton11/2008
2543(38^109037-1)/37172254Paul Bourdelais10/2017
2544(4*10^172241+89)/3172242Robert Price08/2021
25453*10^172219+73172220Robert Price08/2018
25462^571810+28549172132Enzo Doria01/2024
2547A352736(15)172032Kellen Shenton05/2022
254832298^38149-38149^32298172021Frank Doornink02/2024
25492^571300+25861171979Enzo Doria11/2023
2550(36^110503+1)/37171975Lelio R Paula04/2017
25518*10^171934+71171935Robert Price05/2022
2552(11*10^171933+601)/9171934Robert Price02/2022
2553(22*10^171929-73)/3171930Robert Price04/2019
2554(49*10^171892-319)/9171893Robert Price10/2021
25554*10^171891-63171892Robert Price10/2018
255667*10^171882-9171884Robert Price03/2021
25572^570980-2782289171883Enzo Doria09/2015
2558(25*10^171849-37)/3171850Robert Price10/2019
255910^171832+387909171833Patrick De Geest08/2021
256010^171832-10001171832Robert Price02/2021
2562(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
2561(2^570769-9)/7171818Stefano Morozzi08/2022
2563(74*10^171651-29)/9171652Robert Price06/2022
2564(536*10^171601-23)/9171603Robert Price02/2020
25657*10^171535-99171536Robert Price06/2019
2566(28*10^171534+101)/3171535Robert Price09/2020
25672^569563-1854607171456Enzo Doria09/2015
256832133^38042-38042^32133171454Frank Doornink02/2024
25693*10^171391+59171392Robert Price08/2018
2570(13*10^171306-37)/3171307Robert Price01/2019
25718*10^171296+87171297Robert Price10/2019
2572(55^98419-1)/54171284Paul Bourdelais12/2017
2573(29*10^171275+67)/3171276Robert Price12/2019
2574(457*10^171248-7)/9171250Robert Price09/2022
2575(194*10^171193+1)/3171195Robert Price01/2022
25762^568642+1876129171179Enzo Doria07/2016
25774*10^171146-47171147Robert Price10/2021
2578(19*10^170970+131)/3170971Robert Price06/2020
2579(46*10^170932+143)/9170933Robert Price01/2019
2580(79*10^170901-1)/3170903Robert Price02/2020
2581(58*10^170842+221)/9170843Robert Price02/2017
2582(29*10^170830+583)/9170831Robert Price06/2021
25833*10^170800+73170801Robert Price08/2018
2584(29*10^170799-119)/9170800Robert Price12/2021
258511^164009-270170798Enzo Doria10/2012
25862*10^170767+41170768Robert Price05/2018
25873^357706-112358170670Enzo Doria07/2014
2588TheodorusPrime(170657)170657Eric W. Weisstein08/2013
25892^566871+1876163170646Enzo Doria07/2016
2590(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
25912^566496+7170533Donovan Johnson07/2006
2592(7^201653+1)/8170416Paul Bourdelais02/2010
259332150^37807-37807^32150170403Frank Doornink02/2024
25947*10^170348+33170349Robert Price06/2020
25952^565799+216011170323Enzo Doria12/2023
25962^565183-352021170138Enzo Doria07/2015
25972^565143-114457170125Enzo Doria02/2015
25983*2^565024-5170090Jon Grantham07/2023
25992^564976-49869170075Enzo Doria10/2015
2600(7*10^169944+23)/3169945Robert Price06/2020
2601(37*10^169943+251)/9169944Robert Price09/2021
26022^564526-351401169940Enzo Doria07/2015
26034*10^169759+19169760Robert Price10/2018
2604(2^563903-13)/5169752Stefano Morozzi08/2022
260521^128327-20^128327169677Jean-Louis Charton11/2014
26062^563583+89169656Stefano Morozzi04/2021
26072^563311+215813169574Enzo Doria11/2023
2608(4*10^169559+83)/3169560Robert Price02/2018
2609(194*10^169461-17)/3169463Robert Price09/2020
26102^562749+2793047169405Enzo Doria02/2016
2611(154*10^169337-1)/9169339Serge Batalov12/2014
2612(109*10^169337+11)/3169339Robert Price06/2022
2613(56*10^169311+691)/9169312Robert Price05/2019
26142^562369-29503169290Enzo Doria08/2015
2615(17*10^169283+19)/9169284Robert Price03/2021
261610^169074-5000000001169074Robert Price09/2022
26178*10^169071+59169072Robert Price11/2021
2618(10^169044+173)/3169044Robert Price05/2021
2619(22*10^169019+383)/9169020Robert Price05/2018
2620(64*10^168935+143)/9168936Robert Price05/2021
2621(22*10^168906+47)/3168907Robert Price06/2021
26225*10^168807+87168808Robert Price02/2019
2623(77*10^168803-149)/9168804Robert Price03/2022
26244*10^168788-47168789Robert Price10/2021
2625(154*10^168781+17)/9168783Robert Price06/2022
2626(418*10^168751-31)/9168753Robert Price05/2022
2627(29*10^168711+691)/9168712Robert Price08/2021
26282^560405-39943168699Enzo Doria09/2015
2629(397*10^168634+17)/9168636Robert Price03/2022
263089*10^168614-7168616Robert Price04/2020
2631(23*10^168608-83)/3168609Robert Price08/2019
2632(94*10^168541+11)/3168543Robert Price04/2020
26332^559686-350471168483Enzo Doria06/2015
26342^559672-1855889168479Enzo Doria09/2015
2635(5*10^168379-473)/9168379Robert Price01/2018
26362024^50920+3168353Martin Hopf01/2024
26372^559000-59939168276Enzo Doria11/2015
26382^558830+25009168225Enzo Doria11/2023
2639(16*10^168181+41)/3168182Robert Price03/2019
2640(19*10^168173+77)/3168174Robert Price05/2019
2641(74*10^168170+529)/9168171Robert Price02/2022
26422^558640-114149168168Enzo Doria12/2014
26432^558498-1849277168125Enzo Doria08/2015
26442^558476-1850249168119Enzo Doria08/2015
2645(7*10^168067+71)/3168068Robert Price05/2018
26462^558150-1852211168020Enzo Doria08/2015
26472^558125-113661168013Enzo Doria09/2014
2648393^64747-392^64747167980Jean-Louis Charton08/2012
2649(8*10^167965-11)/3167966Robert Price07/2023
26502^557916+216151167950Enzo Doria12/2023
2651(13*10^167911+179)/3167912Robert Price11/2018
2652(26*10^167861-167)/3167862Robert Price10/2019
265336^107827-107827167812Kellen Shenton06/2023
265432027^37242-37242^32027167795Frank Doornink01/2024
265539^105456+2167788Robert Price04/2015
26562^557322+217519167771Enzo Doria01/2024
2657(28^115877-1)/27167691Paul Bourdelais12/2017
26586*10^167662-13167663Robert Price07/2022
265910^167639+121911167640Patrick De Geest07/2018
266010^167639-8001167639Robert Price03/2018
26612^556504-462059167525Enzo Doria07/2015
2662(88*10^167522-637)/9167523Robert Price11/2020
26635*10^167510+9167511Robert Price08/2015
26647*10^167437-93167438Robert Price08/2020
266525455^37978-37978^25455167323Frank Doornink01/2024
266611^160663+6167314Paul Bourdelais02/2021
2667(7*10^167308-493)/9167308Robert Price04/2021
26682^555759+74333167301Enzo Doria07/2023
26692^555343+1874333167175Enzo Doria06/2016
26702^555210-461261167135Enzo Doria07/2015
26719*10^166996+59166997Robert Price01/2020
2672(68*10^166976-329)/9166977Robert Price03/2021
2673(64*10^166901+683)/9166902Robert Price06/2022
26742^554372+1880527166883Enzo Doria11/2016
26752^554299+72173166861Enzo Doria04/2016
2676(185*10^166837+7)/3166839Robert Price03/2020
2677(14*10^166813+139)/9166814Robert Price11/2021
26782^554037-2797063166782Enzo Doria03/2016
267931861^37028-37028^31861166747Frank Doornink01/2024
2680(49*10^166721-139)/9166722Robert Price03/2019
26812*10^166646+69166647Robert Price06/2020
26822^553484-29819166616Enzo Doria08/2015
2683(188*10^166611+7)/3166613Robert Price03/2020
26842^553383-2784217166585Enzo Doria10/2015
26852^553069+76427166491Enzo Doria05/2016
268625218^37819-37819^25218166469Frank Doornink12/2023
26872*10^166458+51166459Robert Price05/2018
2688589^60089-588^60089166454Jean-Louis Charton09/2012
268925214^37799-37799^25214166378Frank Doornink11/2023
269011^159756-2424166369Mike Oakes06/2010
26912^552649-361275166364Enzo Doria05/2014
26922^552628-113669166358Enzo Doria09/2014
2693(19*10^166325+137)/3166326Robert Price03/2022
269410^166324+550603166325Patrick De Geest07/2018
269510^166324-801166324Robert Price02/2018
2696(85*10^166297-1)/3166299Robert Price02/2020
2697(19*10^166280-7)/3166281Robert Price12/2023
269825533^37726-37726^25533166263Frank Doornink02/2024
26998*10^166227+87166228Robert Price10/2019
27002^552137+1879397166210Enzo Doria09/2016
2701(103*10^166126+11)/3166128Robert Price01/2021
2702(22*10^166077+179)/3166078Robert Price02/2022
2703(23^121949-1)/22166061Paul Bourdelais10/2017
27042^551542+19249166031Payam Samidoost08/2002
27052^551535-23821166029Enzo Doria08/2013
27062^551507-23557166021Enzo Doria08/2013
270732030^36841-36841^32030165990Frank Doornink01/2024
270810^165947-7000000001165947Robert Price12/2021
27094*10^165938-47165939Robert Price10/2021
27107*10^165916-3165917Robert Price08/2015
2711(29*10^165796+67)/3165797Robert Price12/2019
271281^86837-80^86837165728Robert Price01/2015
2713(71*10^165716-17)/9165717Serge Batalov01/2023
2714fibonacci(792909)+3165708Jon Grantham08/2023
2715(71*10^165663-539)/9165664Robert Price07/2019
271625682^37567-37567^25682165657Frank Doornink02/2024
27172^550270-69551165648Enzo Doria12/2015
27182^550250+29329165642Enzo Doria03/2024
2719(202*10^165569-13)/9165571Robert Price01/2020
27202^550000-23625165567Enzo Doria08/2013
272131688^36783-36783^31688165557Frank Doornink01/2024
27222^549675-1852057165469Enzo Doria08/2015
27232^549663+212543165466Enzo Doria08/2023
2724(529*10^165394-7)/9165396Robert Price08/2021
2725-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
2726(28*10^165358-1)/9165359Serge Batalov10/2014
27272^549278+1879669165350Enzo Doria09/2016
2728(7*10^165350-439)/9165350Robert Price02/2018
27292^549252-351269165342Enzo Doria06/2015
273067*10^165327-9165329Robert Price03/2021
2732(14*10^165282+73)/3165283Robert Price12/2018
2731(8*10^165283-629)/9165283Robert Price01/2022
27332^549049+2797607165281Enzo Doria04/2016
2734(218*10^165258+7)/9165260Robert Price06/2022
2735(7*10^165239+107)/3165240Robert Price02/2018
27362^548880+23961165230Enzo Doria10/2023
27375*2^548778+3165200Jon Grantham07/2023
2738(44^100511-1)/43165184Paul Bourdelais11/2017
2739(7*10^165134+107)/3165135Robert Price02/2018
2740(301*10^165082+23)/9165084Robert Price06/2021
2741(23*10^165060-83)/3165061Robert Price08/2019
27427*10^165023-27165024Robert Price11/2022
2743(76*10^164984+77)/9164985Robert Price10/2019
274431058^36715-36715^31058164931Frank Doornink01/2024
2745(4*10^164929-211)/9164929Robert Price03/2022
274610^164878-500001164878Robert Price03/2022
27479*10^164791-89164792Robert Price04/2020
27482^547178-1856501164717Enzo Doria10/2015
274911^158160-60164707Enzo Doria07/2012
2750(26*10^164643-167)/3164644Robert Price10/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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