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 ?
27512^563583+89169656Stefano Morozzi04/2021
27522^563311+215813169574Enzo Doria11/2023
2753(4*10^169559+83)/3169560Robert Price02/2018
2754(194*10^169461-17)/3169463Robert Price09/2020
27552^562749+2793047169405Enzo Doria02/2016
2756(154*10^169337-1)/9169339Serge Batalov12/2014
2757(109*10^169337+11)/3169339Robert Price06/2022
2758(56*10^169311+691)/9169312Robert Price05/2019
27592^562369-29503169290Enzo Doria08/2015
2760(17*10^169283+19)/9169284Robert Price03/2021
2761390151#-2322911169082Hayden Chesnut07/2024
276210^169074-5000000001169074Robert Price09/2022
27638*10^169071+59169072Robert Price11/2021
2764(10^169044+173)/3169044Robert Price05/2021
2765(22*10^169019+383)/9169020Robert Price05/2018
2766(64*10^168935+143)/9168936Robert Price05/2021
2767(22*10^168906+47)/3168907Robert Price06/2021
27685*10^168807+87168808Robert Price02/2019
2769(77*10^168803-149)/9168804Robert Price03/2022
27704*10^168788-47168789Robert Price10/2021
2771(154*10^168781+17)/9168783Robert Price06/2022
2772(418*10^168751-31)/9168753Robert Price05/2022
2773(29*10^168711+691)/9168712Robert Price08/2021
27742^560405-39943168699Enzo Doria09/2015
2775(397*10^168634+17)/9168636Robert Price03/2022
277689*10^168614-7168616Robert Price04/2020
2777(23*10^168608-83)/3168609Robert Price08/2019
2778(94*10^168541+11)/3168543Robert Price04/2020
27792^559686-350471168483Enzo Doria06/2015
27802^559672-1855889168479Enzo Doria09/2015
2781(5*10^168379-473)/9168379Robert Price01/2018
27822024^50920+3168353Martin Hopf01/2024
27832^559000-59939168276Enzo Doria11/2015
27842^558830+25009168225Enzo Doria11/2023
2785(16*10^168181+41)/3168182Robert Price03/2019
2786(19*10^168173+77)/3168174Robert Price05/2019
2787(74*10^168170+529)/9168171Robert Price02/2022
27882^558640-114149168168Enzo Doria12/2014
27892^558498-1849277168125Enzo Doria08/2015
27902^558476-1850249168119Enzo Doria08/2015
2791(7*10^168067+71)/3168068Robert Price05/2018
27922^558150-1852211168020Enzo Doria08/2015
27932^558125-113661168013Enzo Doria09/2014
2794393^64747-392^64747167980Jean-Louis Charton08/2012
2795(8*10^167965-11)/3167966Robert Price07/2023
27962^557916+216151167950Enzo Doria12/2023
2797(13*10^167911+179)/3167912Robert Price11/2018
2798(26*10^167861-167)/3167862Robert Price10/2019
279936^107827-107827167812Kellen Shenton06/2023
280032027^37242-37242^32027167795Frank Doornink01/2024
280139^105456+2167788Robert Price04/2015
28022^557322+217519167771Enzo Doria01/2024
2803(28^115877-1)/27167691Paul Bourdelais12/2017
28046*10^167662-13167663Robert Price07/2022
280510^167639+121911167640Patrick De Geest07/2018
280610^167639-8001167639Robert Price03/2018
28072^556504-462059167525Enzo Doria07/2015
2808(88*10^167522-637)/9167523Robert Price11/2020
28095*10^167510+9167511Robert Price08/2015
28107*10^167437-93167438Robert Price08/2020
281125455^37978-37978^25455167323Frank Doornink01/2024
281211^160663+6167314Paul Bourdelais02/2021
2813(7*10^167308-493)/9167308Robert Price04/2021
28142^555759+74333167301Enzo Doria07/2023
281526084^37871-37871^26084167253Frank Doornink03/2024
28162^555343+1874333167175Enzo Doria06/2016
28172^555210-461261167135Enzo Doria07/2015
28189*10^166996+59166997Robert Price01/2020
2819(68*10^166976-329)/9166977Robert Price03/2021
2820(64*10^166901+683)/9166902Robert Price06/2022
28212^554372+1880527166883Enzo Doria11/2016
28222^554299+72173166861Enzo Doria04/2016
2823(185*10^166837+7)/3166839Robert Price03/2020
2824(14*10^166813+139)/9166814Robert Price11/2021
282526084^37767-37767^26084166794Frank Doornink03/2024
28262^554037-2797063166782Enzo Doria03/2016
282731861^37028-37028^31861166747Frank Doornink01/2024
2828(49*10^166721-139)/9166722Robert Price03/2019
28292*10^166646+69166647Robert Price06/2020
28302^553484-29819166616Enzo Doria08/2015
2831(188*10^166611+7)/3166613Robert Price03/2020
28322^553383-2784217166585Enzo Doria10/2015
28332^553069+76427166491Enzo Doria05/2016
283425218^37819-37819^25218166469Frank Doornink12/2023
28352*10^166458+51166459Robert Price05/2018
2836589^60089-588^60089166454Jean-Louis Charton09/2012
283725214^37799-37799^25214166378Frank Doornink11/2023
283811^159756-2424166369Mike Oakes06/2010
28392^552649-361275166364Enzo Doria05/2014
28402^552628-113669166358Enzo Doria09/2014
2841(19*10^166325+137)/3166326Robert Price03/2022
284210^166324+550603166325Patrick De Geest07/2018
284310^166324-801166324Robert Price02/2018
2844(85*10^166297-1)/3166299Robert Price02/2020
2845(19*10^166280-7)/3166281Robert Price12/2023
284625533^37726-37726^25533166263Frank Doornink02/2024
28478*10^166227+87166228Robert Price10/2019
28482^552137+1879397166210Enzo Doria09/2016
2849(103*10^166126+11)/3166128Robert Price01/2021
2850(22*10^166077+179)/3166078Robert Price02/2022
2851(23^121949-1)/22166061Paul Bourdelais10/2017
28522^551542+19249166031Payam Samidoost08/2002
28532^551535-23821166029Enzo Doria08/2013
28542^551507-23557166021Enzo Doria08/2013
285532030^36841-36841^32030165990Frank Doornink01/2024
285610^165947-7000000001165947Robert Price12/2021
28574*10^165938-47165939Robert Price10/2021
28587*10^165916-3165917Robert Price08/2015
2859(29*10^165796+67)/3165797Robert Price12/2019
286081^86837-80^86837165728Robert Price01/2015
2861(71*10^165716-17)/9165717Serge Batalov01/2023
2862fibonacci(792909)+3165708Jon Grantham08/2023
2863(71*10^165663-539)/9165664Robert Price07/2019
286425682^37567-37567^25682165657Frank Doornink02/2024
28652^550270-69551165648Enzo Doria12/2015
28662^550250+29329165642Enzo Doria03/2024
2867(202*10^165569-13)/9165571Robert Price01/2020
28682^550000-23625165567Enzo Doria08/2013
286931688^36783-36783^31688165557Frank Doornink01/2024
28702^549675-1852057165469Enzo Doria08/2015
28712^549663+212543165466Enzo Doria08/2023
2872(529*10^165394-7)/9165396Robert Price08/2021
287326253^37424-37424^26253165384Frank Doornink03/2024
2874-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
2875(28*10^165358-1)/9165359Serge Batalov10/2014
28762^549278+1879669165350Enzo Doria09/2016
2877(7*10^165350-439)/9165350Robert Price02/2018
28782^549252-351269165342Enzo Doria06/2015
287967*10^165327-9165329Robert Price03/2021
2880(14*10^165282+73)/3165283Robert Price12/2018
2881(8*10^165283-629)/9165283Robert Price01/2022
28822^549049+2797607165281Enzo Doria04/2016
2883(218*10^165258+7)/9165260Robert Price06/2022
2884(7*10^165239+107)/3165240Robert Price02/2018
28852^548880+23961165230Enzo Doria10/2023
28865*2^548778+3165200Jon Grantham07/2023
2887(44^100511-1)/43165184Paul Bourdelais11/2017
2888(7*10^165134+107)/3165135Robert Price02/2018
2889(301*10^165082+23)/9165084Robert Price06/2021
2890(23*10^165060-83)/3165061Robert Price08/2019
28917*10^165023-27165024Robert Price11/2022
2892(76*10^164984+77)/9164985Robert Price10/2019
289331058^36715-36715^31058164931Frank Doornink01/2024
2894(4*10^164929-211)/9164929Robert Price03/2022
289510^164878-500001164878Robert Price03/2022
28969*10^164791-89164792Robert Price04/2020
28972^547178-1856501164717Enzo Doria10/2015
289811^158160-60164707Enzo Doria07/2012
2899(26*10^164643-167)/3164644Robert Price10/2019
2900(10^164643+83)/3164643Robert Price08/2021
29012^546398-59201164483Enzo Doria10/2015
29022^546332-114893164463Enzo Doria05/2015
290332003^36504-36504^32003164458Frank Doornink01/2024
2904(65*10^164427+277)/9164428Robert Price08/2021
29052^545958+1876189164350Enzo Doria07/2016
29062^545878-49841164326Enzo Doria10/2015
2907(10^164284+77)/3164284Robert Price01/2018
29082^545668-4019164263Yves Minet04/2017
290910^164216+780639164217Patrick De Geest08/2021
291110^164216-50000000001164216Robert Price12/2020
291010^164216-891051164216Patrick De Geest08/2021
2912(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
2913(16*10^164122+197)/3164123Robert Price04/2019
29142^545185+76757164118Enzo Doria05/2016
29152^545076-114329164085Enzo Doria01/2015
2916(2*10^164043-143)/3164043Robert Price03/2018
2917(33085^36481-1)/(33085^191-1)164018Ryan Propper11/2023
2918(29^112153+1)/30164011Lelio R Paula03/2017
29192^544757+1874777163989Enzo Doria06/2016
29202^544723+211193163978Enzo Doria08/2023
29212^544444-457199163894Enzo Doria01/2015
2922(32804^36481-1)/(32804^191-1)163883Ryan Propper11/2023
29232^544264-343529163840Enzo Doria07/2015
29247*10^163780+9163781Robert Price09/2015
29252^543989+2793047163758Enzo Doria02/2016
2926(28*10^163709+113)/3163710Robert Price03/2020
2927(2013^49729-1)/(2013^223-1)163561Ryan Propper11/2023
2928(23*10^163523+301)/9163524Robert Price06/2021
2929(68*10^163521-329)/9163522Robert Price03/2021
293035820^35899+35899^35820163489Norbert Schneider11/2021
29312^542870-69551163421Enzo Doria12/2015
29322^542502+24799163310Enzo Doria10/2023
29332^542395+72533163278Enzo Doria04/2016
29342^542258+216949163236Enzo Doria12/2023
29352^542072-3683163180Yves Minet03/2017
2936fibonacci(780566)-4163129Jon Grantham08/2023
2937(682*10^163106-7)/9163108Robert Price08/2021
29382^541779-1867357163092Enzo Doria04/2016
2939(29*10^163056+313)/9163057Robert Price04/2021
29402^541476+214743163001Enzo Doria11/2023
294113^142159+14^142159-2162933Harsh Aggarwal05/2024
29428*10^162924+9162925Robert Price12/2015
29432^540905+81557162829Enzo Doria08/2016
29442^540628-2939162746Yves Minet09/2014
2945919^54919-918^54919162743Jean-Louis Charton01/2013
2946(203*10^162689+1)/3162691Robert Price03/2020
29473*10^162620-59162621Robert Price09/2018
29482^540180+26791162611Enzo Doria12/2023
29493^340694-112960162553Enzo Doria07/2014
29502^539807-114081162499Enzo Doria12/2014
2951414^62093+62093^414162498Norbert Schneider03/2022
29522^539654-114893162453Enzo Doria05/2015
29539*10^162449-71162450Robert Price11/2020
29542^539617-1851583162441Enzo Doria08/2015
2955(509*10^162422+31)/9162424Robert Price08/2022
2956(91*10^162410+11)/3162412Robert Price02/2020
29572^539346+81049162360Enzo Doria07/2016
29582^539220-115499162322Enzo Doria07/2015
29592^539217-113713162321Enzo Doria09/2014
29609^170099-8^170099162316Jean-Louis Charton05/2005
29614*10^162263-39162264Robert Price09/2020
296231243^36098-36098^31243162252Frank Doornink01/2024
296331987^36000-36000^31987162180Frank Doornink01/2024
2964(115*10^162153-1)/3162155Serge Batalov12/2014
2965(10^162138+11)/3162138Serge Batalov07/2015
2966(61*10^162100-403)/9162101Robert Price10/2021
29672^538473-112723162097Enzo Doria06/2014
29682^538157+79337162002Enzo Doria06/2016
29692^538136-114749161996Enzo Doria05/2015
29702^538104+1531161986Lelio R Paula01/2013
2971(9*29^110727-1199)/14161927Curtis Bright05/2015
2972((2^179294-1)^3+2)/11161918Serge Batalov03/2023
297331198^36027-36027^31198161910Frank Doornink01/2024
29742^537815-22737161899Enzo Doria07/2013
29752^537804-39839161896Enzo Doria09/2015
2976(754*10^161816-7)/9161818Robert Price05/2020
29772^537461+29867161792Enzo Doria03/2024
29782^537458-59201161791Enzo Doria10/2015
29792*10^161766+51161767Robert Price05/2018
2980(7*10^161760+131)/3161761Robert Price06/2020
29812^537209-49849161717Enzo Doria10/2015
2982(58*10^161691+329)/9161692Robert Price05/2019
298323*10^161668-3161670Robert Price10/2021
29842^536937+1879397161635Enzo Doria09/2016
29853*2^536868-5161614Jon Grantham07/2023
298634*10^161593-9161595Robert Price06/2020
2987(31*10^161582-1)/3161584Robert Price02/2020
298824494^36813+36813^24494161575Norbert Schneider11/2023
29892^536569-22881161524Enzo Doria07/2013
2990(46*10^161505+593)/9161506Robert Price04/2022
299110^161253+573493161254Patrick De Geest07/2018
299210^161253-8001161253Robert Price03/2018
299397*10^161247-3161249Robert Price05/2020
29947*10^161192-9161193Robert Price10/2015
29952^535415-19161176Stefano Morozzi07/2022
29962^535269-113803161133Enzo Doria09/2014
29972^535205-23295161113Enzo Doria08/2013
2998(49*10^161105+437)/9161106Robert Price09/2021
2999(89^82609+1)/90161036Paul Bourdelais10/2017
30002^534429-19160880Stefano Morozzi07/2022


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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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