PRP Records

Probable Primes Top 10000

(291910 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
2001(194*10^169461-17)/3169463Robert Price09/2020
20022^562749+2793047169405Enzo Doria02/2016
2003(154*10^169337-1)/9169339Serge Batalov12/2014
2004(109*10^169337+11)/3169339Robert Price06/2022
2005(56*10^169311+691)/9169312Robert Price05/2019
20062^562369-29503169290Enzo Doria08/2015
2007(17*10^169283+19)/9169284Robert Price03/2021
200810^169074-5000000001169074Robert Price09/2022
20098*10^169071+59169072Robert Price11/2021
2010(10^169044+173)/3169044Robert Price05/2021
2011(22*10^169019+383)/9169020Robert Price05/2018
2012(64*10^168935+143)/9168936Robert Price05/2021
2013(22*10^168906+47)/3168907Robert Price06/2021
20145*10^168807+87168808Robert Price02/2019
2015(77*10^168803-149)/9168804Robert Price03/2022
20164*10^168788-47168789Robert Price10/2021
2017(154*10^168781+17)/9168783Robert Price06/2022
2018(418*10^168751-31)/9168753Robert Price05/2022
2019(29*10^168711+691)/9168712Robert Price08/2021
20202^560405-39943168699Enzo Doria09/2015
2021(397*10^168634+17)/9168636Robert Price03/2022
202289*10^168614-7168616Robert Price04/2020
2023(23*10^168608-83)/3168609Robert Price08/2019
2024(94*10^168541+11)/3168543Robert Price04/2020
20252^559686-350471168483Enzo Doria06/2015
20262^559672-1855889168479Enzo Doria09/2015
2027(5*10^168379-473)/9168379Robert Price01/2018
20282^559000-59939168276Enzo Doria11/2015
2029(16*10^168181+41)/3168182Robert Price03/2019
2030(19*10^168173+77)/3168174Robert Price05/2019
2031(74*10^168170+529)/9168171Robert Price02/2022
20322^558640-114149168168Enzo Doria12/2014
20332^558498-1849277168125Enzo Doria08/2015
20342^558476-1850249168119Enzo Doria08/2015
2035(7*10^168067+71)/3168068Robert Price05/2018
20362^558150-1852211168020Enzo Doria08/2015
20372^558125-113661168013Enzo Doria09/2014
2038393^64747-392^64747167980Jean-Louis Charton08/2012
2039(13*10^167911+179)/3167912Robert Price11/2018
2040(26*10^167861-167)/3167862Robert Price10/2019
204139^105456+2167788Robert Price04/2015
2042(28^115877-1)/27167691Paul Bourdelais12/2017
20436*10^167662-13167663Robert Price07/2022
204410^167639+121911167640Patrick De Geest07/2018
204510^167639-8001167639Robert Price03/2018
20462^556504-462059167525Enzo Doria07/2015
2047(88*10^167522-637)/9167523Robert Price11/2020
20485*10^167510+9167511Robert Price08/2015
20497*10^167437-93167438Robert Price08/2020
205011^160663+6167314Paul Bourdelais02/2021
2051(7*10^167308-493)/9167308Robert Price04/2021
20522^555343+1874333167175Enzo Doria06/2016
20532^555210-461261167135Enzo Doria07/2015
20549*10^166996+59166997Robert Price01/2020
2055(68*10^166976-329)/9166977Robert Price03/2021
2056(64*10^166901+683)/9166902Robert Price06/2022
20572^554372+1880527166883Enzo Doria11/2016
20582^554299+72173166861Enzo Doria04/2016
2059(185*10^166837+7)/3166839Robert Price03/2020
2060(14*10^166813+139)/9166814Robert Price11/2021
20612^554037-2797063166782Enzo Doria03/2016
2062(49*10^166721-139)/9166722Robert Price03/2019
20632*10^166646+69166647Robert Price06/2020
20642^553484-29819166616Enzo Doria08/2015
2065(188*10^166611+7)/3166613Robert Price03/2020
20662^553383-2784217166585Enzo Doria10/2015
20672^553069+76427166491Enzo Doria05/2016
20682*10^166458+51166459Robert Price05/2018
2069589^60089-588^60089166454Jean-Louis Charton09/2012
207011^159756-2424166369Mike Oakes06/2010
20712^552649-361275166364Enzo Doria05/2014
20722^552628-113669166358Enzo Doria09/2014
2073(19*10^166325+137)/3166326Robert Price03/2022
207410^166324+550603166325Patrick De Geest07/2018
207510^166324-801166324Robert Price02/2018
2076(85*10^166297-1)/3166299Robert Price02/2020
20778*10^166227+87166228Robert Price10/2019
20782^552137+1879397166210Enzo Doria09/2016
2079(103*10^166126+11)/3166128Robert Price01/2021
2080(22*10^166077+179)/3166078Robert Price02/2022
2081(23^121949-1)/22166061Paul Bourdelais10/2017
20822^551542+19249166031Payam Samidoost08/2002
20832^551535-23821166029Enzo Doria08/2013
20842^551507-23557166021Enzo Doria08/2013
208510^165947-7000000001165947Robert Price12/2021
20864*10^165938-47165939Robert Price10/2021
20877*10^165916-3165917Robert Price08/2015
2088(29*10^165796+67)/3165797Robert Price12/2019
208981^86837-80^86837165728Robert Price01/2015
2090(71*10^165716-17)/9165717Serge Batalov01/2023
2091(71*10^165663-539)/9165664Robert Price07/2019
20922^550270-69551165648Enzo Doria12/2015
2093(202*10^165569-13)/9165571Robert Price01/2020
20942^550000-23625165567Enzo Doria08/2013
20952^549675-1852057165469Enzo Doria08/2015
2096(529*10^165394-7)/9165396Robert Price08/2021
2097-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
2098(28*10^165358-1)/9165359Serge Batalov10/2014
20992^549278+1879669165350Enzo Doria09/2016
2100(7*10^165350-439)/9165350Robert Price02/2018
21012^549252-351269165342Enzo Doria06/2015
210267*10^165327-9165329Robert Price03/2021
2104(14*10^165282+73)/3165283Robert Price12/2018
2103(8*10^165283-629)/9165283Robert Price01/2022
21052^549049+2797607165281Enzo Doria04/2016
2106(218*10^165258+7)/9165260Robert Price06/2022
2107(7*10^165239+107)/3165240Robert Price02/2018
2108(44^100511-1)/43165184Paul Bourdelais11/2017
2109(7*10^165134+107)/3165135Robert Price02/2018
2110(301*10^165082+23)/9165084Robert Price06/2021
2111(23*10^165060-83)/3165061Robert Price08/2019
21127*10^165023-27165024Robert Price11/2022
2113(76*10^164984+77)/9164985Robert Price10/2019
2114(4*10^164929-211)/9164929Robert Price03/2022
211510^164878-500001164878Robert Price03/2022
21169*10^164791-89164792Robert Price04/2020
21172^547178-1856501164717Enzo Doria10/2015
211811^158160-60164707Enzo Doria07/2012
2119(26*10^164643-167)/3164644Robert Price10/2019
2120(10^164643+83)/3164643Robert Price08/2021
21212^546398-59201164483Enzo Doria10/2015
21222^546332-114893164463Enzo Doria05/2015
2123(65*10^164427+277)/9164428Robert Price08/2021
21242^545958+1876189164350Enzo Doria07/2016
21252^545878-49841164326Enzo Doria10/2015
2126(10^164284+77)/3164284Robert Price01/2018
21272^545668-4019164263Yves Minet04/2017
212810^164216+780639164217Patrick De Geest08/2021
213010^164216-50000000001164216Robert Price12/2020
212910^164216-891051164216Patrick De Geest08/2021
2131(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
2132(16*10^164122+197)/3164123Robert Price04/2019
21332^545185+76757164118Enzo Doria05/2016
21342^545076-114329164085Enzo Doria01/2015
2135(2*10^164043-143)/3164043Robert Price03/2018
2136(29^112153+1)/30164011Lelio R Paula03/2017
21372^544757+1874777163989Enzo Doria06/2016
21382^544444-457199163894Enzo Doria01/2015
21392^544264-343529163840Enzo Doria07/2015
21407*10^163780+9163781Robert Price09/2015
21412^543989+2793047163758Enzo Doria02/2016
2142(28*10^163709+113)/3163710Robert Price03/2020
2143(23*10^163523+301)/9163524Robert Price06/2021
2144(68*10^163521-329)/9163522Robert Price03/2021
214535820^35899+35899^35820163489Norbert Schneider11/2021
21462^542870-69551163421Enzo Doria12/2015
21472^542395+72533163278Enzo Doria04/2016
21482^542072-3683163180Yves Minet03/2017
2149(682*10^163106-7)/9163108Robert Price08/2021
21502^541779-1867357163092Enzo Doria04/2016
2151(29*10^163056+313)/9163057Robert Price04/2021
21528*10^162924+9162925Robert Price12/2015
21532^540905+81557162829Enzo Doria08/2016
21542^540628-2939162746Yves Minet09/2014
2155919^54919-918^54919162743Jean-Louis Charton01/2013
2156(203*10^162689+1)/3162691Robert Price03/2020
21573*10^162620-59162621Robert Price09/2018
21583^340694-112960162553Enzo Doria07/2014
21592^539807-114081162499Enzo Doria12/2014
2160414^62093+62093^414162498Norbert Schneider03/2022
21612^539654-114893162453Enzo Doria05/2015
21629*10^162449-71162450Robert Price11/2020
21632^539617-1851583162441Enzo Doria08/2015
2164(509*10^162422+31)/9162424Robert Price08/2022
2165(91*10^162410+11)/3162412Robert Price02/2020
21662^539346+81049162360Enzo Doria07/2016
21672^539220-115499162322Enzo Doria07/2015
21682^539217-113713162321Enzo Doria09/2014
21699^170099-8^170099162316Jean-Louis Charton05/2005
21704*10^162263-39162264Robert Price09/2020
2171(115*10^162153-1)/3162155Serge Batalov12/2014
2172(10^162138+11)/3162138Serge Batalov07/2015
2173(61*10^162100-403)/9162101Robert Price10/2021
21742^538473-112723162097Enzo Doria06/2014
21752^538157+79337162002Enzo Doria06/2016
21762^538136-114749161996Enzo Doria05/2015
21772^538104+1531161986Lelio R Paula01/2013
2178(9*29^110727-1199)/14161927Curtis Bright05/2015
21792^537815-22737161899Enzo Doria07/2013
21802^537804-39839161896Enzo Doria09/2015
2181(754*10^161816-7)/9161818Robert Price05/2020
21822^537458-59201161791Enzo Doria10/2015
21832*10^161766+51161767Robert Price05/2018
2184(7*10^161760+131)/3161761Robert Price06/2020
21852^537209-49849161717Enzo Doria10/2015
2186(58*10^161691+329)/9161692Robert Price05/2019
218723*10^161668-3161670Robert Price10/2021
21882^536937+1879397161635Enzo Doria09/2016
218934*10^161593-9161595Robert Price06/2020
2190(31*10^161582-1)/3161584Robert Price02/2020
21912^536569-22881161524Enzo Doria07/2013
2192(46*10^161505+593)/9161506Robert Price04/2022
219310^161253+573493161254Patrick De Geest07/2018
219410^161253-8001161253Robert Price03/2018
219597*10^161247-3161249Robert Price05/2020
21967*10^161192-9161193Robert Price10/2015
21972^535415-19161176Stefano Morozzi07/2022
21982^535269-113803161133Enzo Doria09/2014
21992^535205-23295161113Enzo Doria08/2013
2200(49*10^161105+437)/9161106Robert Price09/2021
2201(89^82609+1)/90161036Paul Bourdelais10/2017
22022^534429-19160880Stefano Morozzi07/2022
22032^534359-23229160859Enzo Doria08/2013
220410^160836-1001160836Robert Price10/2022
2205457^60454+60454^457160803Norbert Schneider07/2021
22068*10^160782+53160783Robert Price08/2020
220767^88037-66^88037160763Robert Price10/2013
2208(88*10^160761-637)/9160762Robert Price11/2020
22092^533948-1852559160735Enzo Doria08/2015
22102^533665-23335160650Enzo Doria08/2013
2211(19*10^160619+77)/3160620Robert Price05/2019
22122^533350-5160555Stefano Morozzi07/2022
2213(38*10^160508+151)/9160509Robert Price03/2022
22143^336353-2^336353160482Mike Oakes10/2007
22152*10^160339-63160340Robert Price01/2022
2216(91*10^160249+11)/3160251Robert Price02/2020
2217(772*10^160239-7)/9160241Robert Price06/2022
2218(2*10^160226+187)/9160226Robert Price06/2022
22192^532253+1868417160225Enzo Doria04/2016
22202^532108-291989160181Enzo Doria07/2015
2221(28*10^160171-79)/3160172Robert Price02/2021
2222(26*10^160166-131)/3160167Robert Price10/2019
222355*10^160145+9160147Robert Price03/2022
2224(17*10^160143+67)/3160144Robert Price01/2019
2225(19*10^159921-49)/3159922Robert Price05/2019
22262^531110-1853771159881Enzo Doria09/2015
2227(275^65536+53^65536)/2159864Kellen Shenton11/2020
22282^530992-1845299159845Enzo Doria07/2015
22292^530810+25159790Stefano Morozzi04/2021
2230(136*10^159736-1)/9159738Serge Batalov12/2014
22312^530417-113833159672Enzo Doria09/2014
22322^530406-69701159669Enzo Doria02/2016
22335*10^159656+41159657Robert Price03/2019
22348*10^159614+29159615Robert Price11/2021
22357^188858-188858^7159604Norbert Schneider05/2018
22367*10^159553-27159554Robert Price11/2022
2237(24^115597-1)/23159547Paul Bourdelais09/2017
2238(17*10^159438-377)/9159439Robert Price03/2018
2239(203*10^159381+1)/3159383Robert Price03/2020
224089*10^159258-9159260Robert Price05/2020
22412^528944-461315159229Enzo Doria07/2015
2242(13*10^159147+161)/3159148Robert Price11/2018
22432^528620-113879159131Enzo Doria10/2014
2244(47*10^159083+259)/9159084Robert Price03/2022
22452^528000-23307158944Enzo Doria08/2013
2246(29*10^158909+61)/9158910Robert Price08/2018
22472^527817+1876817158889Enzo Doria07/2016
22482^527774-49451158876Enzo Doria10/2015
22492^527745-291553158868Enzo Doria07/2015
2250(91*10^158862+11)/3158864Robert Price02/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!