PRP Records

Probable Primes Top 10000

(288949 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 ?
17514*10^168788-47168789Robert Price10/2021
1752(29*10^168711+691)/9168712Robert Price08/2021
17532^560405-39943168699Enzo Doria09/2015
175489*10^168614-7168616Robert Price04/2020
1755(23*10^168608-83)/3168609Robert Price08/2019
1756(94*10^168541+11)/3168543Robert Price04/2020
17572^559686-350471168483Enzo Doria06/2015
17582^559672-1855889168479Enzo Doria09/2015
1759(5*10^168379-473)/9168379Robert Price01/2018
17602^559000-59939168276Enzo Doria11/2015
1761(16*10^168181+41)/3168182Robert Price03/2019
1762(19*10^168173+77)/3168174Robert Price05/2019
17632^558640-114149168168Enzo Doria12/2014
17642^558498-1849277168125Enzo Doria08/2015
17652^558476-1850249168119Enzo Doria08/2015
1766(7*10^168067+71)/3168068Robert Price05/2018
17672^558150-1852211168020Enzo Doria08/2015
17682^558125-113661168013Enzo Doria09/2014
1769393^64747-392^64747167980Jean-Louis Charton08/2012
1770(13*10^167911+179)/3167912Robert Price11/2018
1771(26*10^167861-167)/3167862Robert Price10/2019
177239^105456+2167788Robert Price04/2015
1773(28^115877-1)/27167691Paul Bourdelais12/2017
177410^167639+121911167640Patrick De Geest07/2018
177510^167639-8001167639Robert Price03/2018
17762^556504-462059167525Enzo Doria07/2015
1777(88*10^167522-637)/9167523Robert Price11/2020
17785*10^167510+9167511Robert Price08/2015
17797*10^167437-93167438Robert Price08/2020
178011^160663+6167314Paul Bourdelais02/2021
1781(7*10^167308-493)/9167308Robert Price04/2021
17822^555343+1874333167175Enzo Doria06/2016
17832^555210-461261167135Enzo Doria07/2015
17849*10^166996+59166997Robert Price01/2020
1785(68*10^166976-329)/9166977Robert Price03/2021
17862^554372+1880527166883Enzo Doria11/2016
17872^554299+72173166861Enzo Doria04/2016
1788(185*10^166837+7)/3166839Robert Price03/2020
1789(14*10^166813+139)/9166814Robert Price11/2021
17902^554037-2797063166782Enzo Doria03/2016
1791(49*10^166721-139)/9166722Robert Price03/2019
17922*10^166646+69166647Robert Price06/2020
17932^553484-29819166616Enzo Doria08/2015
1794(188*10^166611+7)/3166613Robert Price03/2020
17952^553383-2784217166585Enzo Doria10/2015
17962^553069+76427166491Enzo Doria05/2016
17972*10^166458+51166459Robert Price05/2018
1798589^60089-588^60089166454Jean-Louis Charton09/2012
179911^159756-2424166369Mike Oakes06/2010
18002^552649-361275166364Enzo Doria05/2014
18012^552628-113669166358Enzo Doria09/2014
180210^166324+550603166325Patrick De Geest07/2018
180310^166324-801166324Robert Price02/2018
1804(85*10^166297-1)/3166299Robert Price02/2020
18058*10^166227+87166228Robert Price10/2019
18062^552137+1879397166210Enzo Doria09/2016
1807(103*10^166126+11)/3166128Robert Price01/2021
1808(23^121949-1)/22166061Paul Bourdelais10/2017
18092^551542+19249166031Payam Samidoost08/2002
18102^551535-23821166029Enzo Doria08/2013
18112^551507-23557166021Enzo Doria08/2013
181210^165947-7000000001165947Robert Price12/2021
18134*10^165938-47165939Robert Price10/2021
18147*10^165916-3165917Robert Price08/2015
1815(29*10^165796+67)/3165797Robert Price12/2019
181681^86837-80^86837165728Robert Price01/2015
1817(71*10^165663-539)/9165664Robert Price07/2019
18182^550270-69551165648Enzo Doria12/2015
1819(202*10^165569-13)/9165571Robert Price01/2020
18202^550000-23625165567Enzo Doria08/2013
18212^549675-1852057165469Enzo Doria08/2015
1822(529*10^165394-7)/9165396Robert Price08/2021
1823-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1824(28*10^165358-1)/9165359Serge Batalov10/2014
18252^549278+1879669165350Enzo Doria09/2016
1826(7*10^165350-439)/9165350Robert Price02/2018
18272^549252-351269165342Enzo Doria06/2015
182867*10^165327-9165329Robert Price03/2021
1829(14*10^165282+73)/3165283Robert Price12/2018
18302^549049+2797607165281Enzo Doria04/2016
1831(7*10^165239+107)/3165240Robert Price02/2018
1832(44^100511-1)/43165184Paul Bourdelais11/2017
1833(7*10^165134+107)/3165135Robert Price02/2018
1834(301*10^165082+23)/9165084Robert Price06/2021
1835(23*10^165060-83)/3165061Robert Price08/2019
1836(76*10^164984+77)/9164985Robert Price10/2019
18379*10^164791-89164792Robert Price04/2020
18382^547178-1856501164717Enzo Doria10/2015
183911^158160-60164707Enzo Doria07/2012
1840(26*10^164643-167)/3164644Robert Price10/2019
1841(10^164643+83)/3164643Robert Price08/2021
18422^546398-59201164483Enzo Doria10/2015
18432^546332-114893164463Enzo Doria05/2015
1844(65*10^164427+277)/9164428Robert Price08/2021
18452^545958+1876189164350Enzo Doria07/2016
18462^545878-49841164326Enzo Doria10/2015
1847(10^164284+77)/3164284Robert Price01/2018
18482^545668-4019164263Yves Minet04/2017
184910^164216+780639164217Patrick De Geest08/2021
185110^164216-50000000001164216Robert Price12/2020
185010^164216-891051164216Patrick De Geest08/2021
1852(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
1853(16*10^164122+197)/3164123Robert Price04/2019
18542^545185+76757164118Enzo Doria05/2016
18552^545076-114329164085Enzo Doria01/2015
1856(2*10^164043-143)/3164043Robert Price03/2018
1857(29^112153+1)/30164011Lelio R Paula03/2017
18582^544757+1874777163989Enzo Doria06/2016
18592^544444-457199163894Enzo Doria01/2015
18602^544264-343529163840Enzo Doria07/2015
18617*10^163780+9163781Robert Price09/2015
18622^543989+2793047163758Enzo Doria02/2016
1863(28*10^163709+113)/3163710Robert Price03/2020
1864(23*10^163523+301)/9163524Robert Price06/2021
1865(68*10^163521-329)/9163522Robert Price03/2021
186635820^35899+35899^35820163489Norbert Schneider11/2021
18672^542870-69551163421Enzo Doria12/2015
18682^542395+72533163278Enzo Doria04/2016
18692^542072-3683163180Yves Minet03/2017
1870(682*10^163106-7)/9163108Robert Price08/2021
18712^541779-1867357163092Enzo Doria04/2016
1872(29*10^163056+313)/9163057Robert Price04/2021
18738*10^162924+9162925Robert Price12/2015
18742^540905+81557162829Enzo Doria08/2016
18752^540628-2939162746Yves Minet09/2014
1876919^54919-918^54919162743Jean-Louis Charton01/2013
1877(203*10^162689+1)/3162691Robert Price03/2020
18783*10^162620-59162621Robert Price09/2018
18793^340694-112960162553Enzo Doria07/2014
18802^539807-114081162499Enzo Doria12/2014
18812^539654-114893162453Enzo Doria05/2015
18829*10^162449-71162450Robert Price11/2020
18832^539617-1851583162441Enzo Doria08/2015
1884(91*10^162410+11)/3162412Robert Price02/2020
18852^539346+81049162360Enzo Doria07/2016
18862^539220-115499162322Enzo Doria07/2015
18872^539217-113713162321Enzo Doria09/2014
18889^170099-8^170099162316Jean-Louis Charton05/2005
18894*10^162263-39162264Robert Price09/2020
1890(115*10^162153-1)/3162155Serge Batalov12/2014
1891(10^162138+11)/3162138Serge Batalov07/2015
1892(61*10^162100-403)/9162101Robert Price10/2021
18932^538473-112723162097Enzo Doria06/2014
18942^538157+79337162002Enzo Doria06/2016
18952^538136-114749161996Enzo Doria05/2015
18962^538104+1531161986Lelio R Paula01/2013
1897(9*29^110727-1199)/14161927Curtis Bright05/2015
18982^537815-22737161899Enzo Doria07/2013
18992^537804-39839161896Enzo Doria09/2015
1900(754*10^161816-7)/9161818Robert Price05/2020
19012^537458-59201161791Enzo Doria10/2015
19022*10^161766+51161767Robert Price05/2018
1903(7*10^161760+131)/3161761Robert Price06/2020
19042^537209-49849161717Enzo Doria10/2015
1905(58*10^161691+329)/9161692Robert Price05/2019
190623*10^161668-3161670Robert Price10/2021
19072^536937+1879397161635Enzo Doria09/2016
190834*10^161593-9161595Robert Price06/2020
1909(31*10^161582-1)/3161584Robert Price02/2020
19102^536569-22881161524Enzo Doria07/2013
191110^161253+573493161254Patrick De Geest07/2018
191210^161253-8001161253Robert Price03/2018
191397*10^161247-3161249Robert Price05/2020
19147*10^161192-9161193Robert Price10/2015
19152^535269-113803161133Enzo Doria09/2014
19162^535205-23295161113Enzo Doria08/2013
1917(49*10^161105+437)/9161106Robert Price09/2021
1918(89^82609+1)/90161036Paul Bourdelais10/2017
19192^534359-23229160859Enzo Doria08/2013
1920457^60454+60454^457160803Norbert Schneider07/2021
19218*10^160782+53160783Robert Price08/2020
192267^88037-66^88037160763Robert Price10/2013
1923(88*10^160761-637)/9160762Robert Price11/2020
19242^533948-1852559160735Enzo Doria08/2015
19252^533665-23335160650Enzo Doria08/2013
1926(19*10^160619+77)/3160620Robert Price05/2019
19273^336353-2^336353160482Mike Oakes10/2007
19282*10^160339-63160340Robert Price01/2022
1929(91*10^160249+11)/3160251Robert Price02/2020
19302^532253+1868417160225Enzo Doria04/2016
19312^532108-291989160181Enzo Doria07/2015
1932(28*10^160171-79)/3160172Robert Price02/2021
1933(26*10^160166-131)/3160167Robert Price10/2019
1934(17*10^160143+67)/3160144Robert Price01/2019
1935(19*10^159921-49)/3159922Robert Price05/2019
19362^531110-1853771159881Enzo Doria09/2015
1937(275^65536+53^65536)/2159864Kellen Shenton11/2020
19382^530992-1845299159845Enzo Doria07/2015
19392^530810+25159790Stefano Morozzi04/2021
1940(136*10^159736-1)/9159738Serge Batalov12/2014
19412^530417-113833159672Enzo Doria09/2014
19422^530406-69701159669Enzo Doria02/2016
19435*10^159656+41159657Robert Price03/2019
19448*10^159614+29159615Robert Price11/2021
19457^188858-188858^7159604Norbert Schneider05/2018
1946(24^115597-1)/23159547Paul Bourdelais09/2017
1947(17*10^159438-377)/9159439Robert Price03/2018
1948(203*10^159381+1)/3159383Robert Price03/2020
194989*10^159258-9159260Robert Price05/2020
19502^528944-461315159229Enzo Doria07/2015
1951(13*10^159147+161)/3159148Robert Price11/2018
19522^528620-113879159131Enzo Doria10/2014
19532^528000-23307158944Enzo Doria08/2013
1954(29*10^158909+61)/9158910Robert Price08/2018
19552^527817+1876817158889Enzo Doria07/2016
19562^527774-49451158876Enzo Doria10/2015
19572^527745-291553158868Enzo Doria07/2015
1958(91*10^158862+11)/3158864Robert Price02/2020
19592^527644-1856999158837Enzo Doria10/2015
1960(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
19612^527573-1863253158816Enzo Doria12/2015
19622^527553-23401158810Enzo Doria08/2013
1963(49*10^158783+437)/9158784Robert Price09/2021
196410^158755+310207158756Patrick De Geest08/2021
196510^158755-50001158755Robert Price08/2020
196611^152420-210158730Enzo Doria09/2012
1967(13*10^158694+401)/9158695Robert Price01/2018
19682^527052-69059158659Enzo Doria11/2015
19692^526849-113233158598Enzo Doria07/2014
1970(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
1971(299*10^158544-17)/3158546Robert Price04/2020
19722^526658-3551158540Yves Minet03/2017
19737*10^158465-11158466Robert Price06/2019
19742^526375-23115158455Enzo Doria08/2013
1975(77*10^158407-293)/9158408Robert Price09/2019
19762^526028-112793158351Enzo Doria07/2014
1977(229*10^158339-1)/3158341Robert Price07/2020
19782^525690-9221158249Lelio R Paula01/2013
19792*10^158242-7158243Robert Price10/2015
19802^525667-525667^2158242Henri Lifchitz12/2017
1981(56*10^158230+187)/9158231Robert Price10/2021
198210^158209-7000000001158209Robert Price12/2021
19832^525186-1857431158097Enzo Doria10/2015
19842^524515-23245157895Enzo Doria08/2013
19852^524499-109087157890Enzo Doria04/2014
19862^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
19872^524288+189093157827Makoto Morimoto01/2016
19882^524288-164073157827Matthias Baur03/2020
1989(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
1990(10^157792+359)/9157792Serge Batalov12/2014
19912^524154+25157787Stefano Morozzi04/2021
19922^523924+1876591157717Enzo Doria07/2016
1993(17*10^157705+67)/3157706Robert Price01/2019
1994(46^94841+1)/47157696Robert Price01/2014
19952^523774+77839157672Enzo Doria05/2016
19962^523587+2799143157616Enzo Doria04/2016
19972^523371+1872113157551Enzo Doria05/2016
19988*10^157477+27157478Robert Price09/2021
1999(8*10^157368+49)/3157369Robert Price05/2020
2000(82*10^157319+449)/9157320Robert Price11/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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