PRP Records

Probable Primes Top 10000

(280932 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 ?
15013*10^171391+59171392Robert Price08/2018
1502(13*10^171306-37)/3171307Robert Price01/2019
15038*10^171296+87171297Robert Price10/2019
1504(55^98419-1)/54171284Paul Bourdelais12/2017
1505(29*10^171275+67)/3171276Robert Price12/2019
15062^568642+1876129171179Enzo Doria07/2016
1507(19*10^170970+131)/3170971Robert Price06/2020
1508(46*10^170932+143)/9170933Robert Price01/2019
1509(79*10^170901-1)/3170903Robert Price02/2020
1510(58*10^170842+221)/9170843Robert Price02/2017
15113*10^170800+73170801Robert Price08/2018
151211^164009-270170798Enzo Doria10/2012
15132*10^170767+41170768Robert Price05/2018
15143^357706-112358170670Enzo Doria07/2014
1515TheodorusPrime(170657)170657Eric W. Weisstein08/2013
15162^566871+1876163170646Enzo Doria07/2016
1517(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
15182^566496+7170533Donovan Johnson07/2006
1519(7^201653+1)/8170416Paul Bourdelais02/2010
15207*10^170348+33170349Robert Price06/2020
15212^565183-352021170138Enzo Doria07/2015
15222^565143-114457170125Enzo Doria02/2015
15232^564976-49869170075Enzo Doria10/2015
1524(7*10^169944+23)/3169945Robert Price06/2020
15252^564526-351401169940Enzo Doria07/2015
15264*10^169759+19169760Robert Price10/2018
152721^128327-20^128327169677Jean-Louis Charton11/2014
1528(4*10^169559+83)/3169560Robert Price02/2018
1529(194*10^169461-17)/3169463Robert Price09/2020
15302^562749+2793047169405Enzo Doria02/2016
1531(154*10^169337-1)/9169339Serge Batalov12/2014
1532(56*10^169311+691)/9169312Robert Price05/2019
15332^562369-29503169290Enzo Doria08/2015
1534(17*10^169283+19)/9169284Robert Price03/2021
1535(22*10^169019+383)/9169020Robert Price05/2018
15365*10^168807+87168808Robert Price02/2019
15372^560405-39943168699Enzo Doria09/2015
153889*10^168614-7168616Robert Price04/2020
1539(23*10^168608-83)/3168609Robert Price08/2019
1540(94*10^168541+11)/3168543Robert Price04/2020
15412^559686-350471168483Enzo Doria06/2015
15422^559672-1855889168479Enzo Doria09/2015
1543(5*10^168379-473)/9168379Robert Price01/2018
15442^559000-59939168276Enzo Doria11/2015
1545(16*10^168181+41)/3168182Robert Price03/2019
1546(19*10^168173+77)/3168174Robert Price05/2019
15472^558640-114149168168Enzo Doria12/2014
15482^558498-1849277168125Enzo Doria08/2015
15492^558476-1850249168119Enzo Doria08/2015
1550(7*10^168067+71)/3168068Robert Price05/2018
15512^558150-1852211168020Enzo Doria08/2015
15522^558125-113661168013Enzo Doria09/2014
1553393^64747-392^64747167980Jean-Louis Charton08/2012
1554(13*10^167911+179)/3167912Robert Price11/2018
1555(26*10^167861-167)/3167862Robert Price10/2019
155639^105456+2167788Robert Price04/2015
1557(28^115877-1)/27167691Paul Bourdelais12/2017
155810^167639+121911167640Patrick De Geest07/2018
155910^167639-8001167639Robert Price03/2018
15602^556504-462059167525Enzo Doria07/2015
1561(88*10^167522-637)/9167523Robert Price11/2020
15625*10^167510+9167511Robert Price08/2015
15637*10^167437-93167438Robert Price08/2020
156411^160663+6167314Paul Bourdelais02/2021
15652^555343+1874333167175Enzo Doria06/2016
15662^555210-461261167135Enzo Doria07/2015
15679*10^166996+59166997Robert Price01/2020
1568(68*10^166976-329)/9166977Robert Price03/2021
15692^554372+1880527166883Enzo Doria11/2016
15702^554299+72173166861Enzo Doria04/2016
1571(185*10^166837+7)/3166839Robert Price03/2020
15722^554037-2797063166782Enzo Doria03/2016
1573(49*10^166721-139)/9166722Robert Price03/2019
15742*10^166646+69166647Robert Price06/2020
15752^553484-29819166616Enzo Doria08/2015
1576(188*10^166611+7)/3166613Robert Price03/2020
15772^553383-2784217166585Enzo Doria10/2015
15782^553069+76427166491Enzo Doria05/2016
15792*10^166458+51166459Robert Price05/2018
1580589^60089-588^60089166454Jean-Louis Charton09/2012
158111^159756-2424166369Mike Oakes06/2010
15822^552649-361275166364Enzo Doria05/2014
15832^552628-113669166358Enzo Doria09/2014
158410^166324+550603166325Patrick De Geest07/2018
158510^166324-801166324Robert Price02/2018
1586(85*10^166297-1)/3166299Robert Price02/2020
15878*10^166227+87166228Robert Price10/2019
15882^552137+1879397166210Enzo Doria09/2016
1589(103*10^166126+11)/3166128Robert Price01/2021
1590(23^121949-1)/22166061Paul Bourdelais10/2017
15912^551542+19249166031Payam Samidoost08/2002
15922^551535-23821166029Enzo Doria08/2013
15932^551507-23557166021Enzo Doria08/2013
15947*10^165916-3165917Robert Price08/2015
1595(29*10^165796+67)/3165797Robert Price12/2019
159681^86837-80^86837165728Robert Price01/2015
1597(71*10^165663-539)/9165664Robert Price07/2019
15982^550270-69551165648Enzo Doria12/2015
1599(202*10^165569-13)/9165571Robert Price01/2020
16002^550000-23625165567Enzo Doria08/2013
16012^549675-1852057165469Enzo Doria08/2015
1602-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1603(28*10^165358-1)/9165359Serge Batalov10/2014
16042^549278+1879669165350Enzo Doria09/2016
1605(7*10^165350-439)/9165350Robert Price02/2018
16062^549252-351269165342Enzo Doria06/2015
160767*10^165327-9165329Robert Price03/2021
1608(14*10^165282+73)/3165283Robert Price12/2018
16092^549049+2797607165281Enzo Doria04/2016
1610(7*10^165239+107)/3165240Robert Price02/2018
1611(44^100511-1)/43165184Paul Bourdelais11/2017
1612(7*10^165134+107)/3165135Robert Price02/2018
1613(23*10^165060-83)/3165061Robert Price08/2019
1614(76*10^164984+77)/9164985Robert Price10/2019
16159*10^164791-89164792Robert Price04/2020
16162^547178-1856501164717Enzo Doria10/2015
161711^158160-60164707Enzo Doria07/2012
1618(26*10^164643-167)/3164644Robert Price10/2019
16192^546398-59201164483Enzo Doria10/2015
16202^546332-114893164463Enzo Doria05/2015
16212^545958+1876189164350Enzo Doria07/2016
16222^545878-49841164326Enzo Doria10/2015
1623(10^164284+77)/3164284Robert Price01/2018
16242^545668-4019164263Yves Minet04/2017
162510^164216-50000000001164216Robert Price12/2020
1626(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
1627(16*10^164122+197)/3164123Robert Price04/2019
16282^545185+76757164118Enzo Doria05/2016
16292^545076-114329164085Enzo Doria01/2015
1630(2*10^164043-143)/3164043Robert Price03/2018
1631(29^112153+1)/30164011Lelio R Paula03/2017
16322^544757+1874777163989Enzo Doria06/2016
16332^544444-457199163894Enzo Doria01/2015
16342^544264-343529163840Enzo Doria07/2015
16357*10^163780+9163781Robert Price09/2015
16362^543989+2793047163758Enzo Doria02/2016
1637(28*10^163709+113)/3163710Robert Price03/2020
1638(68*10^163521-329)/9163522Robert Price03/2021
16392^542870-69551163421Enzo Doria12/2015
16402^542395+72533163278Enzo Doria04/2016
16412^542072-3683163180Yves Minet03/2017
16422^541779-1867357163092Enzo Doria04/2016
16438*10^162924+9162925Robert Price12/2015
16442^540905+81557162829Enzo Doria08/2016
16452^540628-2939162746Yves Minet09/2014
1646919^54919-918^54919162743Jean-Louis Charton01/2013
1647(203*10^162689+1)/3162691Robert Price03/2020
16483*10^162620-59162621Robert Price09/2018
16493^340694-112960162553Enzo Doria07/2014
16502^539807-114081162499Enzo Doria12/2014
16512^539654-114893162453Enzo Doria05/2015
16529*10^162449-71162450Robert Price11/2020
16532^539617-1851583162441Enzo Doria08/2015
1654(91*10^162410+11)/3162412Robert Price02/2020
16552^539346+81049162360Enzo Doria07/2016
16562^539220-115499162322Enzo Doria07/2015
16572^539217-113713162321Enzo Doria09/2014
16589^170099-8^170099162316Jean-Louis Charton05/2005
16594*10^162263-39162264Robert Price09/2020
1660(115*10^162153-1)/3162155Serge Batalov12/2014
1661(10^162138+11)/3162138Serge Batalov07/2015
16622^538473-112723162097Enzo Doria06/2014
16632^538157+79337162002Enzo Doria06/2016
16642^538136-114749161996Enzo Doria05/2015
16652^538104+1531161986Lelio R Paula01/2013
1666(9*29^110727-1199)/14161927Curtis Bright05/2015
16672^537815-22737161899Enzo Doria07/2013
16682^537804-39839161896Enzo Doria09/2015
1669(754*10^161816-7)/9161818Robert Price05/2020
16702^537458-59201161791Enzo Doria10/2015
16712*10^161766+51161767Robert Price05/2018
1672(7*10^161760+131)/3161761Robert Price06/2020
16732^537209-49849161717Enzo Doria10/2015
1674(58*10^161691+329)/9161692Robert Price05/2019
16752^536937+1879397161635Enzo Doria09/2016
167634*10^161593-9161595Robert Price06/2020
1677(31*10^161582-1)/3161584Robert Price02/2020
16782^536569-22881161524Enzo Doria07/2013
167910^161253+573493161254Patrick De Geest07/2018
168010^161253-8001161253Robert Price03/2018
168197*10^161247-3161249Robert Price05/2020
16827*10^161192-9161193Robert Price10/2015
16832^535269-113803161133Enzo Doria09/2014
16842^535205-23295161113Enzo Doria08/2013
1685(89^82609+1)/90161036Paul Bourdelais10/2017
16862^534359-23229160859Enzo Doria08/2013
16878*10^160782+53160783Robert Price08/2020
168867^88037-66^88037160763Robert Price10/2013
1689(88*10^160761-637)/9160762Robert Price11/2020
16902^533948-1852559160735Enzo Doria08/2015
16912^533665-23335160650Enzo Doria08/2013
1692(19*10^160619+77)/3160620Robert Price05/2019
16933^336353-2^336353160482Mike Oakes10/2007
1694(91*10^160249+11)/3160251Robert Price02/2020
16952^532253+1868417160225Enzo Doria04/2016
16962^532108-291989160181Enzo Doria07/2015
1697(28*10^160171-79)/3160172Robert Price02/2021
1698(26*10^160166-131)/3160167Robert Price10/2019
1699(17*10^160143+67)/3160144Robert Price01/2019
1700(19*10^159921-49)/3159922Robert Price05/2019
17012^531110-1853771159881Enzo Doria09/2015
1702(275^65536+53^65536)/2159864Kellen Shenton11/2020
17032^530992-1845299159845Enzo Doria07/2015
1704(136*10^159736-1)/9159738Serge Batalov12/2014
17052^530417-113833159672Enzo Doria09/2014
17062^530406-69701159669Enzo Doria02/2016
17075*10^159656+41159657Robert Price03/2019
17087^188858-188858^7159604Norbert Schneider05/2018
1709(24^115597-1)/23159547Paul Bourdelais09/2017
1710(17*10^159438-377)/9159439Robert Price03/2018
1711(203*10^159381+1)/3159383Robert Price03/2020
171289*10^159258-9159260Robert Price05/2020
17132^528944-461315159229Enzo Doria07/2015
1714(13*10^159147+161)/3159148Robert Price11/2018
17152^528620-113879159131Enzo Doria10/2014
17162^528000-23307158944Enzo Doria08/2013
1717(29*10^158909+61)/9158910Robert Price08/2018
17182^527817+1876817158889Enzo Doria07/2016
17192^527774-49451158876Enzo Doria10/2015
17202^527745-291553158868Enzo Doria07/2015
1721(91*10^158862+11)/3158864Robert Price02/2020
17222^527644-1856999158837Enzo Doria10/2015
1723(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
17242^527573-1863253158816Enzo Doria12/2015
17252^527553-23401158810Enzo Doria08/2013
172610^158755-50001158755Robert Price08/2020
172711^152420-210158730Enzo Doria09/2012
1728(13*10^158694+401)/9158695Robert Price01/2018
17292^527052-69059158659Enzo Doria11/2015
17302^526849-113233158598Enzo Doria07/2014
1731(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
1732(299*10^158544-17)/3158546Robert Price04/2020
17332^526658-3551158540Yves Minet03/2017
17347*10^158465-11158466Robert Price06/2019
17352^526375-23115158455Enzo Doria08/2013
1736(77*10^158407-293)/9158408Robert Price09/2019
17372^526028-112793158351Enzo Doria07/2014
1738(229*10^158339-1)/3158341Robert Price07/2020
17392^525690-9221158249Lelio R Paula01/2013
17402*10^158242-7158243Robert Price10/2015
17412^525667-525667^2158242Henri Lifchitz12/2017
17422^525186-1857431158097Enzo Doria10/2015
17432^524515-23245157895Enzo Doria08/2013
17442^524499-109087157890Enzo Doria04/2014
17452^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
17472^524288+189093157827Makoto Morimoto01/2016
17462^524288-164073157827Matthias Baur03/2020
1748(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
1749(10^157792+359)/9157792Serge Batalov12/2014
17502^523924+1876591157717Enzo Doria07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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