PRP Records

Probable Primes Top 10000

(218736 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 (> 30000) Who ? When ?
1751123^64370+122134528Karsten Bonath04/2018
17522^446782-39701134495Enzo Doria09/2015
17532^446494-16485134409Enzo Doria04/2013
175429504^30069-30069^29504134405Norbert Schneider12/2014
17552^446441+65134393Lelio R Paula08/2017
1756(10^134385+719)/9134385Serge Batalov12/2014
1757(2*10^134364+529)/9134364Robert Price01/2018
1758(13*2^446187-1)/661134314Lelio R Paula07/2015
1759(2^446022-7)/339134264Lelio R Paula07/2015
176063^74568+2134174Lelio R Paula06/2017
17612^445671-22071134161Enzo Doria07/2013
1762(28*10^134122-1)/9134123Serge Batalov10/2014
17632^445515-113859134114Enzo Doria10/2014
17642^445328-216917134058Enzo Doria05/2014
17652^445202+1874899134020Enzo Doria06/2016
1766(13*2^445102+1)/17133989Lelio R Paula07/2015
1767(35*10^133979-593)/9133980Robert Price07/2018
17682*10^133955+51133956Robert Price05/2018
17692^444964-113639133948Enzo Doria08/2014
177028118^30097-30097^28118133902Norbert Schneider01/2015
17712^444784-113859133894Enzo Doria10/2014
1772(89*10^133580+1)/9133581Serge Batalov05/2010
177362^74521-61^74521133571Robert Price05/2013
17742^443198-1867301133416Enzo Doria03/2016
1775(71^72043-1)/70133369Paul Bourdelais09/2017
17762^442799+1874633133296Enzo Doria06/2016
1777L(637751)133283Henri Lifchitz09/2008
1778109^65410-2133269Lelio R Paula10/2017
17792^442688-113489133263Enzo Doria08/2014
1780(7*2^442640-1)/783133246Lelio R Paula07/2015
1781(9*2^442463+1)/17441133192Lelio R Paula07/2015
17822^442437-1849993133187Enzo Doria08/2015
17832^442430-2791721133185Enzo Doria03/2016
1784(13*2^442428-1)/309133183Lelio R Paula07/2015
1785(25*2^442379-1)/71133169Lelio R Paula07/2015
1786(2^441799+78557)/5132995Lelio R Paula07/2015
17872^441781-2787883132990Enzo Doria03/2016
1788(3*2^441685+1)/749132959Lelio R Paula07/2015
17892^441618+37132941Lelio R Paula08/2017
17902^441521-113575132912Enzo Doria08/2014
17912^441396-65132874Lelio R Paula08/2017
17922^441330+1871959132854Enzo Doria05/2016
17932^441063+383132774Lelio R Paula06/2012
17942^440846+1870909132708Enzo Doria05/2016
17952^440656-113489132651Enzo Doria08/2014
1796numbpart(14180123587)132646Serge Batalov04/2017
1797(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
1798(38^83891+1)/39132529Robert Price09/2013
17992*10^132493-43132494Robert Price04/2018
18002^439931-21132433Lelio R Paula08/2017
180147^79201-46^79201132432Robert Price10/2012
18022^439897-113653132423Enzo Doria08/2014
1803(5*2^439822+1)/9132400Lelio R Paula06/2015
1804(112*10^132337-1)/3132339Serge Batalov12/2014
18052^439576-113247132326Enzo Doria07/2014
18062^439497-29143132302Enzo Doria07/2015
18072^439409-114193132276Enzo Doria12/2014
18089*10^132148-7132149Robert Price09/2015
18092^438845+1870217132106Enzo Doria05/2016
18102^438789+87855132089Lelio R Paula01/2016
18112^438774-2786411132085Enzo Doria03/2016
18122^438755-1848205132079Enzo Doria07/2015
18132^438739-112087132074Enzo Doria06/2014
181413907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
1815L(631181)131910Henri Lifchitz09/2008
1816(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
18172^438079-1863877131875Enzo Doria03/2016
1818(2^438067+5)/329131869Lelio R Paula06/2015
18192^437908-113855131824Enzo Doria09/2014
18202^437884-286349131817Enzo Doria07/2015
1821(11*10^131784-17)/3131785Robert Price06/2018
18223^276062-112292131716Enzo Doria07/2014
18232^437343+75953131654Enzo Doria04/2016
182435^85243-34^85243131621Robert Price05/2012
1825(68^71713+1)/69131413Paul Bourdelais09/2017
18262^436451+1884713131385Enzo Doria03/2017
18272^436365+35131359Robert Price11/2015
18282^436300+1866871131340Enzo Doria03/2016
1829(5*10^131223-29)/3131224Robert Price03/2018
1830(23*2^435891-1)/699131215Lelio R Paula07/2015
1831(11*2^435879+1)/3337131211Lelio R Paula06/2015
1833(2^435808+1)/641/6700417131182Lelio R Paula02/2012
1832(2^435808+1)/4294967297131182Serge Batalov12/2016
18342^435773+1875557131181Enzo Doria06/2016
1835(25*10^131144-7)/9131145Robert Price05/2018
18362^435612-2789939131133Enzo Doria12/2015
183766^72047-65^72047131093Robert Price09/2013
1838(5*10^131090+37)/3131091Robert Price03/2018
18392^435468+75631131089Enzo Doria04/2016
184037^83588-2131083Lelio R Paula08/2015
1841(4^217720+11)/3131081Robert Price02/2017
18422^435202-113193131009Enzo Doria07/2014
1843floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
18442^434835-111937130899Enzo Doria05/2014
18452^434685+72257130854Enzo Doria04/2016
1846(7*10^130825+113)/3130826Robert Price02/2018
18472^434539-29317130810Enzo Doria07/2015
18482^434469-114259130789Enzo Doria01/2015
18492^434246+33130722Robert Price11/2015
18502^433911-91130621Lelio R Paula06/2017
18512^433744-114419130570Enzo Doria02/2015
18532^433708+1869451130560Enzo Doria05/2016
18522^433710+93130560Lelio R Paula06/2017
1854(29*2^433547-1)/27130511Lelio R Paula06/2015
18554*10^130480+9130481Robert Price05/2015
1856(23*2^433449-1)/75130481Lelio R Paula06/2015
1857(23*2^433334-1)/3731130445Lelio R Paula06/2015
18582^433023-113497130353Enzo Doria08/2014
18592^433002+1179379130347Enzo Doria06/2016
18602^432974+19130339Robert Price08/2015
1861(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
18622^432217+41130111Lelio R Paula06/2017
1863(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
1864((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
186597^65480-2130094Lelio R Paula05/2017
18662^432117-113215130081Enzo Doria07/2014
18672^431804+72511129986Enzo Doria04/2016
1868(3^272141-3^136071+1)/7129844Serge Batalov03/2014
1869(9*2^431141+1)/17129787Lelio R Paula06/2015
1870(29*2^430881-1)/21129709Lelio R Paula06/2015
18712^430807+1869563129686Enzo Doria05/2016
18722^430721-21429129660Enzo Doria07/2013
18732^430415-276271129568Enzo Doria07/2015
18742^430142-2791721129486Enzo Doria03/2016
1875(7*10^129472-13)/3129473Robert Price07/2018
18762^429568-21017129313Enzo Doria07/2013
18772^429194-112685129201Enzo Doria06/2014
18782^429145-2780449129186Enzo Doria04/2016
18792^428892-113453129110Enzo Doria07/2014
1880(11*2^428881-7)/15129106Renaud Lifchitz03/2011
18812^428727-113959129060Enzo Doria10/2014
1882(7*2^428725-1)/13129059Lelio R Paula05/2014
1883(10^129051-31)/3129051Serge Batalov12/2014
18842^428564+71161129011Enzo Doria04/2016
18852^428502-113285128992Enzo Doria07/2014
18862^428421-21373128968Enzo Doria06/2013
1887L(616787)128901Henri Lifchitz09/2008
188891^65772-2128851Lelio R Paula05/2017
18892^428022+43128848Lelio R Paula05/2017
18902^427999-459397128841Enzo Doria05/2015
18912^427993+76847128839Enzo Doria05/2016
18922^427824-1851507128788Enzo Doria08/2015
18932^427807-21469128783Enzo Doria07/2013
189411^123594-240128710Enzo Doria09/2012
18952^427504-21503128692Enzo Doria07/2013
18962^427420+91128667Lelio R Paula05/2017
18972^427269-113635128621Enzo Doria08/2014
18982^427130+1877569128579Enzo Doria08/2016
18992^427016-115349128545Enzo Doria07/2015
1900(4*10^128510+137)/3128511Robert Price03/2018
19012^426889-112879128507Enzo Doria06/2014
19022^426804+1869931128481Enzo Doria05/2016
19032^426750+77635128465Enzo Doria05/2016
19042^426425-91128367Lelio R Paula05/2017
1905(15*2^426398-1)/11128359Lelio R Paula05/2014
19062^426352+74971128345Enzo Doria04/2016
19072^426300-1863689128330Enzo Doria03/2016
19082^426293+1881017128327Enzo Doria11/2016
19092^426043+35128252Robert Price11/2015
1910(4*10^128244-19)/3128245Robert Price03/2018
19112^425808-459959128181Enzo Doria06/2015
19122^425627-113605128127Enzo Doria08/2014
191318565^30002-30002^18565128070Norbert Schneider01/2015
1914(2^425287-9)/2737128021Lelio R Paula05/2015
1915(3*2^425233-1)/25128007Lelio R Paula05/2014
19162^425205+4911128000Marek Hubal02/2017
19172^425118-113663127974Enzo Doria08/2014
19182^425061+1869761127957Enzo Doria05/2016
19192^424918-21141127914Enzo Doria07/2013
19202^424864-29489127897Enzo Doria08/2015
1921(97*10^127858-1)/3127860Serge Batalov12/2014
19222^424632-2786639127827Enzo Doria03/2016
19232^424577-113755127811Enzo Doria09/2014
1924(7*2^424512-1)/3127792Lelio R Paula05/2014
192511^122629-720127705Enzo Doria11/2012
19262^423696-21429127546Enzo Doria07/2013
19272^423664-1864559127536Enzo Doria03/2016
19283^267267-4127519Henri Lifchitz10/2014
1929(19^99689+5^99689)/24127477Robert Price09/2013
1930(21*2^423372+1)/101127447Lelio R Paula05/2014
19312^423328-21537127435Enzo Doria07/2013
1932(2^423165-7)/25127384Lelio R Paula05/2015
1933(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
1934(234483*27^88884-145)/26127230Curtis Bright05/2015
19352^422515-114997127190Enzo Doria06/2015
19365*10^127179-3127180Robert Price07/2015
1937-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
1938(78^67141-1)/77127036Paul Bourdelais09/2017
19392^421860-113285126993Enzo Doria07/2014
1940(2^421827-7)/11126982Lelio R Paula05/2015
194111^121910-840126957Enzo Doria12/2012
1942(71^68539+1)/72126882Paul Bourdelais09/2017
1943(5*10^126871-119)/3126872Robert Price03/2018
1944331^50339-10004126846Enzo Doria07/2012
19452^421363-2790757126843Enzo Doria03/2016
1946(106*10^126839-1)/3126841Serge Batalov12/2014
1947(7*2^421243+1)/39126807Lelio R Paula05/2014
19482^421161-286183126783Enzo Doria06/2015
19492^420939-113935126716Enzo Doria10/2014
1950177^56363-2126703Lelio R Paula10/2017
19512^420741-113659126656Enzo Doria08/2014
19522^420694-21126642Lelio R Paula05/2017
1953(13*10^126638+437)/9126639Robert Price04/2018
1954(31*2^420556+1)/7126601Lelio R Paula05/2014
19552^420424-59189126561Enzo Doria10/2015
19562^420126+71893126471Enzo Doria04/2016
19572^419866+1877059126393Enzo Doria07/2016
1958F(604711)126377Henri Lifchitz02/2005
19592^419757+72707126360Enzo Doria04/2016
19602^419720-21569126349Enzo Doria07/2013
19612^419637+29126324Henri Lifchitz02/2006
19622^419612+1876741126316Enzo Doria07/2016
19632^419520+2793271126289Enzo Doria03/2016
1964(2^419447-5)/369126264Lelio R Paula05/2014
19652^419328-1859939126231Enzo Doria03/2016
19662^419282-1851507126217Enzo Doria08/2015
19672^419251+1866143126208Enzo Doria03/2016
196811^121185+2126202Robert Price05/2014
1969(23*2^419036-1)/1393126141Lelio R Paula05/2014
19702^418851+23126087Robert Price09/2015
1971(2^418849-9)/2681126083Lelio R Paula05/2014
19722^418829+167126081Lelio R Paula01/2012
1973(31*2^418782-1)/75891126063Lelio R Paula05/2014
1974(19*2^418754-1)/15126058Lelio R Paula05/2014
19752^418319-109501125927Enzo Doria04/2014
19762^418316-112373125926Enzo Doria06/2014
1977(8*10^125894-29)/3125895Robert Price07/2018
1978(26*10^125886-413)/9125887Robert Price05/2018
19792^417968+1869811125821Enzo Doria06/2016
19802^417902+63125802Lelio R Paula09/2015
1981(10^125792-91)/9125792Serge Batalov12/2014
1982(35*10^125754-593)/9125755Robert Price07/2018
1983(32*10^125751-77)/9125752Robert Price06/2018
19842^417704+77011125742Enzo Doria05/2016
1985(10^125706+149)/3125706Serge Batalov12/2014
19862^417419-115309125656Enzo Doria07/2015
19872^417300+77281125620Enzo Doria05/2016
19882^417095-1657125559Yves Minet07/2014
19892^416773-25125462Lelio R Paula09/2015
1990(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
1991(11*2^416691+1)/43125436Lelio R Paula05/2014
19922^416641-2*416641+1125422Robert Price05/2018
1993(21*2^416566-1)/17125399Lelio R Paula05/2014
19942^416530+1870429125389Enzo Doria05/2016
19952^416490+1875109125376Enzo Doria09/2016
19962^416416-114929125354Enzo Doria05/2015
1997(172*10^125292-1)/9125294Serge Batalov12/2014
19982^416134+1865899125269Enzo Doria03/2016
1999(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2000(23^91943-1)/22125201Robert Price01/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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