PRP Records

Probable Primes Top 10000

(252932 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 ?
17512^467780-344429140816Enzo Doria07/2015
17522^467605-1855603140764Enzo Doria09/2015
17535*10^140744-7140745Robert Price09/2015
1754(5^201359-1)/4140744Paul Bourdelais12/2008
17552^467401-1850023140702Enzo Doria08/2015
1756(2^467270+78557)/23247140658Lelio R Paula07/2015
1757(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
17582^467166-1854941140631Enzo Doria09/2015
17592^466866-1840571140541Enzo Doria06/2015
17602^466829-459523140530Enzo Doria05/2015
17612^466692-113213140489Enzo Doria07/2014
1762(44*10^140410-503)/9140411Robert Price12/2018
1763153^64265-2140400Lelio R Paula11/2017
1764(112*10^140357-1)/3140359Serge Batalov12/2014
17652^466181-112735140335Enzo Doria07/2014
1766(5*10^140281-119)/3140282Robert Price03/2018
1767(27*2^465872+1)/691140241Lelio R Paula08/2015
17682^465803-114817140221Enzo Doria05/2015
1769floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
17702^465503-112735140131Enzo Doria07/2014
17716^179964+179964^6-1140040Robert Price04/2014
1772(29*2^465077-1)/9140003Lelio R Paula08/2015
17732^465072-344789140001Enzo Doria07/2015
17745*10^139945+81139946Robert Price03/2019
17752^464864-17139939Lelio R Paula09/2017
1776(17^113621+1)/18139804Paul Bourdelais09/2011
1777(13*10^139782+191)/3139783Robert Price11/2018
1778(19*2^464312-1)/3139773Lelio R Paula08/2015
17793*10^139722+13139723Robert Price07/2018
1780(31*2^463970+1)/5139670Lelio R Paula08/2015
1781(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
17822^463633-2788423139568Enzo Doria11/2015
17832^463271-109501139459Enzo Doria04/2014
1784(5*10^139457+79)/3139458Robert Price03/2018
17852^463237-99139449Lelio R Paula09/2017
1786(49*10^139442+383)/9139443Robert Price04/2019
1787(7*10^139417-547)/9139417Robert Price01/2018
1788(10^139398+191)/3139398Robert Price02/2018
17892^463019+79463139383Enzo Doria06/2016
17903^292129-112756139381Enzo Doria07/2014
1791(15*2^462951+1)/527139361Lelio R Paula08/2015
17922^462855-1865707139334Enzo Doria02/2016
17932^462786-292043139313Enzo Doria08/2015
1794(26*10^139289+1)/9139290Serge Batalov05/2010
1795(17*10^139239+67)/3139240Robert Price01/2019
17962^462238-935139148Yves Minet02/2014
17972^461228+1870441138844Enzo Doria05/2016
17982^461204-113675138837Enzo Doria08/2014
1799(2^461139-7)/47138815Lelio R Paula08/2015
1800(17*10^138812-521)/9138813Robert Price04/2018
18013*10^138811-11138812Robert Price07/2018
1802(17*2^460963+1)/124051613138757Lelio R Paula08/2015
1803(43*10^138648+101)/9138649Robert Price11/2018
18042^460567-113541138645Enzo Doria08/2014
18057*10^138604+3138605Robert Price08/2015
18062^460330+69138574Lelio R Paula09/2017
18072^460078-69581138498Enzo Doria12/2015
18082^459768+1531138404Lelio R Paula06/2012
18092^459343-113611138277Enzo Doria08/2014
18102^459199+1874393138233Enzo Doria06/2016
18112^459063-345307138192Enzo Doria06/2015
18122*10^138162-43138163Robert Price04/2018
18132^458927-112747138151Enzo Doria06/2014
18142^458927-69217138151Enzo Doria11/2015
1815555555*2^458524+1513138036Darren Bedwell08/2009
18162^458465+2^32+1138012T. D. Noe06/2007
18172^458321-113053137969Enzo Doria07/2014
18182^458298+79459137962Enzo Doria06/2016
18192^458248-21815137947Enzo Doria07/2013
18202^458194+1876549137931Enzo Doria07/2016
1821(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
1822(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
18232^457937+57137853Lelio R Paula09/2017
1824(8*10^137845+13)/3137846Robert Price06/2018
18252^457822+105137819Donovan Johnson06/2006
18262^457754-113711137798Enzo Doria09/2014
182711^132315-360137792Enzo Doria09/2012
18282^457347-37137676Lelio R Paula09/2017
18292^457322-2786393137668Enzo Doria10/2015
1830gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
18312^457240-59939137643Enzo Doria10/2015
18322^457120-21575137607Enzo Doria07/2013
1833(11*2^456978+1)/15137564Lelio R Paula07/2015
1834(7*25^98399+10613)/12137556Curtis Bright05/2015
18352^456796-113513137510Enzo Doria08/2014
1836(7*2^456655+1)/39137467Lelio R Paula07/2015
18372^456503-114361137422Enzo Doria01/2015
1838(11*2^456387+1)/19137386Lelio R Paula07/2015
1839(71*10^137250+1)/9137251Serge Batalov05/2010
18402^455922+76249137247Enzo Doria05/2016
184114^119741-119741^14137239Serge Batalov04/2016
1842(19*2^455760+1)/3455137196Lelio R Paula07/2015
1844124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
1843124^65536+57^65536137195Serge Batalov03/2018
18452^455689+72677137177Enzo Doria04/2016
1846(17948!)^2+Prime(17948)137118Robert Price08/2014
1847(37^87421-1)/36137093Robert Price03/2012
18482^455323-57137066Lelio R Paula09/2017
1849(73*17^111333-9)/16136991Curtis Bright05/2015
18502^455025-112723136977Enzo Doria06/2014
18512^454675-1777136871Yves Minet10/2011
18523*10^136829+29136830Robert Price05/2018
18534*10^136813-57136814Robert Price10/2018
1854(6092*28^94536-143)/9136812Curtis Bright05/2015
18552^454348-53136773Lelio R Paula09/2017
185631^91680-2136729Lelio R Paula05/2017
18572^454199-113697136728Enzo Doria09/2014
1858(13*10^136687+47)/3136688Robert Price10/2018
18592^453935-2791357136649Enzo Doria01/2016
18602^453906-69131136640Enzo Doria11/2015
18612^453791+1873913136605Enzo Doria06/2016
1862(21*2^453740-1)/2735136588Lelio R Paula07/2015
1863580^49413+49413^580136550Norbert Schneider02/2019
18642^453503-2788297136519Enzo Doria11/2015
18652^453267-113827136447Enzo Doria09/2014
18662^453102+1877629136398Enzo Doria08/2016
1867(62*10^136384-791)/9136385Robert Price06/2019
1868L(651821)136223Henri Lifchitz09/2008
18692^452460+77701136205Enzo Doria05/2016
18702^452440-114755136199Enzo Doria04/2015
1871(47*10^136141+493)/9136142Robert Price03/2019
18722*10^136057-43136058Robert Price04/2018
1873(2^451956-5)/181136051Lelio R Paula07/2015
18742^451947-22165136050Enzo Doria07/2013
18752^451787-21805136002Enzo Doria07/2013
18762^451734-112817135986Enzo Doria06/2014
1877(11*2^451714+1)/75135979Lelio R Paula07/2015
18782^451705-21879135977Enzo Doria07/2013
18792^451560-112349135934Enzo Doria06/2014
18802^451530+45135925Lelio R Paula08/2017
18812^451450-21743135900Enzo Doria07/2013
18822^450805+65135706Lelio R Paula08/2017
1883(13725^32768+1)/131074135573Lelio R Paula03/2012
1884(5^193939+1)/6135557Paul Bourdelais12/2008
18852^449944-113247135447Enzo Doria07/2014
18862^449770-113247135395Enzo Doria07/2014
18872^449637-21471135355Enzo Doria07/2013
18882^449571-75135335Lelio R Paula08/2017
1889(14*10^135301-53)/3135302Robert Price12/2018
1890(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
1891(13*10^135279+437)/9135280Robert Price04/2018
18922^449330-35135262Lelio R Paula08/2017
1893(19*2^449325+1)/9135261Lelio R Paula07/2015
1894(13*10^135184-43)/3135185Robert Price11/2018
18952^449049-115309135178Enzo Doria07/2015
1896(10^135174+191)/3135174Robert Price02/2018
18972^449030-15135172Lelio R Paula08/2017
1898(27*2^448936-1)/11135144Lelio R Paula07/2015
18992^448762-351401135091Enzo Doria07/2015
19002*10^135083-43135084Robert Price04/2018
19015*10^135019+77135020Robert Price12/2018
1902(10^135011+719)/9135011Serge Batalov12/2014
19032^448386-2786261134978Enzo Doria03/2016
19042^448113-113949134896Enzo Doria11/2014
19052^447888-2786639134828Enzo Doria03/2016
19062^447870-396765134823Enzo Doria07/2013
19072^447766-21791134791Enzo Doria07/2013
1908(19*10^134786-49)/3134787Robert Price05/2019
1909Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
1910(23*2^447647+1)/155134755Lelio R Paula07/2015
19112^447552-1019134727Yves Minet02/2014
1912(2*10^134720-41)/3134720Robert Price02/2018
19132^447437-113569134692Enzo Doria08/2014
19142^447426-65134689Lelio R Paula08/2017
19152^447357-2797573134668Enzo Doria04/2016
19162^447278+93134645Lelio R Paula08/2017
19172^447094-113193134589Enzo Doria07/2014
19183^282041-9934134568Enzo Doria05/2014
19192^447019-109039134567Enzo Doria04/2014
19202^446990-22041134558Enzo Doria07/2013
1921123^64370+122134528Karsten Bonath04/2018
19222^446782-39701134495Enzo Doria09/2015
19232^446494-16485134409Enzo Doria04/2013
192429504^30069-30069^29504134405Norbert Schneider12/2014
19252^446441+65134393Lelio R Paula08/2017
1926(10^134385+719)/9134385Serge Batalov12/2014
1927(2*10^134364+529)/9134364Robert Price01/2018
1928(13*2^446187-1)/661134314Lelio R Paula07/2015
1929(2^446022-7)/339134264Lelio R Paula07/2015
193063^74568+2134174Lelio R Paula06/2017
19312^445671-22071134161Enzo Doria07/2013
1932532^49205+49205^532134129Norbert Schneider02/2019
1933(28*10^134122-1)/9134123Serge Batalov10/2014
19342^445515-113859134114Enzo Doria10/2014
1935(22*10^134111-37)/3134112Robert Price04/2019
19362^445328-216917134058Enzo Doria05/2014
19372^445202+1874899134020Enzo Doria06/2016
1938(13*2^445102+1)/17133989Lelio R Paula07/2015
1939(35*10^133979-593)/9133980Robert Price07/2018
19402*10^133955+51133956Robert Price05/2018
19412^444964-113639133948Enzo Doria08/2014
194228118^30097-30097^28118133902Norbert Schneider01/2015
19432^444784-113859133894Enzo Doria10/2014
1944(89*10^133580+1)/9133581Serge Batalov05/2010
194562^74521-61^74521133571Robert Price05/2013
19462^443198-1867301133416Enzo Doria03/2016
1947(71^72043-1)/70133369Paul Bourdelais09/2017
19482^442799+1874633133296Enzo Doria06/2016
1949L(637751)133283Henri Lifchitz09/2008
1950109^65410-2133269Lelio R Paula10/2017
19512^442688-113489133263Enzo Doria08/2014
1952(7*2^442640-1)/783133246Lelio R Paula07/2015
1953(9*2^442463+1)/17441133192Lelio R Paula07/2015
19542^442437-1849993133187Enzo Doria08/2015
19552^442430-2791721133185Enzo Doria03/2016
1956(13*2^442428-1)/309133183Lelio R Paula07/2015
1957(25*2^442379-1)/71133169Lelio R Paula07/2015
1958(2^441799+78557)/5132995Lelio R Paula07/2015
19592^441781-2787883132990Enzo Doria03/2016
1960(3*2^441685+1)/749132959Lelio R Paula07/2015
19612^441618+37132941Lelio R Paula08/2017
19622^441521-113575132912Enzo Doria08/2014
19632^441396-65132874Lelio R Paula08/2017
19642^441330+1871959132854Enzo Doria05/2016
19652^441063+383132774Lelio R Paula06/2012
19662^440846+1870909132708Enzo Doria05/2016
19672^440656-113489132651Enzo Doria08/2014
1968numbpart(14180123587)132646Serge Batalov04/2017
1969(19*10^132550+191)/3132551Robert Price05/2019
1970(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
1971(38^83891+1)/39132529Robert Price09/2013
19722*10^132493-43132494Robert Price04/2018
19732^439931-21132433Lelio R Paula08/2017
197447^79201-46^79201132432Robert Price10/2012
19752^439897-113653132423Enzo Doria08/2014
1976(5*2^439822+1)/9132400Lelio R Paula06/2015
1977(112*10^132337-1)/3132339Serge Batalov12/2014
19782^439576-113247132326Enzo Doria07/2014
19792^439497-29143132302Enzo Doria07/2015
19802^439409-114193132276Enzo Doria12/2014
1981(44*10^132233-233)/9132234Robert Price01/2019
19829*10^132148-7132149Robert Price09/2015
1983(47*10^132125-119)/9132126Robert Price05/2019
19842^438845+1870217132106Enzo Doria05/2016
19852^438789+87855132089Lelio R Paula01/2016
19862^438774-2786411132085Enzo Doria03/2016
19872^438755-1848205132079Enzo Doria07/2015
19882^438739-112087132074Enzo Doria06/2014
198913907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
1990L(631181)131910Henri Lifchitz09/2008
1991(47*10^131886-119)/9131887Robert Price05/2019
1992(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
19932^438079-1863877131875Enzo Doria03/2016
1994(2^438067+5)/329131869Lelio R Paula06/2015
19952^437908-113855131824Enzo Doria09/2014
19962^437884-286349131817Enzo Doria07/2015
1997(11*10^131784-17)/3131785Robert Price06/2018
19983^276062-112292131716Enzo Doria07/2014
19992^437343+75953131654Enzo Doria04/2016
200035^85243-34^85243131621Robert Price05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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