PRP Records

Probable Primes Top 10000

(211563 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 (> 30000) Who ? When ?
15012^475160-2797859143038Enzo Doria04/2016
1502(2^475069+3)/395143008Lelio R Paula08/2015
15032^475027-461437142998Enzo Doria07/2015
1504(2^474958+78557)/3142977Lelio R Paula07/2015
1505(8*10^142932+43)/3142933Robert Price06/2018
1506(54^82471-1)/53142871Paul Bourdelais09/2017
1507(11*2^474432-1)/95142818Lelio R Paula09/2015
15082^474417-59923142814Enzo Doria10/2015
1509(3*2^474166+1)/7142738Lelio R Paula08/2015
15102^474053+2897142705Lelio R Paula08/2012
1511(10^142699+359)/9142699Serge Batalov12/2014
1512898^48311-897^48311142676Jean-Louis Charton12/2012
15132^473740-1856639142610Enzo Doria09/2015
15142^473617-114223142573Enzo Doria12/2014
15152^473257+1873217142465Enzo Doria06/2016
1516(19*2^473242+1)/11142461Lelio R Paula09/2015
1517(10^142425+359)/9142425Serge Batalov12/2014
15182^473101+773027142418Enzo Doria05/2016
1519(13*2^472838-1)/3142340Lelio R Paula09/2015
1520(17*2^472789-1)/187347142320Lelio R Paula09/2015
15212^472634-109511142278Enzo Doria04/2014
1522(48^84589+1)/49142213Robert Price01/2014
15232^472258+7142164Lelio R Paula08/2015
1524tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
1525(11*2^471913-1)/21142060Lelio R Paula09/2015
15262^471792+1880881142024Enzo Doria11/2016
1527(31*2^471580-1)/135141960Lelio R Paula08/2015
1528(4*10^141926-79)/3141927Robert Price02/2018
1529(904*19^110984-1)/3141924Curtis Bright05/2015
15304*5^202913-9141831Lelio R Paula04/2015
15312*7^167812-3141818Lelio R Paula12/2014
15322^471043+35141799Robert Price11/2015
1533(11*2^470956-1)/7945141770Lelio R Paula08/2015
15342^470692+76771141693Enzo Doria05/2016
1535(21*2^470391+1)/533141601Lelio R Paula09/2015
15362^470305-459373141576Enzo Doria05/2015
15372^470183+72623141540Enzo Doria04/2016
15382^470173-16465141537Enzo Doria04/2013
15392^469974-1841141477Enzo Doria05/2014
1540(23*2^469939+1)/25141466Lelio R Paula08/2015
15412*10^141448+63141449Robert Price05/2018
15422^469824+43141432Lelio R Paula09/2017
15432*10^141407-27141408Robert Price05/2018
15442^469630-59711141373Enzo Doria10/2015
1545(2^469564-3)/611141351Lelio R Paula08/2015
1546197^61601+2141342Lelio R Paula08/2017
15472^469372-112949141296Enzo Doria07/2014
1549143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
1548143^65536+106^65536141253Serge Batalov03/2018
15502^469198+782569141243Enzo Doria10/2016
15512^469076-2786939141206Enzo Doria11/2015
15522^468804+1874941141125Enzo Doria06/2016
15532^468787+81353141119Enzo Doria08/2016
15542^468595-350407141062Enzo Doria06/2015
15552^468564+87855141052Lelio R Paula01/2016
15562^468551-21987141048Enzo Doria07/2013
15572^468523-7141040Lelio R Paula08/2015
15582^468405+87855141004Lelio R Paula01/2016
15592^467978-113051140876Enzo Doria07/2014
15602^467780-344429140816Enzo Doria07/2015
15612^467605-1855603140764Enzo Doria09/2015
15625*10^140744-7140745Robert Price09/2015
1563(5^201359-1)/4140744Paul Bourdelais12/2008
15642^467401-1850023140702Enzo Doria08/2015
1565(2^467270+78557)/23247140658Lelio R Paula07/2015
1566(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
15672^467166-1854941140631Enzo Doria09/2015
15682^466866-1840571140541Enzo Doria06/2015
15692^466829-459523140530Enzo Doria05/2015
15702^466692-113213140489Enzo Doria07/2014
1571153^64265-2140400Lelio R Paula11/2017
1572(112*10^140357-1)/3140359Serge Batalov12/2014
15732^466181-112735140335Enzo Doria07/2014
1574(5*10^140281-119)/3140282Robert Price03/2018
1575(27*2^465872+1)/691140241Lelio R Paula08/2015
15762^465803-114817140221Enzo Doria05/2015
1577floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
15782^465503-112735140131Enzo Doria07/2014
15796^179964+179964^6-1140040Robert Price04/2014
1580(29*2^465077-1)/9140003Lelio R Paula08/2015
15812^465072-344789140001Enzo Doria07/2015
15822^464864-17139939Lelio R Paula09/2017
1583(17^113621+1)/18139804Paul Bourdelais09/2011
1584(19*2^464312-1)/3139773Lelio R Paula08/2015
1585(31*2^463970+1)/5139670Lelio R Paula08/2015
1586(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
15872^463633-2788423139568Enzo Doria11/2015
15882^463271-109501139459Enzo Doria04/2014
1589(5*10^139457+79)/3139458Robert Price03/2018
15902^463237-99139449Lelio R Paula09/2017
1591(7*10^139417-547)/9139417Robert Price01/2018
1592(10^139398+191)/3139398Robert Price02/2018
15932^463019+79463139383Enzo Doria06/2016
15943^292129-112756139381Enzo Doria07/2014
1595(15*2^462951+1)/527139361Lelio R Paula08/2015
15962^462855-1865707139334Enzo Doria02/2016
15972^462786-292043139313Enzo Doria08/2015
1598(26*10^139289+1)/9139290Serge Batalov05/2010
15992^462238-935139148Yves Minet02/2014
16002^461228+1870441138844Enzo Doria05/2016
16012^461204-113675138837Enzo Doria08/2014
1602(2^461139-7)/47138815Lelio R Paula08/2015
1603(17*10^138812-521)/9138813Robert Price04/2018
1604(17*2^460963+1)/124051613138757Lelio R Paula08/2015
16052^460567-113541138645Enzo Doria08/2014
16067*10^138604+3138605Robert Price08/2015
16072^460330+69138574Lelio R Paula09/2017
16082^460078-69581138498Enzo Doria12/2015
16092^459768+1531138404Lelio R Paula06/2012
16102^459343-113611138277Enzo Doria08/2014
16112^459199+1874393138233Enzo Doria06/2016
16122^459063-345307138192Enzo Doria06/2015
16132*10^138162-43138163Robert Price04/2018
16142^458927-112747138151Enzo Doria06/2014
16152^458927-69217138151Enzo Doria11/2015
1616555555*2^458524+1513138036Darren Bedwell08/2009
16172^458465+2^32+1138012T. D. Noe06/2007
16182^458321-113053137969Enzo Doria07/2014
16192^458298+79459137962Enzo Doria06/2016
16202^458248-21815137947Enzo Doria07/2013
16212^458194+1876549137931Enzo Doria07/2016
1622(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
16232^457937+57137853Lelio R Paula09/2017
1624(8*10^137845+13)/3137846Robert Price06/2018
16252^457822+105137819Donovan Johnson06/2006
16262^457754-113711137798Enzo Doria09/2014
162711^132315-360137792Enzo Doria09/2012
16282^457347-37137676Lelio R Paula09/2017
16292^457322-2786393137668Enzo Doria10/2015
1630gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
16312^457240-59939137643Enzo Doria10/2015
16322^457120-21575137607Enzo Doria07/2013
1633(11*2^456978+1)/15137564Lelio R Paula07/2015
1634(7*25^98399+10613)/12137556Curtis Bright05/2015
16352^456796-113513137510Enzo Doria08/2014
1636(7*2^456655+1)/39137467Lelio R Paula07/2015
16372^456503-114361137422Enzo Doria01/2015
1638(11*2^456387+1)/19137386Lelio R Paula07/2015
1639(71*10^137250+1)/9137251Serge Batalov05/2010
16402^455922+76249137247Enzo Doria05/2016
164114^119741-119741^14137239Serge Batalov04/2016
1642(19*2^455760+1)/3455137196Lelio R Paula07/2015
1644124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
1643124^65536+57^65536137195Serge Batalov03/2018
16452^455689+72677137177Enzo Doria04/2016
1646(17948!)^2+Prime(17948)137118Robert Price08/2014
1647(37^87421-1)/36137093Robert Price03/2012
16482^455323-57137066Lelio R Paula09/2017
1649(73*17^111333-9)/16136991Curtis Bright05/2015
16502^455025-112723136977Enzo Doria06/2014
16512^454675-1777136871Yves Minet10/2011
16523*10^136829+29136830Robert Price05/2018
1653(6092*28^94536-143)/9136812Curtis Bright05/2015
16542^454348-53136773Lelio R Paula09/2017
165531^91680-2136729Lelio R Paula05/2017
16562^454199-113697136728Enzo Doria09/2014
16572^453935-2791357136649Enzo Doria01/2016
16582^453906-69131136640Enzo Doria11/2015
16592^453791+1873913136605Enzo Doria06/2016
1660(21*2^453740-1)/2735136588Lelio R Paula07/2015
16612^453503-2788297136519Enzo Doria11/2015
16622^453267-113827136447Enzo Doria09/2014
16632^453102+1877629136398Enzo Doria08/2016
1664L(651821)136223Henri Lifchitz09/2008
16652^452460+77701136205Enzo Doria05/2016
16662^452440-114755136199Enzo Doria04/2015
16672*10^136057-43136058Robert Price04/2018
1668(2^451956-5)/181136051Lelio R Paula07/2015
16692^451947-22165136050Enzo Doria07/2013
16702^451787-21805136002Enzo Doria07/2013
16712^451734-112817135986Enzo Doria06/2014
1672(11*2^451714+1)/75135979Lelio R Paula07/2015
16732^451705-21879135977Enzo Doria07/2013
16742^451560-112349135934Enzo Doria06/2014
16752^451530+45135925Lelio R Paula08/2017
16762^451450-21743135900Enzo Doria07/2013
16772^450805+65135706Lelio R Paula08/2017
1678(13725^32768+1)/131074135573Lelio R Paula03/2012
1679(5^193939+1)/6135557Paul Bourdelais12/2008
16802^449944-113247135447Enzo Doria07/2014
16812^449770-113247135395Enzo Doria07/2014
16822^449637-21471135355Enzo Doria07/2013
16832^449571-75135335Lelio R Paula08/2017
1684(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
1685(13*10^135279+437)/9135280Robert Price04/2018
16862^449330-35135262Lelio R Paula08/2017
1687(19*2^449325+1)/9135261Lelio R Paula07/2015
16882^449049-115309135178Enzo Doria07/2015
1689(10^135174+191)/3135174Robert Price02/2018
16902^449030-15135172Lelio R Paula08/2017
1691(27*2^448936-1)/11135144Lelio R Paula07/2015
16922^448762-351401135091Enzo Doria07/2015
16932*10^135083-43135084Robert Price04/2018
1694(10^135011+719)/9135011Serge Batalov12/2014
16952^448386-2786261134978Enzo Doria03/2016
16962^448113-113949134896Enzo Doria11/2014
16972^447888-2786639134828Enzo Doria03/2016
16982^447870-396765134823Enzo Doria07/2013
16992^447766-21791134791Enzo Doria07/2013
1700(23*2^447647+1)/155134755Lelio R Paula07/2015
17012^447552-1019134727Yves Minet02/2014
1702(2*10^134720-41)/3134720Robert Price02/2018
17032^447437-113569134692Enzo Doria08/2014
17042^447426-65134689Lelio R Paula08/2017
17052^447357-2797573134668Enzo Doria04/2016
17062^447278+93134645Lelio R Paula08/2017
17072^447094-113193134589Enzo Doria07/2014
17083^282041-9934134568Enzo Doria05/2014
17092^447019-109039134567Enzo Doria04/2014
17102^446990-22041134558Enzo Doria07/2013
1711123^64370+122134528Karsten Bonath04/2018
17122^446782-39701134495Enzo Doria09/2015
17132^446494-16485134409Enzo Doria04/2013
171429504^30069-30069^29504134405Norbert Schneider12/2014
17152^446441+65134393Lelio R Paula08/2017
1716(10^134385+719)/9134385Serge Batalov12/2014
1717(2*10^134364+529)/9134364Robert Price01/2018
1718(13*2^446187-1)/661134314Lelio R Paula07/2015
1719(2^446022-7)/339134264Lelio R Paula07/2015
172063^74568+2134174Lelio R Paula06/2017
17212^445671-22071134161Enzo Doria07/2013
1722(28*10^134122-1)/9134123Serge Batalov10/2014
17232^445515-113859134114Enzo Doria10/2014
17242^445328-216917134058Enzo Doria05/2014
17252^445202+1874899134020Enzo Doria06/2016
1726(13*2^445102+1)/17133989Lelio R Paula07/2015
17272*10^133955+51133956Robert Price05/2018
17282^444964-113639133948Enzo Doria08/2014
172928118^30097-30097^28118133902Norbert Schneider01/2015
17302^444784-113859133894Enzo Doria10/2014
1731(89*10^133580+1)/9133581Serge Batalov05/2010
173262^74521-61^74521133571Robert Price05/2013
17332^443198-1867301133416Enzo Doria03/2016
1734(71^72043-1)/70133369Paul Bourdelais09/2017
17352^442799+1874633133296Enzo Doria06/2016
1736L(637751)133283Henri Lifchitz09/2008
1737109^65410-2133269Lelio R Paula10/2017
17382^442688-113489133263Enzo Doria08/2014
1739(7*2^442640-1)/783133246Lelio R Paula07/2015
1740(9*2^442463+1)/17441133192Lelio R Paula07/2015
17412^442437-1849993133187Enzo Doria08/2015
17422^442430-2791721133185Enzo Doria03/2016
1743(13*2^442428-1)/309133183Lelio R Paula07/2015
1744(25*2^442379-1)/71133169Lelio R Paula07/2015
1745(2^441799+78557)/5132995Lelio R Paula07/2015
17462^441781-2787883132990Enzo Doria03/2016
1747(3*2^441685+1)/749132959Lelio R Paula07/2015
17482^441618+37132941Lelio R Paula08/2017
17492^441521-113575132912Enzo Doria08/2014
17502^441396-65132874Lelio R Paula08/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!