PRP Records

Probable Primes Top 10000

(172213 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 ?
1251(21*27^101106-151)/26144720Curtis Bright05/2015
12522^480678+1874239144699Enzo Doria06/2016
1253(8*10^144683+1)/9144683Serge Batalov05/2010
1254L(692147)144651Henri Lifchitz10/2008
12552^480417+35144620Robert Price11/2015
12562^480296-59879144584Enzo Doria10/2015
12572^479844+3144448Donovan Johnson06/2006
1258(27*2^479642+1)/733144386Lelio R Paula08/2015
1259(21*2^479605-1)/11144376Lelio R Paula09/2015
12602^479348-2792219144299Enzo Doria02/2016
12613^302389-6242144277Enzo Doria05/2014
12622*10^144220-3144221Robert Price07/2015
12632^478904-109109144165Enzo Doria04/2014
12642^478337-115333143994Enzo Doria07/2015
1265(7*2^478330-1)/3143993Lelio R Paula08/2015
126688^74047-87^74047143984Robert Price05/2015
12672^478088+27143919Robert Price11/2015
12682^477475-22071143735Enzo Doria07/2013
12692^477417-22123143717Enzo Doria07/2013
12702^477359-3577143700Yves Minet03/2017
12712^476936-396765143573Enzo Doria07/2013
12722^476888-2791229143558Enzo Doria01/2016
12732^476868-1859939143552Enzo Doria11/2015
12742^476558-113627143459Enzo Doria08/2014
1275(2^475854+9)/73143245Lelio R Paula08/2015
12762^475813-113239143234Enzo Doria07/2014
12772^475624-114059143178Enzo Doria11/2014
1278(11*2^475553-7)/15143156Renaud Lifchitz03/2011
12792^475480-2786129143134Enzo Doria10/2015
12802^475299-111937143080Enzo Doria05/2014
12812^475160-2797859143038Enzo Doria04/2016
1282(2^475069+3)/395143008Lelio R Paula08/2015
12832^475027-461437142998Enzo Doria07/2015
1284(2^474958+78557)/3142977Lelio R Paula07/2015
1285(11*2^474432-1)/95142818Lelio R Paula09/2015
12862^474417-59923142814Enzo Doria10/2015
1287(3*2^474166+1)/7142738Lelio R Paula08/2015
12882^474053+2897142705Lelio R Paula08/2012
1289(10^142699+359)/9142699Serge Batalov12/2014
1290898^48311-897^48311142676Jean-Louis Charton12/2012
12912^473740-1856639142610Enzo Doria09/2015
12922^473617-114223142573Enzo Doria12/2014
12932^473257+1873217142465Enzo Doria06/2016
1294(19*2^473242+1)/11142461Lelio R Paula09/2015
1295(10^142425+359)/9142425Serge Batalov12/2014
12962^473101+773027142418Enzo Doria05/2016
1297(13*2^472838-1)/3142340Lelio R Paula09/2015
1298(17*2^472789-1)/187347142320Lelio R Paula09/2015
12992^472634-109511142278Enzo Doria04/2014
1300(48^84589+1)/49142213Robert Price01/2014
13012^472258+7142164Lelio R Paula08/2015
1302tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
1303(11*2^471913-1)/21142060Lelio R Paula09/2015
13042^471792+1880881142024Enzo Doria11/2016
1305(31*2^471580-1)/135141960Lelio R Paula08/2015
1306(904*19^110984-1)/3141924Curtis Bright05/2015
13074*5^202913-9141831Lelio R Paula04/2015
13082*7^167812-3141818Lelio R Paula12/2014
13092^471043+35141799Robert Price11/2015
1310(11*2^470956-1)/7945141770Lelio R Paula08/2015
13112^470692+76771141693Enzo Doria05/2016
1312(21*2^470391+1)/533141601Lelio R Paula09/2015
13132^470305-459373141576Enzo Doria05/2015
13142^470183+72623141540Enzo Doria04/2016
13152^470173-16465141537Enzo Doria04/2013
13162^469974-1841141477Enzo Doria05/2014
1317(23*2^469939+1)/25141466Lelio R Paula08/2015
13182^469630-59711141373Enzo Doria10/2015
1319(2^469564-3)/611141351Lelio R Paula08/2015
13202^469372-112949141296Enzo Doria07/2014
1321143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
13222^469198+782569141243Enzo Doria10/2016
13232^469076-2786939141206Enzo Doria11/2015
13242^468804+1874941141125Enzo Doria06/2016
13252^468787+81353141119Enzo Doria08/2016
13262^468595-350407141062Enzo Doria06/2015
13272^468564+87855141052Lelio R Paula01/2016
13282^468551-21987141048Enzo Doria07/2013
13292^468523-7141040Lelio R Paula08/2015
13302^468405+87855141004Lelio R Paula01/2016
13312^467978-113051140876Enzo Doria07/2014
13322^467780-344429140816Enzo Doria07/2015
13332^467605-1855603140764Enzo Doria09/2015
13345*10^140744-7140745Robert Price09/2015
1335(5^201359-1)/4140744Paul Bourdelais12/2008
13362^467401-1850023140702Enzo Doria08/2015
1337(2^467270+78557)/23247140658Lelio R Paula07/2015
1338(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
13392^467166-1854941140631Enzo Doria09/2015
13402^466866-1840571140541Enzo Doria06/2015
13412^466829-459523140530Enzo Doria05/2015
13422^466692-113213140489Enzo Doria07/2014
1343(112*10^140357-1)/3140359Serge Batalov12/2014
13442^466181-112735140335Enzo Doria07/2014
1345(27*2^465872+1)/691140241Lelio R Paula08/2015
13462^465803-114817140221Enzo Doria05/2015
1347floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
13482^465503-112735140131Enzo Doria07/2014
13496^179964+179964^6-1140040Robert Price04/2014
1350(29*2^465077-1)/9140003Lelio R Paula08/2015
13512^465072-344789140001Enzo Doria07/2015
1352(17^113621+1)/18139804Paul Bourdelais09/2011
1353(19*2^464312-1)/3139773Lelio R Paula08/2015
1354(31*2^463970+1)/5139670Lelio R Paula08/2015
13552^463633-2788423139568Enzo Doria11/2015
13562^463271-109501139459Enzo Doria04/2014
13572^463019+79463139383Enzo Doria06/2016
13583^292129-112756139381Enzo Doria07/2014
1359(15*2^462951+1)/527139361Lelio R Paula08/2015
13602^462855-1865707139334Enzo Doria02/2016
13612^462786-292043139313Enzo Doria08/2015
1362(26*10^139289+1)/9139290Serge Batalov05/2010
13632^462238-935139148Yves Minet02/2014
13642^461228+1870441138844Enzo Doria05/2016
13652^461204-113675138837Enzo Doria08/2014
1366(2^461139-7)/47138815Lelio R Paula08/2015
1367(17*2^460963+1)/124051613138757Lelio R Paula08/2015
13682^460567-113541138645Enzo Doria08/2014
13697*10^138604+3138605Robert Price08/2015
13702^460078-69581138498Enzo Doria12/2015
13712^459768+1531138404Lelio R Paula06/2012
13722^459343-113611138277Enzo Doria08/2014
13732^459199+1874393138233Enzo Doria06/2016
13742^459063-345307138192Enzo Doria06/2015
13752^458927-112747138151Enzo Doria06/2014
13762^458927-69217138151Enzo Doria11/2015
1377555555*2^458524+1513138036Darren Bedwell08/2009
13782^458465+2^32+1138012T. D. Noe06/2007
13792^458321-113053137969Enzo Doria07/2014
13802^458298+79459137962Enzo Doria06/2016
13812^458248-21815137947Enzo Doria07/2013
13822^458194+1876549137931Enzo Doria07/2016
13832^457822+105137819Donovan Johnson06/2006
13842^457754-113711137798Enzo Doria09/2014
138511^132315-360137792Enzo Doria09/2012
13862^457322-2786393137668Enzo Doria10/2015
1387gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
13882^457240-59939137643Enzo Doria10/2015
13892^457120-21575137607Enzo Doria07/2013
1390(11*2^456978+1)/15137564Lelio R Paula07/2015
1391(7*25^98399+10613)/12137556Curtis Bright05/2015
13922^456796-113513137510Enzo Doria08/2014
1393(7*2^456655+1)/39137467Lelio R Paula07/2015
13942^456503-114361137422Enzo Doria01/2015
1395(11*2^456387+1)/19137386Lelio R Paula07/2015
1396(71*10^137250+1)/9137251Serge Batalov05/2010
13972^455922+76249137247Enzo Doria05/2016
139814^119741-119741^14137239Serge Batalov04/2016
1399(19*2^455760+1)/3455137196Lelio R Paula07/2015
1400124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
14012^455689+72677137177Enzo Doria04/2016
1402(17948!)^2+Prime(17948)137118Robert Price08/2014
1403(37^87421-1)/36137093Robert Price03/2012
1404(73*17^111333-9)/16136991Curtis Bright05/2015
14052^455025-112723136977Enzo Doria06/2014
14062^454675-1777136871Yves Minet10/2011
1407(6092*28^94536-143)/9136812Curtis Bright05/2015
14082^454199-113697136728Enzo Doria09/2014
14092^453935-2791357136649Enzo Doria01/2016
14102^453906-69131136640Enzo Doria11/2015
14112^453791+1873913136605Enzo Doria06/2016
1412(21*2^453740-1)/2735136588Lelio R Paula07/2015
14132^453503-2788297136519Enzo Doria11/2015
14142^453267-113827136447Enzo Doria09/2014
14152^453102+1877629136398Enzo Doria08/2016
1416L(651821)136223Henri Lifchitz09/2008
14172^452460+77701136205Enzo Doria05/2016
14182^452440-114755136199Enzo Doria04/2015
1419(2^451956-5)/181136051Lelio R Paula07/2015
14202^451947-22165136050Enzo Doria07/2013
14212^451787-21805136002Enzo Doria07/2013
14222^451734-112817135986Enzo Doria06/2014
1423(11*2^451714+1)/75135979Lelio R Paula07/2015
14242^451705-21879135977Enzo Doria07/2013
14252^451560-112349135934Enzo Doria06/2014
14262^451450-21743135900Enzo Doria07/2013
1427(13725^32768+1)/131074135573Lelio R Paula03/2012
1428(5^193939+1)/6135557Paul Bourdelais12/2008
14292^449944-113247135447Enzo Doria07/2014
14302^449770-113247135395Enzo Doria07/2014
14312^449637-21471135355Enzo Doria07/2013
1432(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
1433(19*2^449325+1)/9135261Lelio R Paula07/2015
14342^449049-115309135178Enzo Doria07/2015
1435(27*2^448936-1)/11135144Lelio R Paula07/2015
14362^448762-351401135091Enzo Doria07/2015
1437(10^135011+719)/9135011Serge Batalov12/2014
14382^448386-2786261134978Enzo Doria03/2016
14392^448113-113949134896Enzo Doria11/2014
14402^447888-2786639134828Enzo Doria03/2016
14412^447870-396765134823Enzo Doria07/2013
14422^447766-21791134791Enzo Doria07/2013
1443(23*2^447647+1)/155134755Lelio R Paula07/2015
14442^447552-1019134727Yves Minet02/2014
14452^447437-113569134692Enzo Doria08/2014
14462^447357-2797573134668Enzo Doria04/2016
14472^447094-113193134589Enzo Doria07/2014
14483^282041-9934134568Enzo Doria05/2014
14492^447019-109039134567Enzo Doria04/2014
14502^446990-22041134558Enzo Doria07/2013
14512^446782-39701134495Enzo Doria09/2015
14522^446494-16485134409Enzo Doria04/2013
145329504^30069-30069^29504134405Norbert Schneider12/2014
1454(10^134385+719)/9134385Serge Batalov12/2014
1455(13*2^446187-1)/661134314Lelio R Paula07/2015
1456(2^446022-7)/339134264Lelio R Paula07/2015
14572^445671-22071134161Enzo Doria07/2013
1458(28*10^134122-1)/9134123Serge Batalov10/2014
14592^445515-113859134114Enzo Doria10/2014
14602^445328-216917134058Enzo Doria05/2014
14612^445202+1874899134020Enzo Doria06/2016
1462(13*2^445102+1)/17133989Lelio R Paula07/2015
14632^444964-113639133948Enzo Doria08/2014
146428118^30097-30097^28118133902Norbert Schneider01/2015
14652^444784-113859133894Enzo Doria10/2014
1466(89*10^133580+1)/9133581Serge Batalov05/2010
146762^74521-61^74521133571Robert Price05/2013
14682^443198-1867301133416Enzo Doria03/2016
14692^442799+1874633133296Enzo Doria06/2016
1470L(637751)133283Henri Lifchitz09/2008
14712^442688-113489133263Enzo Doria08/2014
1472(7*2^442640-1)/783133246Lelio R Paula07/2015
1473(9*2^442463+1)/17441133192Lelio R Paula07/2015
14742^442437-1849993133187Enzo Doria08/2015
14752^442430-2791721133185Enzo Doria03/2016
1476(13*2^442428-1)/309133183Lelio R Paula07/2015
1477(25*2^442379-1)/71133169Lelio R Paula07/2015
1478(2^441799+78557)/5132995Lelio R Paula07/2015
14792^441781-2787883132990Enzo Doria03/2016
1480(3*2^441685+1)/749132959Lelio R Paula07/2015
14812^441521-113575132912Enzo Doria08/2014
14822^441330+1871959132854Enzo Doria05/2016
14832^441063+383132774Lelio R Paula06/2012
14842^440846+1870909132708Enzo Doria05/2016
14852^440656-113489132651Enzo Doria08/2014
1486(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
1487(38^83891+1)/39132529Robert Price09/2013
148847^79201-46^79201132432Robert Price10/2012
14892^439897-113653132423Enzo Doria08/2014
1490(5*2^439822+1)/9132400Lelio R Paula06/2015
1491(112*10^132337-1)/3132339Serge Batalov12/2014
14922^439576-113247132326Enzo Doria07/2014
14932^439497-29143132302Enzo Doria07/2015
14942^439409-114193132276Enzo Doria12/2014
14959*10^132148-7132149Robert Price09/2015
14962^438845+1870217132106Enzo Doria05/2016
14972^438789+87855132089Lelio R Paula01/2016
14982^438774-2786411132085Enzo Doria03/2016
14992^438755-1848205132079Enzo Doria07/2015
15002^438739-112087132074Enzo Doria06/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!