PRP Records

Probable Primes Top 10000

(173006 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 ?
12512^483563-1863457145567Enzo Doria12/2015
12522^483516-1861409145553Enzo Doria11/2015
12532^483384-115019145514Enzo Doria06/2015
12542^483302-3221145489Lelio R Paula12/2012
12552^483046+1874029145412Enzo Doria06/2016
12562^482991-2789317145395Enzo Doria12/2015
12572^482978-2789711145391Enzo Doria12/2015
12582^482966-2789711145388Enzo Doria12/2015
12592^482817-1858843145343Enzo Doria10/2015
12602^482751-113635145323Enzo Doria08/2014
12612^482705-459763145309Enzo Doria05/2015
1262(4^241306+11)/3145281Robert Price03/2017
1263(19*2^482534+1)/7145258Lelio R Paula09/2015
126453^84239-52^84239145252Robert Price01/2013
1265(2^482333+5)/9287145193Lelio R Paula09/2015
12662^482087+72623145123Enzo Doria04/2016
12672^482016-286565145102Enzo Doria07/2015
12682^481840+15145049Robert Price09/2015
12692^481801-481801145037Henri Lifchitz03/2005
12702^481775+1869083145029Enzo Doria05/2016
127129^99167+2145022Ray Chandler08/2011
12722^481663+1875653144996Enzo Doria07/2016
12732^481149-459073144841Enzo Doria05/2015
12742^481045-113215144809Enzo Doria07/2014
12752^480859-113695144753Enzo Doria09/2014
12762^480766-2787191144725Enzo Doria11/2015
1277(21*27^101106-151)/26144720Curtis Bright05/2015
12782^480678+1874239144699Enzo Doria06/2016
1279(8*10^144683+1)/9144683Serge Batalov05/2010
1280L(692147)144651Henri Lifchitz10/2008
12812^480417+35144620Robert Price11/2015
12822^480296-59879144584Enzo Doria10/2015
12832^479844+3144448Donovan Johnson06/2006
1284(27*2^479642+1)/733144386Lelio R Paula08/2015
1285(21*2^479605-1)/11144376Lelio R Paula09/2015
12862^479348-2792219144299Enzo Doria02/2016
12873^302389-6242144277Enzo Doria05/2014
12882*10^144220-3144221Robert Price07/2015
12892^478904-109109144165Enzo Doria04/2014
12902^478337-115333143994Enzo Doria07/2015
1291(7*2^478330-1)/3143993Lelio R Paula08/2015
129288^74047-87^74047143984Robert Price05/2015
12932^478088+27143919Robert Price11/2015
12942^477475-22071143735Enzo Doria07/2013
12952^477417-22123143717Enzo Doria07/2013
12962^477359-3577143700Yves Minet03/2017
12972^476936-396765143573Enzo Doria07/2013
12982^476888-2791229143558Enzo Doria01/2016
12992^476868-1859939143552Enzo Doria11/2015
13002^476558-113627143459Enzo Doria08/2014
1301(2^475854+9)/73143245Lelio R Paula08/2015
13022^475813-113239143234Enzo Doria07/2014
13032^475624-114059143178Enzo Doria11/2014
1304(11*2^475553-7)/15143156Renaud Lifchitz03/2011
13052^475480-2786129143134Enzo Doria10/2015
13062^475299-111937143080Enzo Doria05/2014
13072^475160-2797859143038Enzo Doria04/2016
1308(2^475069+3)/395143008Lelio R Paula08/2015
13092^475027-461437142998Enzo Doria07/2015
1310(2^474958+78557)/3142977Lelio R Paula07/2015
1311(11*2^474432-1)/95142818Lelio R Paula09/2015
13122^474417-59923142814Enzo Doria10/2015
1313(3*2^474166+1)/7142738Lelio R Paula08/2015
13142^474053+2897142705Lelio R Paula08/2012
1315(10^142699+359)/9142699Serge Batalov12/2014
1316898^48311-897^48311142676Jean-Louis Charton12/2012
13172^473740-1856639142610Enzo Doria09/2015
13182^473617-114223142573Enzo Doria12/2014
13192^473257+1873217142465Enzo Doria06/2016
1320(19*2^473242+1)/11142461Lelio R Paula09/2015
1321(10^142425+359)/9142425Serge Batalov12/2014
13222^473101+773027142418Enzo Doria05/2016
1323(13*2^472838-1)/3142340Lelio R Paula09/2015
1324(17*2^472789-1)/187347142320Lelio R Paula09/2015
13252^472634-109511142278Enzo Doria04/2014
1326(48^84589+1)/49142213Robert Price01/2014
13272^472258+7142164Lelio R Paula08/2015
1328tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
1329(11*2^471913-1)/21142060Lelio R Paula09/2015
13302^471792+1880881142024Enzo Doria11/2016
1331(31*2^471580-1)/135141960Lelio R Paula08/2015
1332(904*19^110984-1)/3141924Curtis Bright05/2015
13334*5^202913-9141831Lelio R Paula04/2015
13342*7^167812-3141818Lelio R Paula12/2014
13352^471043+35141799Robert Price11/2015
1336(11*2^470956-1)/7945141770Lelio R Paula08/2015
13372^470692+76771141693Enzo Doria05/2016
1338(21*2^470391+1)/533141601Lelio R Paula09/2015
13392^470305-459373141576Enzo Doria05/2015
13402^470183+72623141540Enzo Doria04/2016
13412^470173-16465141537Enzo Doria04/2013
13422^469974-1841141477Enzo Doria05/2014
1343(23*2^469939+1)/25141466Lelio R Paula08/2015
13442^469630-59711141373Enzo Doria10/2015
1345(2^469564-3)/611141351Lelio R Paula08/2015
13462^469372-112949141296Enzo Doria07/2014
1347143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
13482^469198+782569141243Enzo Doria10/2016
13492^469076-2786939141206Enzo Doria11/2015
13502^468804+1874941141125Enzo Doria06/2016
13512^468787+81353141119Enzo Doria08/2016
13522^468595-350407141062Enzo Doria06/2015
13532^468564+87855141052Lelio R Paula01/2016
13542^468551-21987141048Enzo Doria07/2013
13552^468523-7141040Lelio R Paula08/2015
13562^468405+87855141004Lelio R Paula01/2016
13572^467978-113051140876Enzo Doria07/2014
13582^467780-344429140816Enzo Doria07/2015
13592^467605-1855603140764Enzo Doria09/2015
13605*10^140744-7140745Robert Price09/2015
1361(5^201359-1)/4140744Paul Bourdelais12/2008
13622^467401-1850023140702Enzo Doria08/2015
1363(2^467270+78557)/23247140658Lelio R Paula07/2015
1364(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
13652^467166-1854941140631Enzo Doria09/2015
13662^466866-1840571140541Enzo Doria06/2015
13672^466829-459523140530Enzo Doria05/2015
13682^466692-113213140489Enzo Doria07/2014
1369(112*10^140357-1)/3140359Serge Batalov12/2014
13702^466181-112735140335Enzo Doria07/2014
1371(27*2^465872+1)/691140241Lelio R Paula08/2015
13722^465803-114817140221Enzo Doria05/2015
1373floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
13742^465503-112735140131Enzo Doria07/2014
13756^179964+179964^6-1140040Robert Price04/2014
1376(29*2^465077-1)/9140003Lelio R Paula08/2015
13772^465072-344789140001Enzo Doria07/2015
1378(17^113621+1)/18139804Paul Bourdelais09/2011
1379(19*2^464312-1)/3139773Lelio R Paula08/2015
1380(31*2^463970+1)/5139670Lelio R Paula08/2015
13812^463633-2788423139568Enzo Doria11/2015
13822^463271-109501139459Enzo Doria04/2014
13832^463019+79463139383Enzo Doria06/2016
13843^292129-112756139381Enzo Doria07/2014
1385(15*2^462951+1)/527139361Lelio R Paula08/2015
13862^462855-1865707139334Enzo Doria02/2016
13872^462786-292043139313Enzo Doria08/2015
1388(26*10^139289+1)/9139290Serge Batalov05/2010
13892^462238-935139148Yves Minet02/2014
13902^461228+1870441138844Enzo Doria05/2016
13912^461204-113675138837Enzo Doria08/2014
1392(2^461139-7)/47138815Lelio R Paula08/2015
1393(17*2^460963+1)/124051613138757Lelio R Paula08/2015
13942^460567-113541138645Enzo Doria08/2014
13957*10^138604+3138605Robert Price08/2015
13962^460078-69581138498Enzo Doria12/2015
13972^459768+1531138404Lelio R Paula06/2012
13982^459343-113611138277Enzo Doria08/2014
13992^459199+1874393138233Enzo Doria06/2016
14002^459063-345307138192Enzo Doria06/2015
14012^458927-112747138151Enzo Doria06/2014
14022^458927-69217138151Enzo Doria11/2015
1403555555*2^458524+1513138036Darren Bedwell08/2009
14042^458465+2^32+1138012T. D. Noe06/2007
14052^458321-113053137969Enzo Doria07/2014
14062^458298+79459137962Enzo Doria06/2016
14072^458248-21815137947Enzo Doria07/2013
14082^458194+1876549137931Enzo Doria07/2016
14092^457822+105137819Donovan Johnson06/2006
14102^457754-113711137798Enzo Doria09/2014
141111^132315-360137792Enzo Doria09/2012
14122^457322-2786393137668Enzo Doria10/2015
1413gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
14142^457240-59939137643Enzo Doria10/2015
14152^457120-21575137607Enzo Doria07/2013
1416(11*2^456978+1)/15137564Lelio R Paula07/2015
1417(7*25^98399+10613)/12137556Curtis Bright05/2015
14182^456796-113513137510Enzo Doria08/2014
1419(7*2^456655+1)/39137467Lelio R Paula07/2015
14202^456503-114361137422Enzo Doria01/2015
1421(11*2^456387+1)/19137386Lelio R Paula07/2015
1422(71*10^137250+1)/9137251Serge Batalov05/2010
14232^455922+76249137247Enzo Doria05/2016
142414^119741-119741^14137239Serge Batalov04/2016
1425(19*2^455760+1)/3455137196Lelio R Paula07/2015
1426124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
14272^455689+72677137177Enzo Doria04/2016
1428(17948!)^2+Prime(17948)137118Robert Price08/2014
1429(37^87421-1)/36137093Robert Price03/2012
1430(73*17^111333-9)/16136991Curtis Bright05/2015
14312^455025-112723136977Enzo Doria06/2014
14322^454675-1777136871Yves Minet10/2011
1433(6092*28^94536-143)/9136812Curtis Bright05/2015
14342^454199-113697136728Enzo Doria09/2014
14352^453935-2791357136649Enzo Doria01/2016
14362^453906-69131136640Enzo Doria11/2015
14372^453791+1873913136605Enzo Doria06/2016
1438(21*2^453740-1)/2735136588Lelio R Paula07/2015
14392^453503-2788297136519Enzo Doria11/2015
14402^453267-113827136447Enzo Doria09/2014
14412^453102+1877629136398Enzo Doria08/2016
1442L(651821)136223Henri Lifchitz09/2008
14432^452460+77701136205Enzo Doria05/2016
14442^452440-114755136199Enzo Doria04/2015
1445(2^451956-5)/181136051Lelio R Paula07/2015
14462^451947-22165136050Enzo Doria07/2013
14472^451787-21805136002Enzo Doria07/2013
14482^451734-112817135986Enzo Doria06/2014
1449(11*2^451714+1)/75135979Lelio R Paula07/2015
14502^451705-21879135977Enzo Doria07/2013
14512^451560-112349135934Enzo Doria06/2014
14522^451450-21743135900Enzo Doria07/2013
1453(13725^32768+1)/131074135573Lelio R Paula03/2012
1454(5^193939+1)/6135557Paul Bourdelais12/2008
14552^449944-113247135447Enzo Doria07/2014
14562^449770-113247135395Enzo Doria07/2014
14572^449637-21471135355Enzo Doria07/2013
1458(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
1459(19*2^449325+1)/9135261Lelio R Paula07/2015
14602^449049-115309135178Enzo Doria07/2015
1461(27*2^448936-1)/11135144Lelio R Paula07/2015
14622^448762-351401135091Enzo Doria07/2015
1463(10^135011+719)/9135011Serge Batalov12/2014
14642^448386-2786261134978Enzo Doria03/2016
14652^448113-113949134896Enzo Doria11/2014
14662^447888-2786639134828Enzo Doria03/2016
14672^447870-396765134823Enzo Doria07/2013
14682^447766-21791134791Enzo Doria07/2013
1469(23*2^447647+1)/155134755Lelio R Paula07/2015
14702^447552-1019134727Yves Minet02/2014
14712^447437-113569134692Enzo Doria08/2014
14722^447357-2797573134668Enzo Doria04/2016
14732^447094-113193134589Enzo Doria07/2014
14743^282041-9934134568Enzo Doria05/2014
14752^447019-109039134567Enzo Doria04/2014
14762^446990-22041134558Enzo Doria07/2013
14772^446782-39701134495Enzo Doria09/2015
14782^446494-16485134409Enzo Doria04/2013
147929504^30069-30069^29504134405Norbert Schneider12/2014
1480(10^134385+719)/9134385Serge Batalov12/2014
1481(13*2^446187-1)/661134314Lelio R Paula07/2015
1482(2^446022-7)/339134264Lelio R Paula07/2015
14832^445671-22071134161Enzo Doria07/2013
1484(28*10^134122-1)/9134123Serge Batalov10/2014
14852^445515-113859134114Enzo Doria10/2014
14862^445328-216917134058Enzo Doria05/2014
14872^445202+1874899134020Enzo Doria06/2016
1488(13*2^445102+1)/17133989Lelio R Paula07/2015
14892^444964-113639133948Enzo Doria08/2014
149028118^30097-30097^28118133902Norbert Schneider01/2015
14912^444784-113859133894Enzo Doria10/2014
1492(89*10^133580+1)/9133581Serge Batalov05/2010
149362^74521-61^74521133571Robert Price05/2013
14942^443198-1867301133416Enzo Doria03/2016
14952^442799+1874633133296Enzo Doria06/2016
1496L(637751)133283Henri Lifchitz09/2008
14972^442688-113489133263Enzo Doria08/2014
1498(7*2^442640-1)/783133246Lelio R Paula07/2015
1499(9*2^442463+1)/17441133192Lelio R Paula07/2015
15002^442437-1849993133187Enzo Doria08/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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