PRP Records

Probable Primes Top 10000

(177649 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 ?
12512^488627-350317147092Enzo Doria06/2015
1252(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
12532^488280-2165146987Yves Minet07/2014
12542^487726-1863341146821Enzo Doria12/2015
12552^487121-39523146639Enzo Doria09/2015
1256(7*2^486967+1)/39146591Lelio R Paula09/2015
12572^486840+1879141146554Enzo Doria08/2016
125896^73877-95^73877146445Robert Price10/2015
12592^485531-114621146160Enzo Doria05/2015
1260(2^485461-9)/4249146135Lelio R Paula09/2015
12612^485389+81887146117Enzo Doria08/2016
1262(10^146063+71)/9146063Serge Batalov07/2015
1263(2^485119+7)/2745146032Lelio R Paula09/2015
12642^484743+1872923145923Enzo Doria05/2016
12652^484341+1879157145802Enzo Doria08/2016
126670^78989-69^78989145743Robert Price01/2014
126751^85334+2145714Robert Price07/2015
12682^483886-1857101145665Enzo Doria10/2015
12692^483563-1863457145567Enzo Doria12/2015
12702^483516-1861409145553Enzo Doria11/2015
12712^483384-115019145514Enzo Doria06/2015
12722^483302-3221145489Lelio R Paula12/2012
12732^483046+1874029145412Enzo Doria06/2016
12742^482991-2789317145395Enzo Doria12/2015
12752^482978-2789711145391Enzo Doria12/2015
12762^482966-2789711145388Enzo Doria12/2015
12772^482817-1858843145343Enzo Doria10/2015
12782^482751-113635145323Enzo Doria08/2014
12792^482705-459763145309Enzo Doria05/2015
1280(4^241306+11)/3145281Robert Price03/2017
1281(19*2^482534+1)/7145258Lelio R Paula09/2015
128253^84239-52^84239145252Robert Price01/2013
1283(2^482333+5)/9287145193Lelio R Paula09/2015
12842^482087+72623145123Enzo Doria04/2016
12852^482016-286565145102Enzo Doria07/2015
12862^481840+15145049Robert Price09/2015
12872^481801-481801145037Henri Lifchitz03/2005
12882^481775+1869083145029Enzo Doria05/2016
128929^99167+2145022Ray Chandler08/2011
12902^481663+1875653144996Enzo Doria07/2016
12912^481149-459073144841Enzo Doria05/2015
12922^481045-113215144809Enzo Doria07/2014
12932^480859-113695144753Enzo Doria09/2014
12942^480766-2787191144725Enzo Doria11/2015
1295(21*27^101106-151)/26144720Curtis Bright05/2015
12962^480678+1874239144699Enzo Doria06/2016
1297(8*10^144683+1)/9144683Serge Batalov05/2010
1298L(692147)144651Henri Lifchitz10/2008
12992^480417+35144620Robert Price11/2015
13002^480296-59879144584Enzo Doria10/2015
13012^479844+3144448Donovan Johnson06/2006
1302(27*2^479642+1)/733144386Lelio R Paula08/2015
1303(21*2^479605-1)/11144376Lelio R Paula09/2015
13042^479348-2792219144299Enzo Doria02/2016
13053^302389-6242144277Enzo Doria05/2014
13062*10^144220-3144221Robert Price07/2015
13072^478904-109109144165Enzo Doria04/2014
13082^478337-115333143994Enzo Doria07/2015
1309(7*2^478330-1)/3143993Lelio R Paula08/2015
131088^74047-87^74047143984Robert Price05/2015
13112^478088+27143919Robert Price11/2015
13122^477475-22071143735Enzo Doria07/2013
13132^477417-22123143717Enzo Doria07/2013
13142^477359-3577143700Yves Minet03/2017
13152^476936-396765143573Enzo Doria07/2013
13162^476888-2791229143558Enzo Doria01/2016
13172^476868-1859939143552Enzo Doria11/2015
13182^476558-113627143459Enzo Doria08/2014
1319(2^475854+9)/73143245Lelio R Paula08/2015
13202^475813-113239143234Enzo Doria07/2014
13212^475624-114059143178Enzo Doria11/2014
1322(11*2^475553-7)/15143156Renaud Lifchitz03/2011
13232^475480-2786129143134Enzo Doria10/2015
13242^475299-111937143080Enzo Doria05/2014
13252^475160-2797859143038Enzo Doria04/2016
1326(2^475069+3)/395143008Lelio R Paula08/2015
13272^475027-461437142998Enzo Doria07/2015
1328(2^474958+78557)/3142977Lelio R Paula07/2015
1329(11*2^474432-1)/95142818Lelio R Paula09/2015
13302^474417-59923142814Enzo Doria10/2015
1331(3*2^474166+1)/7142738Lelio R Paula08/2015
13322^474053+2897142705Lelio R Paula08/2012
1333(10^142699+359)/9142699Serge Batalov12/2014
1334898^48311-897^48311142676Jean-Louis Charton12/2012
13352^473740-1856639142610Enzo Doria09/2015
13362^473617-114223142573Enzo Doria12/2014
13372^473257+1873217142465Enzo Doria06/2016
1338(19*2^473242+1)/11142461Lelio R Paula09/2015
1339(10^142425+359)/9142425Serge Batalov12/2014
13402^473101+773027142418Enzo Doria05/2016
1341(13*2^472838-1)/3142340Lelio R Paula09/2015
1342(17*2^472789-1)/187347142320Lelio R Paula09/2015
13432^472634-109511142278Enzo Doria04/2014
1344(48^84589+1)/49142213Robert Price01/2014
13452^472258+7142164Lelio R Paula08/2015
1346tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
1347(11*2^471913-1)/21142060Lelio R Paula09/2015
13482^471792+1880881142024Enzo Doria11/2016
1349(31*2^471580-1)/135141960Lelio R Paula08/2015
1350(904*19^110984-1)/3141924Curtis Bright05/2015
13514*5^202913-9141831Lelio R Paula04/2015
13522*7^167812-3141818Lelio R Paula12/2014
13532^471043+35141799Robert Price11/2015
1354(11*2^470956-1)/7945141770Lelio R Paula08/2015
13552^470692+76771141693Enzo Doria05/2016
1356(21*2^470391+1)/533141601Lelio R Paula09/2015
13572^470305-459373141576Enzo Doria05/2015
13582^470183+72623141540Enzo Doria04/2016
13592^470173-16465141537Enzo Doria04/2013
13602^469974-1841141477Enzo Doria05/2014
1361(23*2^469939+1)/25141466Lelio R Paula08/2015
13622^469630-59711141373Enzo Doria10/2015
1363(2^469564-3)/611141351Lelio R Paula08/2015
13642^469372-112949141296Enzo Doria07/2014
1365143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
13662^469198+782569141243Enzo Doria10/2016
13672^469076-2786939141206Enzo Doria11/2015
13682^468804+1874941141125Enzo Doria06/2016
13692^468787+81353141119Enzo Doria08/2016
13702^468595-350407141062Enzo Doria06/2015
13712^468564+87855141052Lelio R Paula01/2016
13722^468551-21987141048Enzo Doria07/2013
13732^468523-7141040Lelio R Paula08/2015
13742^468405+87855141004Lelio R Paula01/2016
13752^467978-113051140876Enzo Doria07/2014
13762^467780-344429140816Enzo Doria07/2015
13772^467605-1855603140764Enzo Doria09/2015
13785*10^140744-7140745Robert Price09/2015
1379(5^201359-1)/4140744Paul Bourdelais12/2008
13802^467401-1850023140702Enzo Doria08/2015
1381(2^467270+78557)/23247140658Lelio R Paula07/2015
1382(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
13832^467166-1854941140631Enzo Doria09/2015
13842^466866-1840571140541Enzo Doria06/2015
13852^466829-459523140530Enzo Doria05/2015
13862^466692-113213140489Enzo Doria07/2014
1387(112*10^140357-1)/3140359Serge Batalov12/2014
13882^466181-112735140335Enzo Doria07/2014
1389(27*2^465872+1)/691140241Lelio R Paula08/2015
13902^465803-114817140221Enzo Doria05/2015
1391floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
13922^465503-112735140131Enzo Doria07/2014
13936^179964+179964^6-1140040Robert Price04/2014
1394(29*2^465077-1)/9140003Lelio R Paula08/2015
13952^465072-344789140001Enzo Doria07/2015
1396(17^113621+1)/18139804Paul Bourdelais09/2011
1397(19*2^464312-1)/3139773Lelio R Paula08/2015
1398(31*2^463970+1)/5139670Lelio R Paula08/2015
13992^463633-2788423139568Enzo Doria11/2015
14002^463271-109501139459Enzo Doria04/2014
14012^463019+79463139383Enzo Doria06/2016
14023^292129-112756139381Enzo Doria07/2014
1403(15*2^462951+1)/527139361Lelio R Paula08/2015
14042^462855-1865707139334Enzo Doria02/2016
14052^462786-292043139313Enzo Doria08/2015
1406(26*10^139289+1)/9139290Serge Batalov05/2010
14072^462238-935139148Yves Minet02/2014
14082^461228+1870441138844Enzo Doria05/2016
14092^461204-113675138837Enzo Doria08/2014
1410(2^461139-7)/47138815Lelio R Paula08/2015
1411(17*2^460963+1)/124051613138757Lelio R Paula08/2015
14122^460567-113541138645Enzo Doria08/2014
14137*10^138604+3138605Robert Price08/2015
14142^460078-69581138498Enzo Doria12/2015
14152^459768+1531138404Lelio R Paula06/2012
14162^459343-113611138277Enzo Doria08/2014
14172^459199+1874393138233Enzo Doria06/2016
14182^459063-345307138192Enzo Doria06/2015
14192^458927-112747138151Enzo Doria06/2014
14202^458927-69217138151Enzo Doria11/2015
1421555555*2^458524+1513138036Darren Bedwell08/2009
14222^458465+2^32+1138012T. D. Noe06/2007
14232^458321-113053137969Enzo Doria07/2014
14242^458298+79459137962Enzo Doria06/2016
14252^458248-21815137947Enzo Doria07/2013
14262^458194+1876549137931Enzo Doria07/2016
14272^457822+105137819Donovan Johnson06/2006
14282^457754-113711137798Enzo Doria09/2014
142911^132315-360137792Enzo Doria09/2012
14302^457322-2786393137668Enzo Doria10/2015
1431gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
14322^457240-59939137643Enzo Doria10/2015
14332^457120-21575137607Enzo Doria07/2013
1434(11*2^456978+1)/15137564Lelio R Paula07/2015
1435(7*25^98399+10613)/12137556Curtis Bright05/2015
14362^456796-113513137510Enzo Doria08/2014
1437(7*2^456655+1)/39137467Lelio R Paula07/2015
14382^456503-114361137422Enzo Doria01/2015
1439(11*2^456387+1)/19137386Lelio R Paula07/2015
1440(71*10^137250+1)/9137251Serge Batalov05/2010
14412^455922+76249137247Enzo Doria05/2016
144214^119741-119741^14137239Serge Batalov04/2016
1443(19*2^455760+1)/3455137196Lelio R Paula07/2015
1444124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
14452^455689+72677137177Enzo Doria04/2016
1446(17948!)^2+Prime(17948)137118Robert Price08/2014
1447(37^87421-1)/36137093Robert Price03/2012
1448(73*17^111333-9)/16136991Curtis Bright05/2015
14492^455025-112723136977Enzo Doria06/2014
14502^454675-1777136871Yves Minet10/2011
1451(6092*28^94536-143)/9136812Curtis Bright05/2015
145231^91680-2136729Lelio R Paula05/2017
14532^454199-113697136728Enzo Doria09/2014
14542^453935-2791357136649Enzo Doria01/2016
14552^453906-69131136640Enzo Doria11/2015
14562^453791+1873913136605Enzo Doria06/2016
1457(21*2^453740-1)/2735136588Lelio R Paula07/2015
14582^453503-2788297136519Enzo Doria11/2015
14592^453267-113827136447Enzo Doria09/2014
14602^453102+1877629136398Enzo Doria08/2016
1461L(651821)136223Henri Lifchitz09/2008
14622^452460+77701136205Enzo Doria05/2016
14632^452440-114755136199Enzo Doria04/2015
1464(2^451956-5)/181136051Lelio R Paula07/2015
14652^451947-22165136050Enzo Doria07/2013
14662^451787-21805136002Enzo Doria07/2013
14672^451734-112817135986Enzo Doria06/2014
1468(11*2^451714+1)/75135979Lelio R Paula07/2015
14692^451705-21879135977Enzo Doria07/2013
14702^451560-112349135934Enzo Doria06/2014
14712^451450-21743135900Enzo Doria07/2013
1472(13725^32768+1)/131074135573Lelio R Paula03/2012
1473(5^193939+1)/6135557Paul Bourdelais12/2008
14742^449944-113247135447Enzo Doria07/2014
14752^449770-113247135395Enzo Doria07/2014
14762^449637-21471135355Enzo Doria07/2013
1477(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
1478(19*2^449325+1)/9135261Lelio R Paula07/2015
14792^449049-115309135178Enzo Doria07/2015
1480(27*2^448936-1)/11135144Lelio R Paula07/2015
14812^448762-351401135091Enzo Doria07/2015
1482(10^135011+719)/9135011Serge Batalov12/2014
14832^448386-2786261134978Enzo Doria03/2016
14842^448113-113949134896Enzo Doria11/2014
14852^447888-2786639134828Enzo Doria03/2016
14862^447870-396765134823Enzo Doria07/2013
14872^447766-21791134791Enzo Doria07/2013
1488(23*2^447647+1)/155134755Lelio R Paula07/2015
14892^447552-1019134727Yves Minet02/2014
14902^447437-113569134692Enzo Doria08/2014
14912^447357-2797573134668Enzo Doria04/2016
14922^447094-113193134589Enzo Doria07/2014
14933^282041-9934134568Enzo Doria05/2014
14942^447019-109039134567Enzo Doria04/2014
14952^446990-22041134558Enzo Doria07/2013
14962^446782-39701134495Enzo Doria09/2015
14972^446494-16485134409Enzo Doria04/2013
149829504^30069-30069^29504134405Norbert Schneider12/2014
1499(10^134385+719)/9134385Serge Batalov12/2014
1500(13*2^446187-1)/661134314Lelio R Paula07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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