PRP Records

Probable Primes Top 10000

(253476 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 ?
4501(41*10^93207+49)/993208Robert Price04/2016
450214^81312-5793194Lelio R Paula06/2016
450341^57783-4093192Theodore Burton02/2007
45043*10^93179-9793180Robert Price08/2017
45055*7^110252-493175Lelio R Paula11/2014
45062^309380-2793133Lelio R Paula11/2012
450723*10^93116-793118Robert Price03/2016
4508(29*10^93082+1)/393083Robert Price11/2015
4509(58*10^93062-13)/993063Robert Price09/2015
45102^309131+186938393058Enzo Doria05/2016
45112^309066-9393039Lelio R Paula11/2012
45122^309063-11326993038Enzo Doria07/2014
45133^194965+1693022Robert Price10/2013
45142^308979+186914393012Enzo Doria05/2016
45155^133064+5493008Lelio R Paula04/2016
4516(2^308905-509203)/11992988Lelio R Paula06/2013
4517(94*10^92981-49)/9992981Ray Chandler07/2011
4518(2*10^92976-17)/392976Robert Price08/2014
45192^308809+3796792961Phil Moore03/2008
4520(3^194825+5)/1165692952Lelio R Paula04/2013
4521(2^308679+5)/157392919Lelio R Paula06/2013
45222^308650+51392913Lelio R Paula02/2016
45235*7^109936+692908Lelio R Paula10/2014
45242*10^92897+8992898Robert Price07/2016
452512^86073-2992889Lelio R Paula06/2016
45262^308566-11792888Lelio R Paula11/2012
4527(17*10^92869-11)/392870Robert Price07/2015
45282^308459+7543192856Enzo Doria04/2016
45292^308426-186637792846Enzo Doria03/2016
4530(96^46831-1)/9592830Paul Bourdelais09/2017
45312^308349-11211192823Enzo Doria06/2014
45329*10^92821+1992822Robert Price05/2016
45332^308337-7592819Lelio R Paula11/2012
45344*3^194508+792805Lelio R Paula08/2014
453522*25^66379-11392796Curtis Bright05/2015
453611^89101-108092790Enzo Doria12/2012
45372^308236-186785992789Enzo Doria04/2016
453812^85963+2592770Lelio R Paula06/2016
45397^109750-6692750Lelio R Paula04/2016
45409*10^92742+1192743Robert Kinser01/2017
4541(21*2^308046-1)/885792729Lelio R Paula02/2014
45422^307997-11065592717Enzo Doria05/2014
4543L(443609)92709Renaud Lifchitz11/2003
454410^92691+992692Robert Price03/2011
454510^92691-25229192691Patrick De Geest08/2013
45462^307879-252192681Yves Minet07/2014
4547(2^307780-7)/1995966992644Lelio R Paula06/2013
454814^80831+4792643Lelio R Paula06/2016
454915^78744+9292611Lelio R Paula07/2016
455065^51083-6492610Norbert Schneider11/2014
4551131^43737-13092604Norbert Schneider02/2019
45526^118996-1694392597Enzo Doria02/2013
4553(16*10^92591+41)/392592Robert Price10/2017
4554(3^194014-7)/292568Lelio R Paula04/2013
4555(63^51439+1)/6492555Paul Bourdelais08/2017
4556(26*10^92546-77)/392547Robert Price02/2017
45573^193954+34092540Lelio R Paula04/2016
45582^307407-307407^292539Henri Lifchitz05/2005
4559(17*10^92513-11)/392514Robert Price07/2015
45602^307318-421192512Yves Minet06/2011
45612^307280+19392501Lelio R Paula11/2012
456220^71075-3392471Lelio R Paula05/2016
45632^307126-7879592455Lelio R Paula02/2016
45642^307125-4978992454Henri Lifchitz08/2005
45652^307099+2392447Lelio R Paula11/2012
4566129^43798+12892440Norbert Schneider01/2019
4567Phi(277314,10)/332776992430Makoto Kamada05/2019
45687*10^92414-6992415Robert Price01/2017
4569(9787*2^306975-1)/212915592407Lelio R Paula04/2015
45702^306915+187337392391Enzo Doria06/2016
45712^306908+1291592389Lelio R Paula02/2016
457219^72244-8092383Lelio R Paula06/2016
45742^306849+7592371Lelio R Paula11/2012
4573(397*10^92369+53)/992371Robert Price11/2017
45752^306813-86968810592360Lelio R Paula08/2016
45762^306672-10905992318Enzo Doria04/2014
45776^118604-1706392292Enzo Doria02/2013
4578(31*2^306487-1)/229192260Lelio R Paula02/2014
45792^306467-183561192256Enzo Doria04/2015
45802^306433+7642792246Enzo Doria05/2016
45822^306430-11331392245Enzo Doria07/2014
4581(23*10^92244-59)/992245Robert Price03/2017
4583(47*2^306398+1)/138480392231Lelio R Paula04/2015
4584(25*10^92186+59)/392187Robert Price05/2016
45852^306213-28618392180Enzo Doria06/2015
458610^92178+6192179Robert Price04/2011
458710^92178-17550992178Patrick De Geest07/2013
45882^306200+118592176Lelio R Paula02/2016
45892^306153+1192162Lelio R Paula11/2012
4590(2^306141-7)/592157Lelio R Paula06/2013
4591(26*10^92152-23)/392153Robert Price08/2016
4592(2*10^92152+67)/392152Robert Price04/2017
45934*10^92099+3*7^9209992100Mike Oakes12/2010
4594115^44684+11492081Norbert Schneider07/2018
4595(2^305867-2^152934+1)/59207511/2006
45962^305851-10949592071Enzo Doria04/2014
459812^85300+3592055Lelio R Paula06/2016
4597((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
45993^192911+9292042Lelio R Paula04/2016
46002^305723-27627192032Enzo Doria07/2015
46012^305676+9392018Donovan Johnson06/2008
46023^192819+491999Lelio R Paula04/2013
4603(38*10^91997-83)/9991997Ray Chandler07/2011
46042^305539+7291191977Enzo Doria04/2016
4605Phi(212014,10)91960Makoto Kamada04/2019
4606(2^305427-5)/129799821391934Lelio R Paula06/2013
460785^47642+8491922Norbert Schneider10/2015
460810^91920+18765191921Patrick De Geest07/2013
460910^91920-3991920Robert Price05/2011
4610(22*10^91903+41)/991904Robert Price02/2015
46122^305275-2791897Lelio R Paula11/2012
46113^192607-772691897Enzo Doria05/2014
4613(7*10^91856-61)/991856Erik Branger12/2009
4614(89*10^91839-53)/991840Robert Price11/2015
46158*5^131351+791812Lelio R Paula10/2014
46163^192426-6891811Lelio R Paula04/2016
46172^304973+11791807Lelio R Paula11/2012
46182^304939-186372791796Enzo Doria03/2016
46192^304902+841591785Lelio R Paula02/2016
462018^73119+6191785Lelio R Paula06/2016
4621(78557*2^304740+1)/15991739Lelio R Paula06/2014
46222^304747+7135591738Lelio R Paula02/2016
46238*3^192251+591728Lelio R Paula08/2014
46242^304674-8791717Lelio R Paula11/2012
4625(28*10^91715+701)/991716Robert Price11/2017
4626(2^304698+9)/136280995391715Lelio R Paula06/2013
4627(5*10^91707-119)/391708Robert Price04/2016
46282^304633-11277191704Enzo Doria06/2014
46299*10^91693+2391694Robert Price11/2017
46302^304578-1671391688Enzo Doria05/2013
46316^117824-1871391685Enzo Doria03/2013
4632(17^74509-1)/1691679Paul Bourdelais03/2010
4633(2^304551-7)/891223191673Lelio R Paula06/2013
4634(2^304532-3)/301391670Lelio R Paula06/2013
46352^304507-1664591666Enzo Doria04/2013
4636(29*2^304489+1)/3191661Lelio R Paula09/2013
46372^304471-183612791655Enzo Doria04/2015
46382^304433+3276991644Lelio R Paula02/2016
46392^304410-1662591637Enzo Doria04/2013
4640183^40500-291630Lelio R Paula10/2017
4641(203*10^91613+1)/391615Robert Price09/2017
46424*5^131052+791603Lelio R Paula10/2014
46432^304278-400191597Yves Minet04/2017
46442^304272-186637791595Enzo Doria03/2016
46452^304268+1968391594Lelio R Paula02/2016
46462^304162-16191562Lelio R Paula11/2012
46475*7^108331+691552Lelio R Paula10/2014
46482^304082-278782191538Enzo Doria03/2016
46492^304015+6413391518David Broadhurst06/2002
4650(7*2^303963+1)/391503Lelio R Paula09/2013
4651(2^303945-9)/361791494Lelio R Paula06/2013
46522^303930+188052791493Enzo Doria10/2016
46533^191684-6891457Lelio R Paula04/2016
4654(21*2^303813-1)/16991456Lelio R Paula02/2014
465511^87797-12091432Enzo Doria07/2012
46562^303698-184723191423Enzo Doria07/2015
4657(38^28933-1)^2-291416Norbert Schneider06/2016
46582^303554+7729991379Enzo Doria05/2016
46592^303542+1270591376Lelio R Paula02/2016
466031^61269-291375Lelio R Paula09/2013
46612^303516-6487591368Lelio R Paula02/2016
4662(24737*2^303428+1)/391345Lelio R Paula06/2014
4663(21181*2^303357+1)/3236191320Lelio R Paula06/2014
46642^303344-278696991316Enzo Doria03/2016
46656^117346+6591313Lelio R Paula05/2016
46662^303321+85591309Lelio R Paula02/2016
466712^84606+4791306Lelio R Paula06/2016
46682^303288+187431191299Enzo Doria06/2016
4669197^39788-291293Lelio R Paula10/2017
467011^87663-171091292Enzo Doria12/2012
46712^303224+253391280Henri Lifchitz05/2005
46726^117302+14391279Lelio R Paula05/2016
46733^191306-11288091277Enzo Doria07/2014
46742^303207+1291591275Lelio R Paula02/2016
46752^303191-11125991270Enzo Doria05/2014
467610^91230+9^(91230+1)91231Robert Price08/2016
467710^91230+792191231Patrick De Geest11/2016
467810^91230-91114191230Patrick De Geest11/2016
467910^91229+34879391230Patrick De Geest07/2019
468010^91229-247191229Patrick De Geest01/2019
468110^91225+527191226Patrick De Geest01/2019
46836^117232-1742391225Enzo Doria02/2013
468210^91225-14721991225Patrick De Geest07/2019
46857*10^91215+391216Erik Branger11/2009
468410^91215+23061191216Patrick De Geest07/2019
468610^91215-453991215Patrick De Geest01/2019
468710^91210+242191211Patrick De Geest01/2019
468810^91210-173791210Patrick De Geest01/2019
468997*10^91205-391207Robert Price01/2017
46902^302979-16118191206Enzo Doria04/2013
46912^302949+8191197Henri Lifchitz02/2007
469210^91194+20036191195Patrick De Geest07/2019
46944*6^117192-591194Lelio R Paula10/2014
469310^91194-866391194Patrick De Geest01/2019
46952^302918+9991188Lelio R Paula11/2012
469610^91186+26811191187Patrick De Geest07/2019
469710^91186-776391186Patrick De Geest01/2019
469810^91181+55047191182Patrick De Geest07/2019
469910^91181-136791181Patrick De Geest01/2019
470010^91178+7188391179Patrick De Geest07/2019
470110^91178-471991178Patrick De Geest01/2019
470210^91165+304391166Patrick De Geest01/2019
470310^91165-39941391165Patrick De Geest07/2019
470410^91156+386191157Patrick De Geest01/2019
470510^91156-23149791156Patrick De Geest07/2019
47062^302797+186958791151Enzo Doria05/2016
4707265^37614+37614^26591148Norbert Schneider01/2015
47087^107852+8291146Lelio R Paula04/2016
4709(38*10^91144-11)/991145Robert Price05/2015
4710(55*10^91142+377)/991143Robert Price10/2017
471110^91128+996191129Patrick De Geest01/2019
4713249^38030+38030^24991128Norbert Schneider01/2015
471210^91128-18915391128Patrick De Geest07/2019
47146^117094-21104991117Mike Oakes05/2011
47162^302602-186718191093Enzo Doria03/2016
471510^91092+5612791093Patrick De Geest07/2019
471710^91092-910791092Patrick De Geest01/2019
4718(1017*2^302592-1)/5391091Lelio R Paula04/2015
471915^77445-1691083Lelio R Paula07/2016
47202^302505+8191064Henri Lifchitz02/2007
47212^302496-11234991061Enzo Doria06/2014
472217^73999-7291052Lelio R Paula07/2016
472310^91047+933191048Patrick De Geest01/2019
472410^91047-67116991047Patrick De Geest07/2019
472510^91044+207791045Patrick De Geest01/2019
472610^91044-13635991044Patrick De Geest07/2019
472710^91041+934991042Patrick De Geest01/2019
472810^91041-782391041Patrick De Geest01/2019
472910^91040+407791041Patrick De Geest01/2019
473010^91040-11942191040Patrick De Geest07/2019
473110^91037+276991038Patrick De Geest01/2019
473210^91037-2264991037Patrick De Geest07/2019
4733(16*10^91032+41)/391033Robert Price10/2017
473410^91023+5803991024Patrick De Geest07/2019
473510^91023-647191023Patrick De Geest01/2019
473610^91018+787391019Patrick De Geest01/2019
473710^91018-33317791018Patrick De Geest07/2019
473810^91017+6876791018Patrick De Geest07/2019
473910^91017-42832791017Patrick De Geest07/2019
474010^91016+7311191017Patrick De Geest07/2019
474110^91016-797391016Patrick De Geest01/2019
47422^302332+57729457591012Lelio R Paula08/2016
474310^91004+907391005Patrick De Geest01/2019
474410^91004-49151991004Patrick De Geest07/2019
474510^91003+7426991004Patrick De Geest07/2019
474610^91003-390391003Patrick De Geest01/2019
47472^302274+7420990994Enzo Doria04/2016
474810^90991+8114790992Patrick De Geest07/2019
474910^90991-627990991Patrick De Geest01/2019
475010^90983+139390984Patrick De Geest01/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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