PRP Records

Probable Primes Top 10000

(172742 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 ?
35015^133064+5493008Lelio R Paula04/2016
3502(2^308905-509203)/11992988Lelio R Paula06/2013
3503(94*10^92981-49)/9992981Ray Chandler07/2011
3504(2*10^92976-17)/392976Robert Price08/2014
35052^308809+3796792961Phil Moore03/2008
3506(3^194825+5)/1165692952Lelio R Paula04/2013
3507(2^308679+5)/157392919Lelio R Paula06/2013
35082^308650+51392913Lelio R Paula02/2016
35095*7^109936+692908Lelio R Paula10/2014
35102*10^92897+8992898Robert Price07/2016
351112^86073-2992889Lelio R Paula06/2016
35122^308566-11792888Lelio R Paula11/2012
3513(17*10^92869-11)/392870Robert Price07/2015
35142^308459+7543192856Enzo Doria04/2016
35152^308426-186637792846Enzo Doria03/2016
35162^308349-11211192823Enzo Doria06/2014
35179*10^92821+1992822Robert Price05/2016
35182^308337-7592819Lelio R Paula11/2012
35194*3^194508+792805Lelio R Paula08/2014
352022*25^66379-11392796Curtis Bright05/2015
352111^89101-108092790Enzo Doria12/2012
35222^308236-186785992789Enzo Doria04/2016
352312^85963+2592770Lelio R Paula06/2016
35247^109750-6692750Lelio R Paula04/2016
35259*10^92742+1192743Robert Kinser01/2017
3526(21*2^308046-1)/885792729Lelio R Paula02/2014
35272^307997-11065592717Enzo Doria05/2014
3528L(443609)92709Renaud Lifchitz11/2003
352910^92691+992692Robert Price03/2011
353010^92691-25229192691Patrick De Geest08/2013
35312^307879-252192681Yves Minet07/2014
3532(2^307780-7)/1995966992644Lelio R Paula06/2013
353314^80831+4792643Lelio R Paula06/2016
353415^78744+9292611Lelio R Paula07/2016
353565^51083-6492610Norbert Schneider11/2014
35366^118996-1694392597Enzo Doria02/2013
3537(3^194014-7)/292568Lelio R Paula04/2013
3538(26*10^92546-77)/392547Robert Price02/2017
35393^193954+34092540Lelio R Paula04/2016
35402^307407-307407^292539Henri Lifchitz05/2005
3541(17*10^92513-11)/392514Robert Price07/2015
35422^307318-421192512Yves Minet06/2011
35432^307280+19392501Lelio R Paula11/2012
354420^71075-3392471Lelio R Paula05/2016
35452^307126-7879592455Lelio R Paula02/2016
35462^307125-4978992454Henri Lifchitz08/2005
35472^307099+2392447Lelio R Paula11/2012
35487*10^92414-6992415Robert Price01/2017
3549(9787*2^306975-1)/212915592407Lelio R Paula04/2015
35502^306915+187337392391Enzo Doria06/2016
35512^306908+1291592389Lelio R Paula02/2016
355219^72244-8092383Lelio R Paula06/2016
35532^306849+7592371Lelio R Paula11/2012
35542^306813-86968810592360Lelio R Paula08/2016
35552^306672-10905992318Enzo Doria04/2014
35566^118604-1706392292Enzo Doria02/2013
3557(31*2^306487-1)/229192260Lelio R Paula02/2014
35582^306467-183561192256Enzo Doria04/2015
35592^306433+7642792246Enzo Doria05/2016
35602^306430-11331392245Enzo Doria07/2014
3561(23*10^92244-59)/992245Robert Price03/2017
3562(47*2^306398+1)/138480392231Lelio R Paula04/2015
3563(25*10^92186+59)/392187Robert Price05/2016
35642^306213-28618392180Enzo Doria06/2015
356510^92178+6192179Robert Price04/2011
356610^92178-17550992178Patrick De Geest07/2013
35672^306200+118592176Lelio R Paula02/2016
35682^306153+1192162Lelio R Paula11/2012
3569(2^306141-7)/592157Lelio R Paula06/2013
3570(26*10^92152-23)/392153Robert Price08/2016
35714*10^92099+3*7^9209992100Mike Oakes12/2010
3572(2^305867-2^152934+1)/59207511/2006
35732^305851-10949592071Enzo Doria04/2014
357412^85300+3592055Lelio R Paula06/2016
35753^192911+9292042Lelio R Paula04/2016
35762^305723-27627192032Enzo Doria07/2015
35772^305676+9392018Donovan Johnson06/2008
35783^192819+491999Lelio R Paula04/2013
3579(38*10^91997-83)/9991997Ray Chandler07/2011
35802^305539+7291191977Enzo Doria04/2016
3581(2^305427-5)/129799821391934Lelio R Paula06/2013
358285^47642+8491922Norbert Schneider10/2015
358310^91920+18765191921Patrick De Geest07/2013
358410^91920-3991920Robert Price05/2011
3585(22*10^91903+41)/991904Robert Price02/2015
35872^305275-2791897Lelio R Paula11/2012
35863^192607-772691897Enzo Doria05/2014
3588(7*10^91856-61)/991856Erik Branger12/2009
3589(89*10^91839-53)/991840Robert Price11/2015
35908*5^131351+791812Lelio R Paula10/2014
35913^192426-6891811Lelio R Paula04/2016
35922^304973+11791807Lelio R Paula11/2012
35932^304939-186372791796Enzo Doria03/2016
35942^304902+841591785Lelio R Paula02/2016
359518^73119+6191785Lelio R Paula06/2016
3596(78557*2^304740+1)/15991739Lelio R Paula06/2014
35972^304747+7135591738Lelio R Paula02/2016
35988*3^192251+591728Lelio R Paula08/2014
35992^304674-8791717Lelio R Paula11/2012
3600(2^304698+9)/136280995391715Lelio R Paula06/2013
3601(5*10^91707-119)/391708Robert Price04/2016
36022^304633-11277191704Enzo Doria06/2014
36032^304578-1671391688Enzo Doria05/2013
36046^117824-1871391685Enzo Doria03/2013
3605(17^74509-1)/1691679Paul Bourdelais03/2010
3606(2^304551-7)/891223191673Lelio R Paula06/2013
3607(2^304532-3)/301391670Lelio R Paula06/2013
36082^304507-1664591666Enzo Doria04/2013
3609(29*2^304489+1)/3191661Lelio R Paula09/2013
36102^304471-183612791655Enzo Doria04/2015
36112^304433+3276991644Lelio R Paula02/2016
36122^304410-1662591637Enzo Doria04/2013
36134*5^131052+791603Lelio R Paula10/2014
36142^304272-186637791595Enzo Doria03/2016
36152^304268+1968391594Lelio R Paula02/2016
36162^304162-16191562Lelio R Paula11/2012
36175*7^108331+691552Lelio R Paula10/2014
36182^304082-278782191538Enzo Doria03/2016
36192^304015+6413391518David Broadhurst06/2002
3620(7*2^303963+1)/391503Lelio R Paula09/2013
3621(2^303945-9)/361791494Lelio R Paula06/2013
36222^303930+188052791493Enzo Doria10/2016
36233^191684-6891457Lelio R Paula04/2016
3624(21*2^303813-1)/16991456Lelio R Paula02/2014
362511^87797-12091432Enzo Doria07/2012
36262^303698-184723191423Enzo Doria07/2015
3627(38^28933-1)^2-291416Norbert Schneider06/2016
36282^303554+7729991379Enzo Doria05/2016
36292^303542+1270591376Lelio R Paula02/2016
363031^61269-291375Lelio R Paula09/2013
36312^303516-6487591368Lelio R Paula02/2016
3632(24737*2^303428+1)/391345Lelio R Paula06/2014
3633(21181*2^303357+1)/3236191320Lelio R Paula06/2014
36342^303344-278696991316Enzo Doria03/2016
36356^117346+6591313Lelio R Paula05/2016
36362^303321+85591309Lelio R Paula02/2016
363712^84606+4791306Lelio R Paula06/2016
36382^303288+187431191299Enzo Doria06/2016
363911^87663-171091292Enzo Doria12/2012
36402^303224+253391280Henri Lifchitz05/2005
36416^117302+14391279Lelio R Paula05/2016
36423^191306-11288091277Enzo Doria07/2014
36432^303207+1291591275Lelio R Paula02/2016
36442^303191-11125991270Enzo Doria05/2014
364510^91230+9^(91230+1)91231Robert Price08/2016
364610^91230+792191231Patrick De Geest11/2016
364710^91230-91114191230Patrick De Geest11/2016
36486^117232-1742391225Enzo Doria02/2013
36497*10^91215+391216Erik Branger11/2009
365097*10^91205-391207Robert Price01/2017
36512^302979-16118191206Enzo Doria04/2013
36522^302949+8191197Henri Lifchitz02/2007
36534*6^117192-591194Lelio R Paula10/2014
36542^302918+9991188Lelio R Paula11/2012
36552^302797+186958791151Enzo Doria05/2016
3656265^37614+37614^26591148Norbert Schneider01/2015
36577^107852+8291146Lelio R Paula04/2016
3658(38*10^91144-11)/991145Robert Price05/2015
3659249^38030+38030^24991128Norbert Schneider01/2015
36606^117094-21104991117Mike Oakes05/2011
36612^302602-186718191093Enzo Doria03/2016
3662(1017*2^302592-1)/5391091Lelio R Paula04/2015
366315^77445-1691083Lelio R Paula07/2016
36642^302505+8191064Henri Lifchitz02/2007
36652^302496-11234991061Enzo Doria06/2014
366617^73999-7291052Lelio R Paula07/2016
36672^302332+57729457591012Lelio R Paula08/2016
36682^302274+7420990994Enzo Doria04/2016
3669(3^190668+2)/8990970Lelio R Paula04/2013
36702^302188+9019590968Lelio R Paula02/2016
3671(53*10^90965-71)/990966Robert Price09/2015
36722^302113+7410590946Enzo Doria04/2016
36732^302102-655590942Lelio R Paula02/2016
3674156*(10^(4*22731)-1)/101-190925Robert Price05/2014
36753^190568+3890925Lelio R Paula04/2016
36762^302009-1644990914Enzo Doria04/2013
3677(17*2^301951-1)/16590896Lelio R Paula02/2014
36783^190497+7490891Lelio R Paula04/2016
3679(24737*2^301896+1)/39990882Lelio R Paula06/2014
368018^72397+8990878Lelio R Paula06/2016
36816^116769-4790864Lelio R Paula05/2016
36822^301712-46590825Lelio R Paula02/2016
36832^301693-6990819Lelio R Paula11/2012
36842^301683-301683^290816Henri Lifchitz05/2005
368511^87187-171090796Enzo Doria12/2012
36865*10^90793+2190794Robert Price01/2017
3687(22*10^90792-13)/990793Robert Price03/2015
36882^301591-161590788Lelio R Paula02/2016
36892^301546-10903790775Enzo Doria04/2014
369014^79195-390768Lelio R Paula06/2016
36912^301517-186169390766Enzo Doria11/2015
36922^301460-17390749Lelio R Paula11/2012
36932^301312-8990704Lelio R Paula11/2012
36942^301285-12990696Lelio R Paula11/2012
36952^301282-10999190695Enzo Doria04/2014
36962^301228-185426990679Enzo Doria09/2015
3697(151*10^90669-1)/390671Robert Price04/2017
3698(32*10^90669+13)/990670Robert Price04/2015
36993*5^129698+890656Lelio R Paula10/2014
3700F(433781)90655Henri Lifchitz09/2003
370119^70891+8290653Lelio R Paula06/2016
3702(29*2^301124-1)/1390648Lelio R Paula02/2014
37037*3^189953-890632Lelio R Paula08/2014
370411^87022-180090625Enzo Doria12/2012
3705(2^301042+47)/1203696990616Lelio R Paula06/2013
37062^301004-278693990612Enzo Doria03/2016
37072^300980-2790605Lelio R Paula11/2012
37082*10^90597-790598Dmitry Domanov11/2010
3709197^39485+290597Lelio R Paula06/2013
37107^107198+4890593Lelio R Paula04/2016
3711(86*10^90588+121)/990589Robert Price03/2017
37122^300923+5390587Lelio R Paula11/2012
37132^300874+790573Lelio R Paula10/2012
37145^129568-5690565Lelio R Paula04/2016
37152^300847-11283190564Enzo Doria06/2014
37162^300718+25525590526Lelio R Paula02/2016
37172^300637+9590501Lelio R Paula11/2012
37187^107087-2490500Lelio R Paula04/2016
3720(10^90499+3^90499)/1390498Robert Price01/2013
371913^81241+9090498Lelio R Paula06/2016
37216^116273-8590478Lelio R Paula05/2016
37226^116256-1757390465Enzo Doria02/2013
37232^300502+5461590461Lelio R Paula02/2016
3724(13*2^300487+1)/4590456Lelio R Paula09/2013
3725(3^189545-8)/590436Lelio R Paula01/2013
3726(7*2^300406-1)/390432Lelio R Paula02/2014
37274*5^129332+390400Lelio R Paula10/2014
37282^300249-1624590384Enzo Doria04/2013
3729(7*10^90371-313)/990371Robert Price11/2016
37302*6^116118+790358Lelio R Paula10/2014
3731(24737*2^300101+1)/2590343Lelio R Paula06/2014
37324*10^90334-2190335Robert Price04/2016
37332^300019-11033590315Enzo Doria05/2014
37342^299949-100590294Lelio R Paula11/2013
37352^299868-10961390270Enzo Doria04/2014
37365*2^299799-390250Lelio R Paula08/2014
373713^81008-290239Lelio R Paula09/2013
373864^49957-63^4995790232Robert Price07/2013
373910^90227+5628190228Patrick De Geest06/2016
37422^299725+31590227Lelio R Paula11/2013
374010^90227-100000000190227Robert Price05/2016
374110^90227-6876390227Patrick De Geest06/2016
37435^129082+4890225Lelio R Paula03/2016
37442^299699+19590219Lelio R Paula10/2012
3745(55*10^90211-1)/990212Ray Chandler02/2012
37463^189053+28090202Lelio R Paula04/2016
37472^299639-18790201Lelio R Paula10/2012
37482^299631+18390198Lelio R Paula10/2012
3749(21*2^299611-1)/2990192Lelio R Paula02/2014
37502^299567+11390179Lelio R Paula10/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!