PRP Records

Probable Primes Top 10000

(172142 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 ?
20012^372950+7112270Lelio R Paula03/2013
20022^372945+1872167112268Enzo Doria05/2016
20032^372695+72113112193Enzo Doria04/2016
20042^372689-2563112191Yves Minet07/2014
20052^372638-1859441112176Enzo Doria03/2016
20063^235074-113056112159Enzo Doria07/2014
2007(91*10^112098-1)/9112100Robert Price04/2015
20082^372310-85061112077Paul Bourdelais02/2012
2009(10^112067+53)/9112067Serge Batalov07/2015
201075^59760+2112054Lelio R Paula08/2013
20112^372108+74221112016Enzo Doria04/2016
20122^371970-459491111975Enzo Doria05/2015
201341^69427-40^69427111971Robert Price07/2012
2014(10^111902+71)/9111902Serge Batalov07/2015
20152^371440-112865111815Enzo Doria06/2014
20162^371426-459161111811Enzo Doria05/2015
20172^371276-461267111766Enzo Doria07/2015
20182^371098-113261111712Enzo Doria07/2014
2019(7*10^111706-61)/9111706Erik Branger01/2011
20202^371044+1869391111696Enzo Doria05/2016
202188^57416+87111645Norbert Schneider11/2015
20222^370829-109693111631Enzo Doria04/2014
202315^94906-2111619Lelio R Paula11/2013
20242^370643-37111575Yves Minet01/2012
2025(2^370655-5)/2439111575Lelio R Paula03/2014
2026286^45405+45405^286111532Norbert Schneider04/2015
20274*5^159563-9111531Lelio R Paula11/2014
20282^370393-2797093111500Enzo Doria03/2016
2029(21*2^370382-1)/629111495Lelio R Paula03/2014
20302^370292-2791979111469Enzo Doria03/2016
20312^370177-461551111435Enzo Doria07/2015
2032109^54683-108111413Norbert Schneider02/2017
2033numbpart(10^10+76282)111391Serge Batalov04/2015
20342^369974+733111374Lelio R Paula05/2013
20352^369915-286267111356Enzo Doria07/2015
20367*10^111325+3111326Robert Price08/2015
203751^65176+2111293Lelio R Paula08/2013
20382^369643-1865767111274Enzo Doria03/2016
2039L(532277)111240Renaud Lifchitz03/2004
20402^369354-3413111187Yves Minet12/2016
20412^369296-27111170Lelio R Paula02/2013
20422^369239-109837111153Enzo Doria05/2014
20432^369224-291839111148Enzo Doria07/2015
20442^369216+2798881111146Enzo Doria04/2016
204510^111111+163849111112Patrick De Geest03/2017
204610^111111-312911111111Patrick De Geest03/2017
20472^369092-216923111108Enzo Doria05/2014
20482^369081-55111105Lelio R Paula02/2013
204988^57124-87111077Norbert Schneider11/2015
20502^368980+753111075Lelio R Paula05/2013
20512^368946-3623111064Yves Minet03/2017
20524^184463-3^184463111058Jean-Louis Charton12/2004
2053(4*10^111032-7)/3111033Ray Chandler04/2011
20542^368641-460303110972Enzo Doria06/2015
20552^368619-109087110966Enzo Doria04/2014
20563*2^368489+7110927Lelio R Paula09/2014
2057(9179*2^368330-1)/35110881Lelio R Paula05/2015
2058(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
20592^368048+25110794Lelio R Paula02/2013
206069^60239-2110771Lelio R Paula10/2013
2061(23*2^367952+1)/15717110762Lelio R Paula03/2014
20622^367924-69110757Lelio R Paula02/2013
20632^367709-109723110692Enzo Doria04/2014
2064(3*2^367644-1)/107110671Lelio R Paula03/2014
2065(23*2^367398+1)/57963110595Lelio R Paula03/2014
20662^367215+1879223110543Enzo Doria09/2016
20672^367141+41110521Lelio R Paula02/2013
2068(31*2^366976+1)/7110472Lelio R Paula03/2014
2069(21181*2^366833+1)/3110432Lelio R Paula07/2014
20702^366775-2787037110411Enzo Doria03/2016
2071(112*10^110405-1)/3110407Serge Batalov12/2014
20722^366751+2797553110404Enzo Doria03/2016
20732^366738-2985110400Yves Minet09/2014
2074(23*2^366739+1)/74575110396Lelio R Paula03/2014
20752^366716+1871791110393Enzo Doria05/2016
20762^366649+1871687110373Enzo Doria05/2016
20772^366629-351205110367Enzo Doria06/2015
20782^366558+1874479110345Enzo Doria06/2016
207918^87853-4409110280Enzo Doria03/2013
20802^366218-23110243Lelio R Paula02/2013
2081(21*2^366193-1)/197110235Lelio R Paula03/2014
20822^366178-343991110231Enzo Doria07/2015
20832^365944+1871341110161Enzo Doria05/2016
20842^365838-461267110129Enzo Doria07/2015
2085(2^365689+2^182845+1)/511008311/2006
20862^365666-459161110077Enzo Doria05/2015
20873*10^110076-7110077Robert Price08/2015
208813^98785-72110041Lelio R Paula03/2017
2089(25^78707+1)/26110027Robert Price06/2013
20906^141361-7110001Lelio R Paula11/2014
209120^84536+81109984Lelio R Paula03/2017
20925*2^365347-9109982Lelio R Paula09/2014
20939*6^141303+7109957Lelio R Paula11/2014
209478^58099+77109929Norbert Schneider02/2015
20952*10^109928-7109929Robert Price10/2015
2096(27*2^365137-1)/2021109916Lelio R Paula03/2014
2097(4441*29^75152-24)/7109905Curtis Bright05/2015
2098(2^365087+7)/6015109899Lelio R Paula01/2014
20992^364982-5109871Henri Lifchitz04/2006
21002^364936-1867979109857Enzo Doria04/2016
21012^364867-112087109836Enzo Doria06/2014
21024^182415-85061109825Mike Oakes06/2011
2103(17^89227+16^89227)/33109788Robert Price08/2013
21042^364687-187109782Lelio R Paula01/2012
21052^364644+67109769Lelio R Paula01/2012
2106(9787*2^364625-1)/24947109763Lelio R Paula05/2015
2107(2^364616+5)/9109760Lelio R Paula01/2014
210813^98518-66109744Lelio R Paula03/2017
21092^364478-113261109719Enzo Doria07/2014
2110(24737*2^364454+1)/3109716Lelio R Paula07/2014
2111(62*10^109673+1)/9109674Serge Batalov11/2010
21122^364169-112813109626Enzo Doria06/2014
211310^109615+21109616Lelio R Paula03/2017
21142^364094-113109604Lelio R Paula01/2012
2115(4^182026+11)/3109591Robert Price02/2017
21162^364041-6883109588Lelio R Paula09/2011
21172^363842-2787101109528Enzo Doria03/2016
2118(22699*2^363782+1)/763109511Lelio R Paula07/2014
2119(31*2^363748+1)/49109499Lelio R Paula03/2014
2120p(22245)#/2-8109462Robert Price01/2017
21212^363556+55109442Lelio R Paula01/2012
2122(55459*2^363411+1)/81109401Lelio R Paula07/2014
21232^363406+1871569109397Enzo Doria05/2016
2124(2^363349+7)/9109378Lelio R Paula01/2014
21252^363191-112321109332Enzo Doria06/2014
21262^363120+3109311Donovan Johnson04/2006
2127(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
21282^363042-114641109287Enzo Doria04/2015
21292^363020-112793109280Enzo Doria06/2014
2130(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2131(9*2^362644+1)/5109167Lelio R Paula03/2014
21325^156181+38109166Lelio R Paula02/2017
2133(10223*2^362376+1)/9109090Lelio R Paula07/2014
213465^60167-64^60167109078Robert Price08/2013
21357*3^228589-2109066Lelio R Paula09/2014
2136(78557*2^362188+1)/189109033Lelio R Paula07/2014
21372*7^129008+9109025Lelio R Paula11/2014
21382^361957+76367108960Enzo Doria05/2016
21392^361873-1411108935Yves Minet01/2013
2140(24737*2^361857+1)/35108933Lelio R Paula07/2014
214113^97745-24108883Lelio R Paula03/2017
21422^361567+51108843Lelio R Paula01/2012
21432^361563-109501108842Enzo Doria04/2014
21442^361497+767108822Lelio R Paula01/2012
21452^361280-112349108757Enzo Doria06/2014
2146(19^85009-5^85009)/14108705Robert Price07/2013
2147(11*2^361027+1)/40463108677Lelio R Paula03/2014
21482^360959-109101108660Enzo Doria04/2014
21496*5^155454+7108659Lelio R Paula11/2014
215010^108656+79108657Lelio R Paula02/2017
21512^360918-35108648Lelio R Paula01/2012
2152(11*2^360886-1)/7108638Lelio R Paula03/2014
21532^360706-458903108584Enzo Doria04/2015
21542^360641-113185108564Enzo Doria07/2014
21552^360618+75019108557Enzo Doria04/2016
21563*5^155286+2108541Lelio R Paula11/2014
21577^128422+4108530Lelio R Paula11/2014
21587^128421-80108529Lelio R Paula03/2017
21592^360497+53807108521Yves Minet07/2010
21602^360366+1459108481Lelio R Paula09/2011
21612^360364-1499108481Yves Minet05/2013
21624*10^108412+9108413Robert Price05/2015
21632^360093-351103108399Enzo Doria06/2015
21642^360042+723108384Lelio R Paula01/2012
216585^56164-2108364Lelio R Paula10/2013
21662^359937-29323108352Enzo Doria07/2015
21672^359898-19997108341Enzo Doria06/2013
21682*5^154948-7108305Lelio R Paula11/2014
216910^108303+13108304Lelio R Paula02/2017
21702^359730+753108290Lelio R Paula12/2011
21712^359650-19797108266Enzo Doria06/2013
217291^55259-90^55259108255Robert Price07/2015
21733^226845+68108233Lelio R Paula03/2017
21745^154822-12866108216Enzo Doria05/2014
2175(9*2^359480+1)/5108215Lelio R Paula03/2014
21762^359454-177108207Lelio R Paula12/2011
21776^139022-59108181Lelio R Paula02/2017
21782^359352-179108176Lelio R Paula12/2011
21792^359338-1858781108172Enzo Doria04/2016
2180(25*2^359297-1)/137108159Lelio R Paula03/2014
2181(2^359262-509203)/9108148Lelio R Paula12/2013
2182(3^226648-8)/352715633108131Lelio R Paula12/2013
21836^138956-59108129Lelio R Paula02/2017
218413^97059+10108119Lelio R Paula03/2017
21852^359137-81108112Lelio R Paula12/2011
2186(15185*2^359105-1)/567108103Lelio R Paula05/2015
21878*6^138875+5108067Lelio R Paula11/2014
21882^358987-216919108066Enzo Doria05/2014
218939^67918-67918^39108062Norbert Schneider02/2017
21902^358785-16933108006Enzo Doria05/2013
2191(2^358783+5)/33383108000Lelio R Paula12/2013
21926^138770-77107985Lelio R Paula02/2017
2193(2^358727-1017)/94178479107980Lelio R Paula12/2013
219410^107976+19107977Lelio R Paula02/2017
21952^358684+75781107975Enzo Doria04/2016
219699^54094+2107952Lelio R Paula06/2013
2197(2^358583-9)/391107942Lelio R Paula12/2013
21982^358538+55107931Lelio R Paula12/2011
21992^358517-109009107925Enzo Doria03/2014
22003^226159+104107906Lelio R Paula03/2017
22012^358275-112987107852Enzo Doria07/2014
22022^358233-20005107839Enzo Doria06/2013
22032^358194+175107828Lelio R Paula12/2011
2204107^53125-106107812Norbert Schneider12/2016
22053^225922-2107793Lelio R Paula10/2013
22062^358030-171107778Lelio R Paula12/2011
220711^103488-4170107772Enzo Doria12/2012
22082^357911-20089107742Enzo Doria06/2013
22092^357885+12857107735Yves Minet07/2010
22107^127473+40107728Lelio R Paula03/2017
22115*2^357850+9107725Lelio R Paula09/2014
22122^357786-291191107705Enzo Doria06/2015
22132^357688-1854269107675Enzo Doria09/2015
22142^357671-112225107670Enzo Doria06/2014
22152^357618-21005107654Enzo Doria06/2013
22162^357615-17505107653Enzo Doria05/2013
2217(30^72871-1)/29107638Robert Price12/2011
22182^357521+1870217107625Enzo Doria05/2016
22195^153894-18107568Lelio R Paula02/2017
22202^357324-69059107566Enzo Doria11/2015
22212^357283-869688105107553Lelio R Paula01/2017
22222^357280-16805107552Enzo Doria05/2013
222310^107547-47107547Lelio R Paula02/2017
22242^357081+107107493Lelio R Paula12/2011
22253^225274+64107484Lelio R Paula03/2017
22263^225248-130107471Lelio R Paula03/2017
2227(5*2^356961+1)/143107455Lelio R Paula03/2014
22282^356935-18085107449Enzo Doria05/2013
222910^107409+37107410Lelio R Paula02/2017
22302^356787-109027107404Enzo Doria04/2014
2231(2^356767+78557)/5107397Lelio R Paula12/2013
22325^153622-42107378Lelio R Paula02/2017
22332^356654+85107364Lelio R Paula11/2011
22342^356641-19921107360Enzo Doria06/2013
223519^83945-92107345Lelio R Paula02/2017
223610^107334-83107334Lelio R Paula02/2017
2237(3*2^356506-1)/467107317Lelio R Paula03/2014
22382^356442-114713107300Enzo Doria04/2015
22392^356425+72257107295Enzo Doria04/2016
22402^356351-112237107273Enzo Doria06/2014
2242(6^137845-11)/5107264Paul Bourdelais11/2011
22412^356322+74539107264Enzo Doria04/2016
22432^356274+1874479107250Enzo Doria06/2016
224420^82422-93107234Lelio R Paula02/2017
22452^356157-20365107214Enzo Doria06/2013
22462^356129-18949107206Enzo Doria05/2013
22472^356100-109587107197Enzo Doria04/2014
2248(31*2^355970+1)/5107159Lelio R Paula03/2014
22492^355968-64875107158Lelio R Paula01/2017
22502^355952+1870321107153Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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