PRP Records

Probable Primes Top 10000

(183432 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 ?
8251(23*2^187174-1)/2071988356340Lelio R Paula01/2014
82522^187125-283356331Yves Minet09/2014
82539*7^66655-456331Lelio R Paula09/2014
825418^44874-9756330Lelio R Paula02/2013
825560*79^29679+1956322Serge Batalov03/2016
82565^80571+5656317Lelio R Paula10/2012
82575^80551-2256303Lelio R Paula10/2012
8258(76*10^56281+41)/956282Robert Price10/2015
8259(88*10^56271-43)/956272Robert Price11/2015
8260(5*10^56256-119)/356257Robert Price04/2016
82611508^17691+17691^150856230Serge Batalov05/2014
82623^117844-5856226Lelio R Paula10/2012
8263(19*10^56224+737)/956225Robert Price10/2017
826495^28427+256221Lelio R Paula05/2013
82652^186713+7681756207Enzo Doria05/2016
826616534^2505+2505^1653456196Hans Havermann06/2016
826714428^7849+7849^1442856195Hans Havermann06/2016
826814898^5909+5909^1489856189Hans Havermann06/2016
826918^44758+9556184Lelio R Paula02/2013
82702^186555-74156159Lelio R Paula05/2011
8271(4*10^56156+173)/356157Robert Price01/2017
8272(3^117708+7)/44789656156Lelio R Paula03/2012
827315711^3752+3752^1571156156Hans Havermann06/2016
8274(23*2^186549-1)/242902556152Lelio R Paula01/2014
8275387^21694+21694^38756138Norbert Schneider08/2014
82762^186422+1723956119Yves Minet01/2010
82772^186418+424242956118Jason Earls10/2008
8278136^26300+13556113Norbert Schneider04/2015
82795*2^186392+956111Lelio R Paula03/2014
828014345^8152+8152^1434556108Hans Havermann07/2016
8281(5*2^186351-1)/3956097Lelio R Paula01/2014
82822^186319-54123756088Paul Bourdelais11/2012
82832*10^56083-4356084Robert Price07/2017
8284(16*10^56082-61)/956083Serge Batalov05/2009
8285(14*10^56080-143)/356081Robert Price01/2017
8286(265*10^56076+17)/356078Robert Price05/2016
82877^66346-5056069Lelio R Paula10/2012
828820^43094-3356067Lelio R Paula02/2013
828920^43090-138356062Enzo Doria03/2013
82903^117482+266056054Lelio R Paula10/2012
8291(22699*2^186193+1)/11156052Lelio R Paula05/2014
8292(68*10^56042+13)/956043Ray Chandler09/2010
82933*6^71992+5^7199256022Mike Oakes03/2010
829413691^12352+12352^1369156020Hans Havermann07/2016
8295(2^186095+7)/7556019Lelio R Paula02/2012
8296247^23412+23412^24756018Norbert Schneider08/2014
82971839^17156+17156^183956008Serge Batalov05/2014
829813736^11949+11949^1373656007Hans Havermann04/2016
8299(5*2^186036-1)/1156003Lelio R Paula01/2014
8300(299*10^55998-17)/356000Robert Price01/2017
8301p(12103)#/2-12855994Robert Price05/2017
83022^186003-17433755993Gary Barnes09/2009
8303(2^186010+78557)/12355993Lelio R Paula05/2012
830420^43037-9355993Lelio R Paula02/2013
830516375^2626+2626^1637555991Hans Havermann03/2016
830615631^3816+3816^1563155985Hans Havermann03/2016
830721^42335-255977Lelio R Paula08/2013
8308Phi(64736,139)55959Enzo Doria07/2012
830915215^4762+4762^1521555958Hans Havermann03/2016
831019317^788+788^1931755953Anatoly F. Selevich12/2006
831113582^13165+13165^1358255950Hans Havermann08/2016
8312(78557*2^185842+1)/18955947Lelio R Paula06/2014
831315^47562-8655938Lelio R Paula02/2013
83143^117222+455930Lelio R Paula03/2012
831524^40519-23^4051955925Robert Price07/2012
831613636^12623+12623^1363655924Hans Havermann07/2016
83172^185767-9955922Lelio R Paula03/2011
8318(19*2^185750-1)/1555917Lelio R Paula01/2014
831915^47542-5855914Lelio R Paula02/2013
832052211!4+255914Robert Price08/2017
832120^42973-558355910Enzo Doria03/2013
83224*10^55906+2155907Robert Price08/2016
83232^185713-11155906Lelio R Paula03/2011
832413^50174+8855891Lelio R Paula01/2013
832514569^6846+6846^1456955879Hans Havermann08/2016
8326Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
83273^117087-8055865Lelio R Paula10/2012
8328(7*10^55851-43)/955851Robert Price10/2014
83292^185519-16955847Lelio R Paula03/2011
83307^66074+1055840Lelio R Paula10/2012
8331(19*10^55833-49)/355834Robert Price02/2017
8332(2*10^55834-59)/355834Robert Price05/2017
833312^51732+555829Lelio R Paula01/2013
83343*2^185429+755821Lelio R Paula03/2014
8335(60^31393+1)/6155820Paul Bourdelais08/2017
8336(9787*2^185420-1)/38155819Lelio R Paula04/2015
833714427^7396+7396^1442755819Hans Havermann08/2016
833810^55811+2155812Robert Price01/2011
833910^55811-7410355811Patrick De Geest12/2012
834011^53591-153055810Enzo Doria11/2012
8341(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
83422^185355-214555798Lelio R Paula03/2011
834314531^6912+6912^1453155794Hans Havermann07/2016
83442^185327-161555789Lelio R Paula03/2011
83452^185280-1277955775Enzo Doria10/2012
834615504^3955+3955^1550455771Hans Havermann07/2016
8347(2*10^55762-59)/355762Robert Price05/2017
83485^79770-4455757Lelio R Paula10/2012
834918^44416-8555755Lelio R Paula02/2013
83502^185208-45999555754Enzo Doria06/2015
83512^185200+118555751Lelio R Paula03/2011
83527^65964+6^(65964-1)55747Robert Price03/2016
83532^185151-23715755737Gary Barnes09/2009
8354110017^11055-10255734Enzo Doria07/2012
835514754^5987+5987^1475455729Hans Havermann07/2016
835640090!3-955711Robert Price09/2014
83579*10^55707+8955708Robert Price11/2016
83582^185023-225755698Yves Minet06/2009
835918628^977+977^1862855696Anatoly F. Selevich01/2007
83602^185006-9355693Lelio R Paula03/2011
83612^185003-251555692Yves Minet07/2014
83626^71524-1955657Lelio R Paula10/2012
83632^184872-219555653Yves Minet08/2013
8364507^20572+20572^50755648Norbert Schneider06/2016
8365134^26151-13355626Norbert Schneider03/2015
836615340^4221+4221^1534055614Hans Havermann07/2016
836727743!2+255612Robert Price01/2013
836820^42744+8155612Lelio R Paula02/2013
836914609^6406+6406^1460955611Hans Havermann07/2016
83702^184724-11288355608Enzo Doria06/2014
837113507^13074+13074^1350755601Hans Havermann07/2016
83722^184689+12955597Lelio R Paula03/2011
8373(9179*2^184672-1)/19355594Lelio R Paula03/2015
8374(22*10^55592-19)/355593Robert Price02/2017
8375Phi(59984,89)55582Enzo Doria05/2012
837611^53368+1655578Lelio R Paula01/2013
837720^42717-192355577Enzo Doria03/2013
8378117^26870+26870^11755573Serge Batalov05/2014
837912^51488+5555565Lelio R Paula01/2013
8381(44*10^55558-17)/955559Robert Price06/2015
8380(2*10^55559-23)/355559Robert Price09/2017
838210^55555+3285755556Patrick De Geest06/2010
838310^55555-13672155555Patrick De Geest06/2010
8384(11*2^184541-1)/35155551Lelio R Paula01/2014
838520^42696-204355549Enzo Doria03/2013
8386(2*10^55544+1)/355544Serge Batalov06/2009
8387(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
83885003^15013-16055537Enzo Doria07/2012
838939^34896-255522Lelio R Paula08/2013
8390(6^71345-61)/555517Lelio R Paula05/2014
83912^184407-301955513Yves Minet10/2014
8392(43*10^55512-61)/955513Robert Price06/2015
839320^42667-84355512Enzo Doria03/2013
8394133^26134-13255505Norbert Schneider03/2015
8395(31*2^184378-1)/71155502Lelio R Paula01/2014
83969*7^65667-455497Lelio R Paula09/2014
83972^184342-17355493Lelio R Paula03/2011
839815^47182+9255491Lelio R Paula02/2013
83995^79378+655483Lelio R Paula10/2012
8400581^20068+20068^58155472Norbert Schneider06/2016
8401(2^184232+1)/25755457Donovan Johnson03/2005
840218^44177-141555455Enzo Doria03/2013
84032^184203-279786755451Enzo Doria04/2016
84042^184189+1755447Lelio R Paula03/2011
84052^184183+2612355445Yves Minet01/2010
8406Phi(77077,10)55441Ray Chandler05/2009
84072^184141-11325155432Enzo Doria07/2014
84082^184093-50461355418Gary Barnes09/2009
8409(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
84102^184044-11126955403Enzo Doria05/2014
841114051^8766+8766^1405155401Hans Havermann07/2016
841298^27819+27819^9855394Serge Batalov05/2014
8413(178*10^55390-7)/955392Robert Price08/2017
841458046^9+9^5804655390Andrey Kulsha02/2004
84157^65536+2*59232-255385Jiahao He07/2017
84162^183980+7524155384Enzo Doria04/2016
841710^55372+3755373Robert Price01/2011
841810^55372-4996755372Patrick De Geest12/2012
8419(13*10^55367+17)/355368Robert Price06/2015
84202*6^71150+755366Lelio R Paula09/2014
842119^43296-6255365Lelio R Paula02/2013
842219^43295+1055364Lelio R Paula02/2013
8423(29*10^55362-11)/955363Robert Price04/2015
8424(37*10^55359+53)/955360Robert Price05/2015
842519^43283+7255349Lelio R Paula02/2013
84262^183800-6555330Lelio R Paula03/2011
842721001^12801-11055329Enzo Doria07/2012
842833^36433-32^3643355325Robert Price04/2012
8429(17*2^183729+1)/14555308Lelio R Paula07/2012
84309^57952+8^(57952-1)55301Robert Price03/2016
843114872^5229+5229^1487255301Hans Havermann08/2016
843261^30972-255296Lelio R Paula08/2013
84332^183671-11253755291Enzo Doria06/2014
8434(2^183687+7)/49793974555287Lelio R Paula02/2012
84353^115873+5655286Lelio R Paula10/2012
843613^49629-8455284Lelio R Paula01/2013
84372^183632-555279Henri Lifchitz08/2005
843813981^8988+8988^1398155277Hans Havermann07/2016
8439(5*2^183585+1)/1355265Lelio R Paula07/2012
84402^183576+17155262Lelio R Paula03/2011
844113^49604+8255257Lelio R Paula01/2013
8442(11*10^55254+1)/355255Erik Branger03/2014
84433^115802-2655252Lelio R Paula10/2012
84442^183534-364555250Lelio R Paula01/2011
8445(15*2^183533-1)/11355249Lelio R Paula01/2014
84465^79032-1376655241Enzo Doria02/2013
84478*3^115759-755232Lelio R Paula03/2014
84486^70974-13755229Lelio R Paula10/2012
84492^183446-11307355223Enzo Doria07/2014
84502^183441+57729457555222Lelio R Paula03/2013
84515^79000-655219Lelio R Paula10/2012
84522^183413-90155213Yves Minet01/2012
845319^43168-5055202Lelio R Paula02/2013
84542^183340+1968355191Lelio R Paula02/2012
84556^70923+3555189Lelio R Paula10/2012
84562^183317-403555184Lelio R Paula01/2011
84572^183284-1555174Lelio R Paula03/2011
84582^183255+14955166Lelio R Paula02/2011
84594*10^55165+8755166Robert Price05/2016
8460(3^115574+4)/6303755139Lelio R Paula03/2012
84612^183165-11233355139Enzo Doria06/2014
8462(109^27061-1)/10855133Richard Fischer09/2017
84632^183142+85555132Lelio R Paula01/2011
8464(49*10^55129+383)/955130Robert Price04/2017
84652^183019+25525555095Lelio R Paula01/2011
8466(10^55084-19)/955084Robert Price10/2017
84673*10^55077+755078Erik Branger11/2013
8468(62*10^55075-71)/955076Robert Price09/2015
846927499!2-3255070Robert Price10/2015
847015307^3958+3958^1530755067Hans Havermann08/2016
847170^29836-6955051Norbert Schneider10/2012
847218^43854-8355049Lelio R Paula02/2013
84737^65126+5855038Lelio R Paula10/2012
84742^182827-161555037Lelio R Paula11/2009
84757*10^55030-955031Dmitry Domanov11/2010
84766^70702+2355017Lelio R Paula10/2012
8477(23*2^182753+1)/15155014Lelio R Paula07/2012
84782^182743-161555012Lelio R Paula11/2009
8479(24737*2^182736+1)/39955011Lelio R Paula05/2014
84803^115280-956855003Enzo Doria02/2013
84812^182656-1284954985Enzo Doria10/2012
84829*19^42995+1654981Curtis Bright05/2015
84832^182627+2842554977Lelio R Paula11/2009
84842^182597-11305354968Enzo Doria07/2014
8485(3^115213+2)/3090672554964Lelio R Paula03/2012
84862^182581-197554963Yves Minet09/2012
848727449!!-1654959Robert Price06/2015
8488(22*10^54958-73)/354959Robert Price09/2017
84904^91283-3^9128354958Jean-Louis Charton01/2004
84892^182565+10754958Lelio R Paula11/2009
84912^182560+205354957Lelio R Paula12/2010
84922^182451-18245154924Henri Lifchitz10/2004
84932^182444+8154922Henri Lifchitz10/2005
84942^182433+7410554918Enzo Doria04/2016
849520^42206-524354912Enzo Doria03/2013
84962^182394+8554907Lelio R Paula02/2011
84972^182374-11228754901Enzo Doria06/2014
8498(47^32833-33^32833)/1454899Serge Batalov12/2016
84992^182363-11316754897Enzo Doria07/2014
85002^182359-11222154896Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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