PRP Records

Probable Primes Top 10000

(247113 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 ?
9001(7*2^188215-1)/149731512556651Lelio R Paula01/2014
9002(1017*2^188171-1)/3556647Lelio R Paula03/2015
9003(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
9004(2^188176-1017)/45381454356638Lelio R Paula02/2012
900533*10^56634+756636Robert Price07/2016
9006(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
900714^49413+3356634Lelio R Paula02/2013
90083^118680+11056625Lelio R Paula10/2012
9009(13*10^56624+161)/356625Robert Price04/2017
9010(3^118676-2)/751665326356613Lelio R Paula03/2012
9011(13*2^188062+1)/1756613Lelio R Paula07/2012
90122^188056-131356611Yves Minet08/2012
901320^43510-558356608Enzo Doria03/2013
90142^188032+1228556604Lelio R Paula03/2011
9015(19*10^56597-43)/356598Robert Price10/2017
9016(265*10^56588+17)/356590Robert Price05/2016
90172^187959+577556582Lelio R Paula03/2011
9018(5*2^187959+1)/5356581Lelio R Paula07/2012
90193*10^56575-1356576Robert Price11/2017
9020(11*2^187889-1)/35156559Lelio R Paula01/2014
9021(100049^11311+1)/10005056553Faysal YAtim09/2007
9022(19*10^56544-1)/956545Serge Batalov03/2009
902320^43447-892356526Enzo Doria03/2013
902410423^14066-14066^1042356518Norbert Schneider11/2018
90252^187743-11217756517Enzo Doria06/2014
9026(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
90275^80831-2256499Lelio R Paula10/2012
90285^80828-1316656497Enzo Doria02/2013
90297*2^187590-556472Lelio R Paula03/2014
90302^187555+7547356460Enzo Doria04/2016
90312^187541-28356456Yves Minet01/2012
9033(55*10^56453-1)/956454Serge Batalov03/2009
903212933^13730-13730^1293356454Norbert Schneider09/2018
90342^187506-145156445Yves Minet08/2012
9035189^24794-256443Lelio R Paula10/2017
903613600^13653-13653^1360056436Norbert Schneider08/2018
90376^72522+14356434Lelio R Paula10/2012
9038(15185*2^187452-1)/94956430Lelio R Paula03/2015
90392^187390+7956411Lelio R Paula03/2011
90402^187386+1290956409Lelio R Paula03/2011
90412^187382+61356408Jason Earls04/2008
9042(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
904320^43337-956383Lelio R Paula02/2013
9044(26*10^56371-173)/356372Robert Price10/2017
9045(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
90462^187230+42756362Henri Lifchitz01/2005
904711^54121-948056362Enzo Doria02/2013
904810758^13979-13979^1075856360Norbert Schneider09/2018
904910635^13996-13996^1063556359Norbert Schneider09/2018
9050(21*2^187202-1)/4356354Lelio R Paula01/2014
90512^187173-9156345Lelio R Paula03/2011
9052(23*2^187174-1)/2071988356340Lelio R Paula01/2014
90532^187125-283356331Yves Minet09/2014
90549*7^66655-456331Lelio R Paula09/2014
905518^44874-9756330Lelio R Paula02/2013
905613304^13659-13659^1330456330Norbert Schneider08/2018
905760*79^29679+1956322Serge Batalov03/2016
90585^80571+5656317Lelio R Paula10/2012
90595^80551-2256303Lelio R Paula10/2012
9060(76*10^56281+41)/956282Robert Price10/2015
9061(88*10^56271-43)/956272Robert Price11/2015
9062(5*10^56256-119)/356257Robert Price04/2016
90631508^17691+17691^150856230Serge Batalov05/2014
90643^117844-5856226Lelio R Paula10/2012
9065(19*10^56224+737)/956225Robert Price10/2017
906695^28427+256221Lelio R Paula05/2013
90672^186713+7681756207Enzo Doria05/2016
906816534^2505+2505^1653456196Hans Havermann06/2016
906914428^7849+7849^1442856195Hans Havermann06/2016
90702*10^56194-5156195Robert Price11/2017
907114898^5909+5909^1489856189Hans Havermann06/2016
907218^44758+9556184Lelio R Paula02/2013
90737478^14503-14503^747856182Norbert Schneider11/2018
90742^186555-74156159Lelio R Paula05/2011
9075(4*10^56156+173)/356157Robert Price01/2017
9077(3^117708+7)/44789656156Lelio R Paula03/2012
907615711^3752+3752^1571156156Hans Havermann06/2016
9078(23*2^186549-1)/242902556152Lelio R Paula01/2014
9079387^21694+21694^38756138Norbert Schneider08/2014
90802^186422+1723956119Yves Minet01/2010
90812^186418+424242956118Jason Earls10/2008
9082136^26300+13556113Norbert Schneider04/2015
90835*2^186392+956111Lelio R Paula03/2014
908414345^8152+8152^1434556108Hans Havermann07/2016
9085(5*2^186351-1)/3956097Lelio R Paula01/2014
90862^186319-54123756088Paul Bourdelais11/2012
90872*10^56083-4356084Robert Price07/2017
9088(16*10^56082-61)/956083Serge Batalov05/2009
9089(14*10^56080-143)/356081Robert Price01/2017
9090(265*10^56076+17)/356078Robert Price05/2016
90917^66346-5056069Lelio R Paula10/2012
909220^43094-3356067Lelio R Paula02/2013
909320^43090-138356062Enzo Doria03/2013
90943^117482+266056054Lelio R Paula10/2012
9095(22699*2^186193+1)/11156052Lelio R Paula05/2014
9096(68*10^56042+13)/956043Ray Chandler09/2010
90973*6^71992+5^7199256022Mike Oakes03/2010
909813691^12352+12352^1369156020Hans Havermann07/2016
9099(2^186095+7)/7556019Lelio R Paula02/2012
9100247^23412+23412^24756018Norbert Schneider08/2014
91011839^17156+17156^183956008Serge Batalov05/2014
910213736^11949+11949^1373656007Hans Havermann04/2016
9103(5*2^186036-1)/1156003Lelio R Paula01/2014
9104(299*10^55998-17)/356000Robert Price01/2017
9105p(12103)#/2-12855994Robert Price05/2017
91062^186003-17433755993Gary Barnes09/2009
9107(2^186010+78557)/12355993Lelio R Paula05/2012
910820^43037-9355993Lelio R Paula02/2013
910916375^2626+2626^1637555991Hans Havermann03/2016
911011083^13842-13842^1108355987Norbert Schneider11/2018
911115631^3816+3816^1563155985Hans Havermann03/2016
911221^42335-255977Lelio R Paula08/2013
9113Phi(64736,139)55959Enzo Doria07/2012
911415215^4762+4762^1521555958Hans Havermann03/2016
911519317^788+788^1931755953Anatoly F. Selevich12/2006
911613582^13165+13165^1358255950Hans Havermann08/2016
9117(78557*2^185842+1)/18955947Lelio R Paula06/2014
911811867^13730-13730^1186755941Norbert Schneider09/2018
911915^47562-8655938Lelio R Paula02/2013
91204*10^55932+9155933Robert Price11/2017
91213^117222+455930Lelio R Paula03/2012
912224^40519-23^4051955925Robert Price07/2012
912313636^12623+12623^1363655924Hans Havermann07/2016
91242^185767-9955922Lelio R Paula03/2011
9125(19*2^185750-1)/1555917Lelio R Paula01/2014
912715^47542-5855914Lelio R Paula02/2013
912652211!4+255914Robert Price08/2017
912820^42973-558355910Enzo Doria03/2013
91294*10^55906+2155907Robert Price08/2016
91302^185713-11155906Lelio R Paula03/2011
913113^50174+8855891Lelio R Paula01/2013
913214569^6846+6846^1456955879Hans Havermann08/2016
9133Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
91343^117087-8055865Lelio R Paula10/2012
9135(7*10^55851-43)/955851Robert Price10/2014
91362^185519-16955847Lelio R Paula03/2011
91377^66074+1055840Lelio R Paula10/2012
9138(19*10^55833-49)/355834Robert Price02/2017
9139(2*10^55834-59)/355834Robert Price05/2017
91402^185463-423755830Yves Minet08/2018
914112^51732+555829Lelio R Paula01/2013
914211252^13779-13779^1125255822Norbert Schneider10/2018
91433*2^185429+755821Lelio R Paula03/2014
9144(60^31393+1)/6155820Paul Bourdelais08/2017
9146(9787*2^185420-1)/38155819Lelio R Paula04/2015
914514427^7396+7396^1442755819Hans Havermann08/2016
914710^55811+2155812Robert Price01/2011
914810^55811-7410355811Patrick De Geest12/2012
914911^53591-153055810Enzo Doria11/2012
9150(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
91512^185355-214555798Lelio R Paula03/2011
915214531^6912+6912^1453155794Hans Havermann07/2016
91532^185327-161555789Lelio R Paula03/2011
91542^185280-1277955775Enzo Doria10/2012
915515504^3955+3955^1550455771Hans Havermann07/2016
9156(2*10^55762-59)/355762Robert Price05/2017
91575^79770-4455757Lelio R Paula10/2012
915818^44416-8555755Lelio R Paula02/2013
91592^185208-45999555754Enzo Doria06/2015
91602^185200+118555751Lelio R Paula03/2011
9161(536*10^55748-23)/955750Robert Price11/2017
91627^65964+6^(65964-1)55747Robert Price03/2016
91632^185151-23715755737Gary Barnes09/2009
9164110017^11055-10255734Enzo Doria07/2012
916514754^5987+5987^1475455729Hans Havermann07/2016
916612591^13592-13592^1259155729Norbert Schneider07/2018
916740090!3-955711Robert Price09/2014
91689*10^55707+8955708Robert Price11/2016
91692^185023-225755698Yves Minet06/2009
917018628^977+977^1862855696Anatoly F. Selevich01/2007
91712^185006-9355693Lelio R Paula03/2011
91722^185003-251555692Yves Minet07/2014
91732^184992-7855755689Jorge Menendez02/2018
91743*10^55679+3755680Robert Price10/2017
91756^71524-1955657Lelio R Paula10/2012
91762^184872-219555653Yves Minet08/2013
9177507^20572+20572^50755648Norbert Schneider06/2016
9178(86*10^55645-311)/955646Robert Price10/2017
9179134^26151-13355626Norbert Schneider03/2015
918015340^4221+4221^1534055614Hans Havermann07/2016
918127743!2+255612Robert Price01/2013
918220^42744+8155612Lelio R Paula02/2013
918314609^6406+6406^1460955611Hans Havermann07/2016
91842^184724-11288355608Enzo Doria06/2014
918513507^13074+13074^1350755601Hans Havermann07/2016
91862^184689+12955597Lelio R Paula03/2011
9187(9179*2^184672-1)/19355594Lelio R Paula03/2015
9188(22*10^55592-19)/355593Robert Price02/2017
9189Phi(59984,89)55582Enzo Doria05/2012
91908815^14088-14088^881555581Norbert Schneider11/2018
919111^53368+1655578Lelio R Paula01/2013
919220^42717-192355577Enzo Doria03/2013
9193117^26870+26870^11755573Serge Batalov05/2014
919412^51488+5555565Lelio R Paula01/2013
9196(44*10^55558-17)/955559Robert Price06/2015
9195(2*10^55559-23)/355559Robert Price09/2017
919710^55555+3285755556Patrick De Geest06/2010
919810^55555-13672155555Patrick De Geest06/2010
9199(11*2^184541-1)/35155551Lelio R Paula01/2014
920020^42696-204355549Enzo Doria03/2013
9201(35*10^55547-737)/955548Robert Price11/2017
9202(2*10^55544+1)/355544Serge Batalov06/2009
9203(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
92045003^15013-16055537Enzo Doria07/2012
920539^34896-255522Lelio R Paula08/2013
9206(6^71345-61)/555517Lelio R Paula05/2014
92072^184407-301955513Yves Minet10/2014
9208(43*10^55512-61)/955513Robert Price06/2015
920920^42667-84355512Enzo Doria03/2013
9210133^26134-13255505Norbert Schneider03/2015
9211(31*2^184378-1)/71155502Lelio R Paula01/2014
92129*7^65667-455497Lelio R Paula09/2014
92132^184342-17355493Lelio R Paula03/2011
921415^47182+9255491Lelio R Paula02/2013
92155^79378+655483Lelio R Paula10/2012
9216581^20068+20068^58155472Norbert Schneider06/2016
9217(2^184232+1)/25755457Donovan Johnson03/2005
921818^44177-141555455Enzo Doria03/2013
92192^184203-279786755451Enzo Doria04/2016
92202^184189+1755447Lelio R Paula03/2011
92212^184183+2612355445Yves Minet01/2010
9222Phi(77077,10)55441Ray Chandler05/2009
92232^184141-11325155432Enzo Doria07/2014
92242^184093-50461355418Gary Barnes09/2009
9225(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
92262^184044-11126955403Enzo Doria05/2014
922714051^8766+8766^1405155401Hans Havermann07/2016
922898^27819+27819^9855394Serge Batalov05/2014
9229(178*10^55390-7)/955392Robert Price08/2017
923058046^9+9^5804655390Andrey Kulsha02/2004
92317^65536+2*59232-255385Jiahao He07/2017
92322^183980+7524155384Enzo Doria04/2016
923310^55372+3755373Robert Price01/2011
923410^55372-4996755372Patrick De Geest12/2012
9235(13*10^55367+17)/355368Robert Price06/2015
92362*6^71150+755366Lelio R Paula09/2014
923719^43296-6255365Lelio R Paula02/2013
923819^43295+1055364Lelio R Paula02/2013
9239(29*10^55362-11)/955363Robert Price04/2015
9240(37*10^55359+53)/955360Robert Price05/2015
924119^43283+7255349Lelio R Paula02/2013
92422^183800-6555330Lelio R Paula03/2011
924321001^12801-11055329Enzo Doria07/2012
924433^36433-32^3643355325Robert Price04/2012
9245(17*2^183729+1)/14555308Lelio R Paula07/2012
92469932^13837-13837^993255307Norbert Schneider11/2018
92489^57952+8^(57952-1)55301Robert Price03/2016
924714872^5229+5229^1487255301Hans Havermann08/2016
924961^30972-255296Lelio R Paula08/2013
92502^183671-11253755291Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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