PRP Records

Probable Primes Top 10000

(172213 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 ?
7751(2^188176-1017)/45381454356638Lelio R Paula02/2012
775233*10^56634+756636Robert Price07/2016
7753(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
775414^49413+3356634Lelio R Paula02/2013
77553^118680+11056625Lelio R Paula10/2012
7756(3^118676-2)/751665326356613Lelio R Paula03/2012
7757(13*2^188062+1)/1756613Lelio R Paula07/2012
77582^188056-131356611Yves Minet08/2012
775920^43510-558356608Enzo Doria03/2013
77602^188032+1228556604Lelio R Paula03/2011
7761(265*10^56588+17)/356590Robert Price05/2016
77622^187959+577556582Lelio R Paula03/2011
7763(5*2^187959+1)/5356581Lelio R Paula07/2012
7764(11*2^187889-1)/35156559Lelio R Paula01/2014
7765(100049^11311+1)/10005056553Faysal YAtim09/2007
7766(19*10^56544-1)/956545Serge Batalov03/2009
776720^43447-892356526Enzo Doria03/2013
77682^187743-11217756517Enzo Doria06/2014
7769(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
77705^80831-2256499Lelio R Paula10/2012
77715^80828-1316656497Enzo Doria02/2013
77727*2^187590-556472Lelio R Paula03/2014
77732^187555+7547356460Enzo Doria04/2016
77742^187541-28356456Yves Minet01/2012
7775(55*10^56453-1)/956454Serge Batalov03/2009
77762^187506-145156445Yves Minet08/2012
77776^72522+14356434Lelio R Paula10/2012
7778(15185*2^187452-1)/94956430Lelio R Paula03/2015
77792^187390+7956411Lelio R Paula03/2011
77802^187386+1290956409Lelio R Paula03/2011
77812^187382+61356408Jason Earls04/2008
7782(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
778320^43337-956383Lelio R Paula02/2013
7784(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
77862^187230+42756362Henri Lifchitz01/2005
778511^54121-948056362Enzo Doria02/2013
7787(21*2^187202-1)/4356354Lelio R Paula01/2014
77882^187173-9156345Lelio R Paula03/2011
7789(23*2^187174-1)/2071988356340Lelio R Paula01/2014
77902^187125-283356331Yves Minet09/2014
77919*7^66655-456331Lelio R Paula09/2014
779218^44874-9756330Lelio R Paula02/2013
779360*79^29679+1956322Serge Batalov03/2016
77945^80571+5656317Lelio R Paula10/2012
77955^80551-2256303Lelio R Paula10/2012
7796(76*10^56281+41)/956282Robert Price10/2015
7797(88*10^56271-43)/956272Robert Price11/2015
7798(5*10^56256-119)/356257Robert Price04/2016
77991508^17691+17691^150856230Serge Batalov05/2014
78003^117844-5856226Lelio R Paula10/2012
780195^28427+256221Lelio R Paula05/2013
78022^186713+7681756207Enzo Doria05/2016
780316534^2505+2505^1653456196Hans Havermann06/2016
780414428^7849+7849^1442856195Hans Havermann06/2016
780514898^5909+5909^1489856189Hans Havermann06/2016
780618^44758+9556184Lelio R Paula02/2013
78072^186555-74156159Lelio R Paula05/2011
7808(4*10^56156+173)/356157Robert Price01/2017
7810(3^117708+7)/44789656156Lelio R Paula03/2012
780915711^3752+3752^1571156156Hans Havermann06/2016
7811(23*2^186549-1)/242902556152Lelio R Paula01/2014
7812387^21694+21694^38756138Norbert Schneider08/2014
78132^186422+1723956119Yves Minet01/2010
78142^186418+424242956118Jason Earls10/2008
7815136^26300+13556113Norbert Schneider04/2015
78165*2^186392+956111Lelio R Paula03/2014
781714345^8152+8152^1434556108Hans Havermann07/2016
7818(5*2^186351-1)/3956097Lelio R Paula01/2014
78192^186319-54123756088Paul Bourdelais11/2012
7820(16*10^56082-61)/956083Serge Batalov05/2009
7821(14*10^56080-143)/356081Robert Price01/2017
7822(265*10^56076+17)/356078Robert Price05/2016
78237^66346-5056069Lelio R Paula10/2012
782420^43094-3356067Lelio R Paula02/2013
782520^43090-138356062Enzo Doria03/2013
78263^117482+266056054Lelio R Paula10/2012
7827(22699*2^186193+1)/11156052Lelio R Paula05/2014
7828(68*10^56042+13)/956043Ray Chandler09/2010
78293*6^71992+5^7199256022Mike Oakes03/2010
783013691^12352+12352^1369156020Hans Havermann07/2016
7831(2^186095+7)/7556019Lelio R Paula02/2012
7832247^23412+23412^24756018Norbert Schneider08/2014
78331839^17156+17156^183956008Serge Batalov05/2014
783413736^11949+11949^1373656007Hans Havermann04/2016
7835(5*2^186036-1)/1156003Lelio R Paula01/2014
7836(299*10^55998-17)/356000Robert Price01/2017
78382^186003-17433755993Gary Barnes09/2009
7837(2^186010+78557)/12355993Lelio R Paula05/2012
783920^43037-9355993Lelio R Paula02/2013
784016375^2626+2626^1637555991Hans Havermann03/2016
784115631^3816+3816^1563155985Hans Havermann03/2016
784221^42335-255977Lelio R Paula08/2013
7843Phi(64736,139)55959Enzo Doria07/2012
784415215^4762+4762^1521555958Hans Havermann03/2016
784519317^788+788^1931755953Anatoly F. Selevich12/2006
784613582^13165+13165^1358255950Hans Havermann08/2016
7847(78557*2^185842+1)/18955947Lelio R Paula06/2014
784815^47562-8655938Lelio R Paula02/2013
78493^117222+455930Lelio R Paula03/2012
785024^40519-23^4051955925Robert Price07/2012
785113636^12623+12623^1363655924Hans Havermann07/2016
78522^185767-9955922Lelio R Paula03/2011
7853(19*2^185750-1)/1555917Lelio R Paula01/2014
785415^47542-5855914Lelio R Paula02/2013
785520^42973-558355910Enzo Doria03/2013
78564*10^55906+2155907Robert Price08/2016
78572^185713-11155906Lelio R Paula03/2011
785813^50174+8855891Lelio R Paula01/2013
785914569^6846+6846^1456955879Hans Havermann08/2016
7860Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
78613^117087-8055865Lelio R Paula10/2012
7862(7*10^55851-43)/955851Robert Price10/2014
78632^185519-16955847Lelio R Paula03/2011
78647^66074+1055840Lelio R Paula10/2012
7865(19*10^55833-49)/355834Robert Price02/2017
786612^51732+555829Lelio R Paula01/2013
78673*2^185429+755821Lelio R Paula03/2014
7868(9787*2^185420-1)/38155819Lelio R Paula04/2015
786914427^7396+7396^1442755819Hans Havermann08/2016
787010^55811+2155812Robert Price01/2011
787110^55811-7410355811Patrick De Geest12/2012
787211^53591-153055810Enzo Doria11/2012
78732^185355-214555798Lelio R Paula03/2011
787414531^6912+6912^1453155794Hans Havermann07/2016
78752^185327-161555789Lelio R Paula03/2011
78762^185280-1277955775Enzo Doria10/2012
787715504^3955+3955^1550455771Hans Havermann07/2016
78785^79770-4455757Lelio R Paula10/2012
787918^44416-8555755Lelio R Paula02/2013
78802^185208-45999555754Enzo Doria06/2015
78812^185200+118555751Lelio R Paula03/2011
78827^65964+6^(65964-1)55747Robert Price03/2016
78832^185151-23715755737Gary Barnes09/2009
7884110017^11055-10255734Enzo Doria07/2012
788514754^5987+5987^1475455729Hans Havermann07/2016
788640090!3-955711Robert Price09/2014
78879*10^55707+8955708Robert Price11/2016
78882^185023-225755698Yves Minet06/2009
788918628^977+977^1862855696Anatoly F. Selevich01/2007
78902^185006-9355693Lelio R Paula03/2011
78912^185003-251555692Yves Minet07/2014
78926^71524-1955657Lelio R Paula10/2012
78932^184872-219555653Yves Minet08/2013
7894507^20572+20572^50755648Norbert Schneider06/2016
7895134^26151-13355626Norbert Schneider03/2015
789615340^4221+4221^1534055614Hans Havermann07/2016
789727743!2+255612Robert Price01/2013
789820^42744+8155612Lelio R Paula02/2013
789914609^6406+6406^1460955611Hans Havermann07/2016
79002^184724-11288355608Enzo Doria06/2014
790113507^13074+13074^1350755601Hans Havermann07/2016
79022^184689+12955597Lelio R Paula03/2011
7903(9179*2^184672-1)/19355594Lelio R Paula03/2015
7904(22*10^55592-19)/355593Robert Price02/2017
7905Phi(59984,89)55582Enzo Doria05/2012
790611^53368+1655578Lelio R Paula01/2013
790720^42717-192355577Enzo Doria03/2013
7908117^26870+26870^11755573Serge Batalov05/2014
790912^51488+5555565Lelio R Paula01/2013
7910(44*10^55558-17)/955559Robert Price06/2015
791110^55555+3285755556Patrick De Geest06/2010
791210^55555-13672155555Patrick De Geest06/2010
7913(11*2^184541-1)/35155551Lelio R Paula01/2014
791420^42696-204355549Enzo Doria03/2013
7915(2*10^55544+1)/355544Serge Batalov06/2009
79165003^15013-16055537Enzo Doria07/2012
791739^34896-255522Lelio R Paula08/2013
7918(6^71345-61)/555517Lelio R Paula05/2014
79192^184407-301955513Yves Minet10/2014
7920(43*10^55512-61)/955513Robert Price06/2015
792120^42667-84355512Enzo Doria03/2013
7922133^26134-13255505Norbert Schneider03/2015
7923(31*2^184378-1)/71155502Lelio R Paula01/2014
79249*7^65667-455497Lelio R Paula09/2014
79252^184342-17355493Lelio R Paula03/2011
792615^47182+9255491Lelio R Paula02/2013
79275^79378+655483Lelio R Paula10/2012
7928581^20068+20068^58155472Norbert Schneider06/2016
7929(2^184232+1)/25755457Donovan Johnson03/2005
793018^44177-141555455Enzo Doria03/2013
79312^184203-279786755451Enzo Doria04/2016
79322^184189+1755447Lelio R Paula03/2011
79332^184183+2612355445Yves Minet01/2010
7934Phi(77077,10)55441Ray Chandler05/2009
79352^184141-11325155432Enzo Doria07/2014
79362^184093-50461355418Gary Barnes09/2009
79372^184044-11126955403Enzo Doria05/2014
793814051^8766+8766^1405155401Hans Havermann07/2016
793998^27819+27819^9855394Serge Batalov05/2014
794058046^9+9^5804655390Andrey Kulsha02/2004
79412^183980+7524155384Enzo Doria04/2016
794210^55372+3755373Robert Price01/2011
794310^55372-4996755372Patrick De Geest12/2012
7944(13*10^55367+17)/355368Robert Price06/2015
79452*6^71150+755366Lelio R Paula09/2014
794619^43296-6255365Lelio R Paula02/2013
794719^43295+1055364Lelio R Paula02/2013
7948(29*10^55362-11)/955363Robert Price04/2015
7949(37*10^55359+53)/955360Robert Price05/2015
795019^43283+7255349Lelio R Paula02/2013
79512^183800-6555330Lelio R Paula03/2011
795221001^12801-11055329Enzo Doria07/2012
795333^36433-32^3643355325Robert Price04/2012
7954(17*2^183729+1)/14555308Lelio R Paula07/2012
79569^57952+8^(57952-1)55301Robert Price03/2016
795514872^5229+5229^1487255301Hans Havermann08/2016
795761^30972-255296Lelio R Paula08/2013
79582^183671-11253755291Enzo Doria06/2014
7959(2^183687+7)/49793974555287Lelio R Paula02/2012
79603^115873+5655286Lelio R Paula10/2012
796113^49629-8455284Lelio R Paula01/2013
79622^183632-555279Henri Lifchitz08/2005
796313981^8988+8988^1398155277Hans Havermann07/2016
7964(5*2^183585+1)/1355265Lelio R Paula07/2012
79652^183576+17155262Lelio R Paula03/2011
796613^49604+8255257Lelio R Paula01/2013
7967(11*10^55254+1)/355255Erik Branger03/2014
79683^115802-2655252Lelio R Paula10/2012
79692^183534-364555250Lelio R Paula01/2011
7970(15*2^183533-1)/11355249Lelio R Paula01/2014
79715^79032-1376655241Enzo Doria02/2013
79728*3^115759-755232Lelio R Paula03/2014
79736^70974-13755229Lelio R Paula10/2012
79742^183446-11307355223Enzo Doria07/2014
79752^183441+57729457555222Lelio R Paula03/2013
79765^79000-655219Lelio R Paula10/2012
79772^183413-90155213Yves Minet01/2012
797819^43168-5055202Lelio R Paula02/2013
79792^183340+1968355191Lelio R Paula02/2012
79806^70923+3555189Lelio R Paula10/2012
79812^183317-403555184Lelio R Paula01/2011
79822^183284-1555174Lelio R Paula03/2011
79832^183255+14955166Lelio R Paula02/2011
79844*10^55165+8755166Robert Price05/2016
7985(3^115574+4)/6303755139Lelio R Paula03/2012
79862^183165-11233355139Enzo Doria06/2014
79872^183142+85555132Lelio R Paula01/2011
79882^183019+25525555095Lelio R Paula01/2011
79893*10^55077+755078Erik Branger11/2013
7990(62*10^55075-71)/955076Robert Price09/2015
799127499!2-3255070Robert Price10/2015
799215307^3958+3958^1530755067Hans Havermann08/2016
799370^29836-6955051Norbert Schneider10/2012
799418^43854-8355049Lelio R Paula02/2013
79957^65126+5855038Lelio R Paula10/2012
79962^182827-161555037Lelio R Paula11/2009
79977*10^55030-955031Dmitry Domanov11/2010
79986^70702+2355017Lelio R Paula10/2012
7999(23*2^182753+1)/15155014Lelio R Paula07/2012
80002^182743-161555012Lelio R Paula11/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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