PRP Records

Probable Primes Top 10000

(218736 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 ?
8751(2^188176-1017)/45381454356638Lelio R Paula02/2012
875233*10^56634+756636Robert Price07/2016
8753(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
875414^49413+3356634Lelio R Paula02/2013
87553^118680+11056625Lelio R Paula10/2012
8756(13*10^56624+161)/356625Robert Price04/2017
8757(3^118676-2)/751665326356613Lelio R Paula03/2012
8758(13*2^188062+1)/1756613Lelio R Paula07/2012
87592^188056-131356611Yves Minet08/2012
876020^43510-558356608Enzo Doria03/2013
87612^188032+1228556604Lelio R Paula03/2011
8762(19*10^56597-43)/356598Robert Price10/2017
8763(265*10^56588+17)/356590Robert Price05/2016
87642^187959+577556582Lelio R Paula03/2011
8765(5*2^187959+1)/5356581Lelio R Paula07/2012
87663*10^56575-1356576Robert Price11/2017
8767(11*2^187889-1)/35156559Lelio R Paula01/2014
8768(100049^11311+1)/10005056553Faysal YAtim09/2007
8769(19*10^56544-1)/956545Serge Batalov03/2009
877020^43447-892356526Enzo Doria03/2013
87712^187743-11217756517Enzo Doria06/2014
8772(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
87735^80831-2256499Lelio R Paula10/2012
87745^80828-1316656497Enzo Doria02/2013
87757*2^187590-556472Lelio R Paula03/2014
87762^187555+7547356460Enzo Doria04/2016
87772^187541-28356456Yves Minet01/2012
8778(55*10^56453-1)/956454Serge Batalov03/2009
87792^187506-145156445Yves Minet08/2012
8780189^24794-256443Lelio R Paula10/2017
87816^72522+14356434Lelio R Paula10/2012
8782(15185*2^187452-1)/94956430Lelio R Paula03/2015
87832^187390+7956411Lelio R Paula03/2011
87842^187386+1290956409Lelio R Paula03/2011
87852^187382+61356408Jason Earls04/2008
8786(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
878720^43337-956383Lelio R Paula02/2013
8788(26*10^56371-173)/356372Robert Price10/2017
8789(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
87912^187230+42756362Henri Lifchitz01/2005
879011^54121-948056362Enzo Doria02/2013
8792(21*2^187202-1)/4356354Lelio R Paula01/2014
87932^187173-9156345Lelio R Paula03/2011
8794(23*2^187174-1)/2071988356340Lelio R Paula01/2014
87952^187125-283356331Yves Minet09/2014
87969*7^66655-456331Lelio R Paula09/2014
879718^44874-9756330Lelio R Paula02/2013
879860*79^29679+1956322Serge Batalov03/2016
87995^80571+5656317Lelio R Paula10/2012
88005^80551-2256303Lelio R Paula10/2012
8801(76*10^56281+41)/956282Robert Price10/2015
8802(88*10^56271-43)/956272Robert Price11/2015
8803(5*10^56256-119)/356257Robert Price04/2016
88041508^17691+17691^150856230Serge Batalov05/2014
88053^117844-5856226Lelio R Paula10/2012
8806(19*10^56224+737)/956225Robert Price10/2017
880795^28427+256221Lelio R Paula05/2013
88082^186713+7681756207Enzo Doria05/2016
880916534^2505+2505^1653456196Hans Havermann06/2016
881014428^7849+7849^1442856195Hans Havermann06/2016
88112*10^56194-5156195Robert Price11/2017
881214898^5909+5909^1489856189Hans Havermann06/2016
881318^44758+9556184Lelio R Paula02/2013
88142^186555-74156159Lelio R Paula05/2011
8815(4*10^56156+173)/356157Robert Price01/2017
8816(3^117708+7)/44789656156Lelio R Paula03/2012
881715711^3752+3752^1571156156Hans Havermann06/2016
8818(23*2^186549-1)/242902556152Lelio R Paula01/2014
8819387^21694+21694^38756138Norbert Schneider08/2014
88202^186422+1723956119Yves Minet01/2010
88212^186418+424242956118Jason Earls10/2008
8822136^26300+13556113Norbert Schneider04/2015
88235*2^186392+956111Lelio R Paula03/2014
882414345^8152+8152^1434556108Hans Havermann07/2016
8825(5*2^186351-1)/3956097Lelio R Paula01/2014
88262^186319-54123756088Paul Bourdelais11/2012
88272*10^56083-4356084Robert Price07/2017
8828(16*10^56082-61)/956083Serge Batalov05/2009
8829(14*10^56080-143)/356081Robert Price01/2017
8830(265*10^56076+17)/356078Robert Price05/2016
88317^66346-5056069Lelio R Paula10/2012
883220^43094-3356067Lelio R Paula02/2013
883320^43090-138356062Enzo Doria03/2013
88343^117482+266056054Lelio R Paula10/2012
8835(22699*2^186193+1)/11156052Lelio R Paula05/2014
8836(68*10^56042+13)/956043Ray Chandler09/2010
88373*6^71992+5^7199256022Mike Oakes03/2010
883813691^12352+12352^1369156020Hans Havermann07/2016
8839(2^186095+7)/7556019Lelio R Paula02/2012
8840247^23412+23412^24756018Norbert Schneider08/2014
88411839^17156+17156^183956008Serge Batalov05/2014
884213736^11949+11949^1373656007Hans Havermann04/2016
8843(5*2^186036-1)/1156003Lelio R Paula01/2014
8844(299*10^55998-17)/356000Robert Price01/2017
8845p(12103)#/2-12855994Robert Price05/2017
88482^186003-17433755993Gary Barnes09/2009
8846(2^186010+78557)/12355993Lelio R Paula05/2012
884720^43037-9355993Lelio R Paula02/2013
884916375^2626+2626^1637555991Hans Havermann03/2016
885015631^3816+3816^1563155985Hans Havermann03/2016
885121^42335-255977Lelio R Paula08/2013
8852Phi(64736,139)55959Enzo Doria07/2012
885315215^4762+4762^1521555958Hans Havermann03/2016
885419317^788+788^1931755953Anatoly F. Selevich12/2006
885513582^13165+13165^1358255950Hans Havermann08/2016
8856(78557*2^185842+1)/18955947Lelio R Paula06/2014
885715^47562-8655938Lelio R Paula02/2013
88584*10^55932+9155933Robert Price11/2017
88593^117222+455930Lelio R Paula03/2012
886024^40519-23^4051955925Robert Price07/2012
886113636^12623+12623^1363655924Hans Havermann07/2016
88622^185767-9955922Lelio R Paula03/2011
8863(19*2^185750-1)/1555917Lelio R Paula01/2014
886515^47542-5855914Lelio R Paula02/2013
886452211!4+255914Robert Price08/2017
886620^42973-558355910Enzo Doria03/2013
88674*10^55906+2155907Robert Price08/2016
88682^185713-11155906Lelio R Paula03/2011
886913^50174+8855891Lelio R Paula01/2013
887014569^6846+6846^1456955879Hans Havermann08/2016
8871Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
88723^117087-8055865Lelio R Paula10/2012
8873(7*10^55851-43)/955851Robert Price10/2014
88742^185519-16955847Lelio R Paula03/2011
88757^66074+1055840Lelio R Paula10/2012
8876(19*10^55833-49)/355834Robert Price02/2017
8877(2*10^55834-59)/355834Robert Price05/2017
88782^185463-423755830Yves Minet08/2018
887912^51732+555829Lelio R Paula01/2013
88803*2^185429+755821Lelio R Paula03/2014
8881(60^31393+1)/6155820Paul Bourdelais08/2017
8883(9787*2^185420-1)/38155819Lelio R Paula04/2015
888214427^7396+7396^1442755819Hans Havermann08/2016
888410^55811+2155812Robert Price01/2011
888510^55811-7410355811Patrick De Geest12/2012
888611^53591-153055810Enzo Doria11/2012
8887(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
88882^185355-214555798Lelio R Paula03/2011
888914531^6912+6912^1453155794Hans Havermann07/2016
88902^185327-161555789Lelio R Paula03/2011
88912^185280-1277955775Enzo Doria10/2012
889215504^3955+3955^1550455771Hans Havermann07/2016
8893(2*10^55762-59)/355762Robert Price05/2017
88945^79770-4455757Lelio R Paula10/2012
889518^44416-8555755Lelio R Paula02/2013
88962^185208-45999555754Enzo Doria06/2015
88972^185200+118555751Lelio R Paula03/2011
8898(536*10^55748-23)/955750Robert Price11/2017
88997^65964+6^(65964-1)55747Robert Price03/2016
89002^185151-23715755737Gary Barnes09/2009
8901110017^11055-10255734Enzo Doria07/2012
890214754^5987+5987^1475455729Hans Havermann07/2016
890312591^13592-13592^1259155729Norbert Schneider07/2018
890440090!3-955711Robert Price09/2014
89059*10^55707+8955708Robert Price11/2016
89062^185023-225755698Yves Minet06/2009
890718628^977+977^1862855696Anatoly F. Selevich01/2007
89082^185006-9355693Lelio R Paula03/2011
89092^185003-251555692Yves Minet07/2014
89102^184992-7855755689Jorge Menendez02/2018
89113*10^55679+3755680Robert Price10/2017
89126^71524-1955657Lelio R Paula10/2012
89132^184872-219555653Yves Minet08/2013
8914507^20572+20572^50755648Norbert Schneider06/2016
8915(86*10^55645-311)/955646Robert Price10/2017
8916134^26151-13355626Norbert Schneider03/2015
891715340^4221+4221^1534055614Hans Havermann07/2016
891827743!2+255612Robert Price01/2013
891920^42744+8155612Lelio R Paula02/2013
892014609^6406+6406^1460955611Hans Havermann07/2016
89212^184724-11288355608Enzo Doria06/2014
892213507^13074+13074^1350755601Hans Havermann07/2016
89232^184689+12955597Lelio R Paula03/2011
8924(9179*2^184672-1)/19355594Lelio R Paula03/2015
8925(22*10^55592-19)/355593Robert Price02/2017
8926Phi(59984,89)55582Enzo Doria05/2012
892711^53368+1655578Lelio R Paula01/2013
892820^42717-192355577Enzo Doria03/2013
8929117^26870+26870^11755573Serge Batalov05/2014
893012^51488+5555565Lelio R Paula01/2013
8931(44*10^55558-17)/955559Robert Price06/2015
8932(2*10^55559-23)/355559Robert Price09/2017
893310^55555+3285755556Patrick De Geest06/2010
893410^55555-13672155555Patrick De Geest06/2010
8935(11*2^184541-1)/35155551Lelio R Paula01/2014
893620^42696-204355549Enzo Doria03/2013
8937(35*10^55547-737)/955548Robert Price11/2017
8938(2*10^55544+1)/355544Serge Batalov06/2009
8939(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
89405003^15013-16055537Enzo Doria07/2012
894139^34896-255522Lelio R Paula08/2013
8942(6^71345-61)/555517Lelio R Paula05/2014
89432^184407-301955513Yves Minet10/2014
8944(43*10^55512-61)/955513Robert Price06/2015
894520^42667-84355512Enzo Doria03/2013
8946133^26134-13255505Norbert Schneider03/2015
8947(31*2^184378-1)/71155502Lelio R Paula01/2014
89489*7^65667-455497Lelio R Paula09/2014
89492^184342-17355493Lelio R Paula03/2011
895015^47182+9255491Lelio R Paula02/2013
89515^79378+655483Lelio R Paula10/2012
8952581^20068+20068^58155472Norbert Schneider06/2016
8953(2^184232+1)/25755457Donovan Johnson03/2005
895418^44177-141555455Enzo Doria03/2013
89552^184203-279786755451Enzo Doria04/2016
89562^184189+1755447Lelio R Paula03/2011
89572^184183+2612355445Yves Minet01/2010
8958Phi(77077,10)55441Ray Chandler05/2009
89592^184141-11325155432Enzo Doria07/2014
89602^184093-50461355418Gary Barnes09/2009
8961(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
89622^184044-11126955403Enzo Doria05/2014
896314051^8766+8766^1405155401Hans Havermann07/2016
896498^27819+27819^9855394Serge Batalov05/2014
8965(178*10^55390-7)/955392Robert Price08/2017
896658046^9+9^5804655390Andrey Kulsha02/2004
89677^65536+2*59232-255385Jiahao He07/2017
89682^183980+7524155384Enzo Doria04/2016
896910^55372+3755373Robert Price01/2011
897010^55372-4996755372Patrick De Geest12/2012
8971(13*10^55367+17)/355368Robert Price06/2015
89722*6^71150+755366Lelio R Paula09/2014
897319^43296-6255365Lelio R Paula02/2013
897419^43295+1055364Lelio R Paula02/2013
8975(29*10^55362-11)/955363Robert Price04/2015
8976(37*10^55359+53)/955360Robert Price05/2015
897719^43283+7255349Lelio R Paula02/2013
89782^183800-6555330Lelio R Paula03/2011
897921001^12801-11055329Enzo Doria07/2012
898033^36433-32^3643355325Robert Price04/2012
8981(17*2^183729+1)/14555308Lelio R Paula07/2012
89839^57952+8^(57952-1)55301Robert Price03/2016
898214872^5229+5229^1487255301Hans Havermann08/2016
898461^30972-255296Lelio R Paula08/2013
89852^183671-11253755291Enzo Doria06/2014
8986(2^183687+7)/49793974555287Lelio R Paula02/2012
89873^115873+5655286Lelio R Paula10/2012
898813^49629-8455284Lelio R Paula01/2013
89892^183632-555279Henri Lifchitz08/2005
899013981^8988+8988^1398155277Hans Havermann07/2016
8991(5*2^183585+1)/1355265Lelio R Paula07/2012
89922^183576+17155262Lelio R Paula03/2011
899313^49604+8255257Lelio R Paula01/2013
8994(11*10^55254+1)/355255Erik Branger03/2014
899512609^13474-13474^1260955253Norbert Schneider05/2018
89963^115802-2655252Lelio R Paula10/2012
89972^183534-364555250Lelio R Paula01/2011
8998(15*2^183533-1)/11355249Lelio R Paula01/2014
89995^79032-1376655241Enzo Doria02/2013
90008*3^115759-755232Lelio R Paula03/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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