PRP Records

Probable Primes Top 10000

(173006 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 ?
55012^245372+5461573865Lelio R Paula05/2013
55022^245362-14373862Lelio R Paula03/2012
55037^87396+6^(87396-1)73859Robert Price03/2016
5504(22*10^73853-37)/373854Robert Price05/2017
55055^105646-1424673844Enzo Doria02/2013
55072^245290-4173840Lelio R Paula03/2012
55062^245290-9439573840Lelio R Paula05/2013
55088*5^105600-773813Lelio R Paula10/2014
55097*5^105573-473794Lelio R Paula10/2014
551018^58742-480573738Enzo Doria03/2013
551113^66179+6673720Lelio R Paula01/2015
5512(82*10^73714-1)/973715Robert Price12/2014
5513(29*2^244856-1)/18612173706Lelio R Paula01/2014
5514(13*2^244840-1)/279973702Lelio R Paula01/2014
5515(13*10^73701+17)/373702Robert Price06/2015
5516(2^244787-1017)/2841173684Lelio R Paula07/2012
5517(3^154421-4)/2373677Lelio R Paula06/2012
55188*7^87170+573669Lelio R Paula10/2014
5519Phi(40100,-40100)73651Henri Lifchitz06/2013
55202^244618-229773638Yves Minet10/2009
55213*5^105344+873633Lelio R Paula10/2014
55225^105334-1409673626Enzo Doria02/2013
5523(2^244584-7)/1323707424303373614Lelio R Paula07/2012
55242^244465-11018573592Enzo Doria05/2014
55252^244443+4075573585Lelio R Paula05/2013
55262^244404+384173573Yves Minet03/2011
55272^244372-11062773564Enzo Doria05/2014
5528(3*2^244255+1)/24573527Lelio R Paula08/2012
5529(11*2^244245+1)/2373525Lelio R Paula08/2012
5530(15185*2^244187-1)/611173509Lelio R Paula04/2015
553118^58521+6573460Lelio R Paula01/2015
553213^65940+3673454Lelio R Paula01/2015
55335^105050-1473427Lelio R Paula08/2014
5534(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
553515^62410-4673400Lelio R Paula01/2015
55362^243733+186970773371Enzo Doria05/2016
553711^70439-543073355Enzo Doria01/2013
55382^243676-8773354Lelio R Paula03/2012
5539(101*10^73346-17)/373348Robert Price08/2016
55402^243621-11318573338Enzo Doria07/2014
5541(5*2^243610-1)/166973332Lelio R Paula01/2014
55422*5^104888-773314Lelio R Paula10/2014
5543(58695*2^243516-1)/98373308Lelio R Paula04/2015
5544(3^153648-2)/3342313809773299Lelio R Paula06/2012
554518^58376-525573278Enzo Doria03/2013
554611^70363+3273276Lelio R Paula02/2015
55472^243413+425773275Lelio R Paula05/2013
5548104824^5+5^10482473269Andrey Kulsha07/2010
55497^86689-6^8668973261Predrag Minovic09/2004
55502^243296+9019573240Lelio R Paula05/2013
5551p(15433)#/2-473218Robert Price12/2016
55522^243127+7135573189Lelio R Paula05/2013
55532^243116-24941973186Paul Bourdelais03/2013
5554(58695*2^243085-1)/1173180Lelio R Paula04/2015
555511^70262-9873171Lelio R Paula02/2015
5556(2^243034+47)/72270330373152Lelio R Paula07/2012
5557(2^242966+47)/4688773136Lelio R Paula07/2012
5558(43^44773-1)/4273134Robert Price04/2014
55596^93980-15835973131Mike Oakes02/2011
55606^93915+5373081Lelio R Paula01/2015
5561(74*10^73076+43)/973077Robert Price10/2015
5562(3^153125+2)/114495573054Lelio R Paula06/2012
55632^242632-11219973040Enzo Doria06/2014
5564V(351646)73029Serge Batalov03/2015
556518^58175-8573026Lelio R Paula01/2015
5566p(15395)#/2-473019Robert Price12/2016
5567(4^121271+3^121271)/773012Jean-Louis Charton03/2011
55688*6^93825-573011Lelio R Paula10/2014
5569(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
55706^93815+14373003Lelio R Paula01/2015
55716^93812+573000Wojciech Florek03/2006
557219^57078-6272989Lelio R Paula01/2015
5573(29*10^72985+91)/372986Robert Price03/2016
557411^70082-252072983Enzo Doria12/2012
55756^93773+13372970Lelio R Paula01/2015
55762^242328-5972948Lelio R Paula03/2012
55775^104358-1301672944Enzo Doria02/2013
5578(75*10^72941-57)/9972941Ray Chandler03/2011
557912^67585-9572937Lelio R Paula02/2015
55802^242230-11328572919Enzo Doria07/2014
5581(5*10^72916-11)/372917Erik Branger12/2013
55822^242220-11039972916Enzo Doria05/2014
55832^242205-11341372911Enzo Doria07/2014
5584(3^152809+3^76405+1)/772908Serge Batalov03/2014
55852^242175+7424372902Yves Minet03/2011
55862^242150+1765972895Lelio R Paula11/2009
558711^69982-234072879Enzo Doria12/2012
5588(23*2^242093+1)/1011772875Lelio R Paula08/2012
5589(67607*2^242043+1)/3326372863Lelio R Paula06/2014
55902^242032+8772859Lelio R Paula03/2012
55912^241968-11059572840Enzo Doria05/2014
5592(10^72821+71)/972821Robert Price11/2014
55932^241852-6487572805Lelio R Paula05/2013
5594F(348307)/2056289086590809372776Donovan Johnson07/2007
5595(67*10^72772+23)/972773Ray Chandler11/2010
5596(8*10^72759+67)/372760Robert Price01/2017
55972^241670+14572750Lelio R Paula03/2012
55985^104074+5272745Lelio R Paula08/2014
5599(3^152466-5)/72472742Lelio R Paula06/2012
560020^55908-4172738Lelio R Paula01/2015
5601(73*10^72735+53)/972736Robert Price10/2015
560210^72730+22401172731Patrick De Geest05/2013
560310^72730-9972730Robert Price05/2011
5604(11^69833+3^69833)/1472723Robert Price03/2013
5605(88*10^72711-43)/972712Robert Price11/2015
56063^152379+28072704Lelio R Paula01/2015
5607(25*10^72703-241)/972704Robert Price01/2017
5608(47*10^72696+133)/972697Robert Price04/2017
560917^59077-9072692Lelio R Paula01/2015
561065^40096+5872691Lelio R Paula01/2016
5611(29*2^241446-1)/24572682Lelio R Paula01/2014
561311^69783-3840000072672Enzo Doria01/2013
56122^241409-11290372672Enzo Doria06/2014
5614(3^152287+1)/472659Paul Bourdelais04/2008
56153^152249-5672642Lelio R Paula01/2015
561610^72631+3772632Robert Price01/2011
561710^72631-881372631Patrick De Geest05/2013
5618(19*2^241254+1)/10172624Lelio R Paula08/2012
5619(9^76103+8^76103)/1772620Robert Price12/2012
56202^241220-11233772615Enzo Doria06/2014
5621(82*10^72612+449)/972613Robert Price02/2017
56222^241169-1579372600Enzo Doria04/2013
56239*10^72595+1172596Robert Kinser01/2017
5624(25*2^241048+1)/8972563Lelio R Paula08/2012
5625(22*10^72560+17)/372561Robert Price09/2015
56262^241032-2372558Lelio R Paula02/2012
562734485*10^72550+2^241004-372555Gilbert Mozzo12/2012
56282^241004-372550M. Frind & P. Underwood07/2002
562997*10^72522-372524Robert Price01/2017
5630(68*10^72516+7)/372518Robert Price03/2016
5631(78557*2^240844+1)/6372505Lelio R Paula06/2014
563267^39701-6672497Norbert Schneider11/2014
5633(185*10^72484+7)/372486Robert Price02/2017
5635(293*27^50631-1736)/1372473Curtis Bright05/2015
5634103^36005-10272473Norbert Schneider10/2016
563615^61616+8872467Lelio R Paula01/2015
563745^43831+272462Lelio R Paula05/2013
56382^240692-49238972456Paul Bourdelais03/2013
5639(646*10^72446-7)/972448Robert Price07/2016
56409*6^93083+772434Lelio R Paula10/2014
56412^240617-364572433Lelio R Paula05/2013
564211^69531-2400072410Enzo Doria12/2012
5643(22699*2^240396+1)/5572370Lelio R Paula06/2014
56446^92995+1372365Lelio R Paula01/2015
5645(11*10^72362-149)/372363Robert Price01/2017
5646(2^240381+3)/5165572358Lelio R Paula05/2012
56476^92974-5572348Lelio R Paula01/2015
56482^240295+1172337Lelio R Paula02/2012
5649(14*10^72326-53)/372327Robert Price12/2016
565015^61493-4672322Lelio R Paula01/2015
5651lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
56535*10^72302+972303Dmitry Domanov11/2010
5652(9787*2^240179-1)/26572303Lelio R Paula04/2015
565411^69419-312072293Enzo Doria12/2012
565510^72267+3372268Robert Price01/2011
565610^72267-55394772267Patrick De Geest05/2013
565711^69389-138072262Enzo Doria12/2012
5658(16^60013-5^60013)/1172262Robert Price07/2013
56597^85507-3072262Lelio R Paula08/2014
5660(19*2^240026-1)/1572256Lelio R Paula02/2014
5661(3^151426-2)/66133772243Lelio R Paula06/2012
5662gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
56632^239863-11226772206Enzo Doria06/2014
56642^239853-11485372203Enzo Doria05/2015
5665(4*10^72174+149)/972174Robert Price03/2017
5667(2^239671+9)/29613172143Lelio R Paula05/2012
56662^239651-11066572143Enzo Doria05/2014
5668(29*2^239650-1)/330572140Lelio R Paula01/2014
5669241^30280+30280^24172128Norbert Schneider11/2014
5670(68*10^72120-23)/972121Robert Price10/2015
5671(9^75571+8^75571)/1772112Robert Price12/2012
5672(15*2^239530-1)/17372105Lelio R Paula01/2014
56732^239513-11251972101Enzo Doria06/2014
5674(10^72097+149)/372097Serge Batalov12/2014
56752^239442-655572080Lelio R Paula05/2012
56762*5^103106+372069Lelio R Paula10/2014
56772^239402-19772068Lelio R Paula02/2012
56782^239356-11187572054Enzo Doria05/2014
5679(38*10^72050-119)/972051Robert Price11/2016
56802^239339+1501572049Lelio R Paula01/2013
5681159^32728+272048Lelio R Paula05/2013
568215^61259-3872047Lelio R Paula01/2015
568392^36683-91^3668372038Robert Price08/2015
56842^239280+5461572031Lelio R Paula05/2012
5685(47*2^239267+1)/7772027Lelio R Paula04/2015
56862^239236-9730572018Lelio R Paula05/2012
56872^239169+5971998Lelio R Paula02/2012
5689lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
5688(15*2^239171-1)/10630171994Lelio R Paula01/2014
5690(29^49211-1)/2871965Robert Price04/2012
5691L(344293)71953Renaud Lifchitz09/2003
5692V(344293)71953Serge Batalov03/2015
56936*10^71951+771952Dmitry Domanov11/2010
56943^150798+4071949Lelio R Paula01/2015
56952^238961+9571935Lelio R Paula02/2012
56962^238936-40771927Yves Minet02/2012
56972^238923-2863571923Lelio R Paula05/2012
569810^71910+2511971911Patrick De Geest05/2016
569910^71910-80171910Robert Price04/2016
57002^238845-11265171900Enzo Doria06/2014
57012^238792-11124571884Enzo Doria05/2014
57026*7^85059+571884Lelio R Paula10/2014
57032^238752-11058971872Enzo Doria05/2014
570412^66581+771853Lelio R Paula07/2014
5705(7*2^238691+1)/4122971850Lelio R Paula06/2012
57064*3^150568-571840Lelio R Paula04/2014
57076^92301+6771825Lelio R Paula01/2015
57082^238568+9876533171817Jason Earls01/2009
57092^238541-11272371808Enzo Doria06/2014
57102^238529-1594971805Enzo Doria04/2013
57119*5^102721-871800Lelio R Paula10/2014
57122^238494-16571794Lelio R Paula02/2012
57132^238389-11090571763Enzo Doria05/2014
5714(145*10^71760-1)/971762Serge Batalov12/2014
57157^84913+506271760Mike Oakes02/2010
5716(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
57172^238268-9730571726Lelio R Paula05/2012
5718gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
57192^238235-11324771716Enzo Doria07/2014
57202*12^66450-5^6645071712Mike Oakes11/2010
5721(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
57222^238199-11181771706Enzo Doria05/2014
5723lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
57242^238144+9876533171689Jason Earls01/2009
572518^57102-426571679Enzo Doria03/2013
5726(73*10^71670-1)/971671Robert Price01/2015
57272^238081+1155*23808171670Henri Lifchitz02/2005
57282^238067-11192571666Enzo Doria05/2014
572936^46030+3571637Norbert Schneider04/2014
57302^237905-9171617Lelio R Paula02/2012
5731(31*2^237902-1)/12371616Lelio R Paula01/2014
5732(15185*2^237866-1)/4396771605Lelio R Paula04/2015
5733(24737*2^237841+1)/2571601Lelio R Paula06/2014
57342^237846+129971599Lelio R Paula05/2012
57356^92004+19980171594Mike Oakes02/2011
5736159^32516+271581Lelio R Paula05/2013
57372^237781+85571580Lelio R Paula05/2012
57382^237720-407971561Yves Minet06/2011
57392^237698-11094571555Enzo Doria05/2014
57402^237695-11323971554Enzo Doria07/2014
57418*5^102362-971549Lelio R Paula10/2014
5742(4*10^71546-31)/971546Erik Branger05/2011
57432^237650+3771540Lelio R Paula02/2012
574418^56977-439171522Enzo Doria03/2013
5745(22699*2^237565+1)/413663771512Lelio R Paula06/2014
5746((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
5747(26*10^71503+7)/371504Erik Branger11/2013
5748(4*10^71498+173)/371499Robert Price01/2017
57493^149848+11071496Lelio R Paula11/2014
57502^237498+51371495Lelio R Paula05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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