PRP Records

Probable Primes Top 10000

(177649 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 ?
55012^246906-121574327Lelio R Paula05/2013
55022^246848+11174309Lelio R Paula03/2012
55036^95490-1844374306Enzo Doria03/2013
550418^59188-236974298Enzo Doria03/2013
5505(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
55062^246744+4075574278Lelio R Paula05/2013
5507(29*10^74276+91)/374277Robert Price03/2016
55086^95441+16374268Lelio R Paula01/2015
5509V(390863)74258Serge Batalov03/2015
551010^74254+9174255Robert Price03/2011
5511(19*10^74253-1)/974254Ray Chandler02/2012
551210^74254-13056974254Patrick De Geest05/2013
5513771^25718+25718^77174250Norbert Schneider10/2016
55142^246618+42774240Henri Lifchitz02/2005
551588*10^74234+374236Robert Price11/2016
55168*10^74234-4974235Robert Price04/2016
55172^246578+1228574228Lelio R Paula05/2013
5518(3^155569-5)/274225Lelio R Paula06/2012
551913^66628+4674220Lelio R Paula01/2015
55202^246476-1729574197Lelio R Paula05/2013
5521(15185*2^246432-1)/1374187Lelio R Paula04/2015
55225*2^246413-374179Lelio R Paula05/2014
55232^246386-2863574170Lelio R Paula05/2013
55242^246334-11124574154Enzo Doria05/2014
55253*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
552615^63045+8274147Lelio R Paula01/2015
552719255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
55282^246268-11050774135Enzo Doria05/2014
55293^155328+266074111Lelio R Paula01/2015
55302^246148-278624974098Enzo Doria03/2016
5531(16*10^74092-19)/374093Robert Price03/2016
55322^246115-11076774088Enzo Doria05/2014
55337^87666-6874087Lelio R Paula08/2014
553410^74079+114514191974080Marisa Kirisame03/2015
553510^74079+621974080Patrick De Geest03/2016
553610^74079-28270774079Patrick De Geest03/2016
5537129^35098+274078Lelio R Paula05/2013
55382^246025-11212374061Enzo Doria06/2014
5539(67*10^74045+17)/374047Robert Price02/2017
55402^245823+6683174001Marek Hubal02/2017
55415^105869+4274000Lelio R Paula08/2014
5542(21*2^245806+1)/63455573991Lelio R Paula08/2012
5543(22699*2^245762+1)/11973985Lelio R Paula06/2014
5544(3^155048-7)/26273975Lelio R Paula06/2012
55459998*2^245696+373966Donovan Johnson10/2004
554613^66400-8073966Lelio R Paula01/2015
5547(2^245704+9)/2573963Lelio R Paula07/2012
554811^71023-717073963Enzo Doria01/2013
5549(31*2^245660-1)/11419573948Lelio R Paula01/2014
55502^245629-279781373942Eric Chen03/2016
55512^245557-15373921Lelio R Paula03/2012
55522^245525+186988173911Enzo Doria06/2016
55532^245522+15973910Lelio R Paula03/2012
555419^57783-5673891Lelio R Paula01/2015
55557*10^73888+7973889Robert Price02/2017
55566^94948+17428173884Mike Oakes02/2011
555711^70939-486073876Enzo Doria01/2013
55582^245372+5461573865Lelio R Paula05/2013
55592^245362-14373862Lelio R Paula03/2012
55607^87396+6^(87396-1)73859Robert Price03/2016
5561(22*10^73853-37)/373854Robert Price05/2017
55625^105646-1424673844Enzo Doria02/2013
55642^245290-4173840Lelio R Paula03/2012
55632^245290-9439573840Lelio R Paula05/2013
55658*5^105600-773813Lelio R Paula10/2014
55667*5^105573-473794Lelio R Paula10/2014
556718^58742-480573738Enzo Doria03/2013
556813^66179+6673720Lelio R Paula01/2015
5569(82*10^73714-1)/973715Robert Price12/2014
5570(29*2^244856-1)/18612173706Lelio R Paula01/2014
5571(13*2^244840-1)/279973702Lelio R Paula01/2014
5572(13*10^73701+17)/373702Robert Price06/2015
5573(2^244787-1017)/2841173684Lelio R Paula07/2012
5574(3^154421-4)/2373677Lelio R Paula06/2012
55758*7^87170+573669Lelio R Paula10/2014
5576Phi(40100,-40100)73651Henri Lifchitz06/2013
5577(4*10^73647-19)/373648Robert Price06/2017
55782^244618-229773638Yves Minet10/2009
55793*5^105344+873633Lelio R Paula10/2014
55805^105334-1409673626Enzo Doria02/2013
5581(2^244584-7)/1323707424303373614Lelio R Paula07/2012
55822^244465-11018573592Enzo Doria05/2014
55832^244443+4075573585Lelio R Paula05/2013
55842^244404+384173573Yves Minet03/2011
55852^244372-11062773564Enzo Doria05/2014
5586(3*2^244255+1)/24573527Lelio R Paula08/2012
5587(11*2^244245+1)/2373525Lelio R Paula08/2012
5588(15185*2^244187-1)/611173509Lelio R Paula04/2015
558918^58521+6573460Lelio R Paula01/2015
559013^65940+3673454Lelio R Paula01/2015
55915^105050-1473427Lelio R Paula08/2014
5592(((((((((((((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
559315^62410-4673400Lelio R Paula01/2015
55942^243733+186970773371Enzo Doria05/2016
559511^70439-543073355Enzo Doria01/2013
55962^243676-8773354Lelio R Paula03/2012
5597(101*10^73346-17)/373348Robert Price08/2016
55982^243621-11318573338Enzo Doria07/2014
5599(5*2^243610-1)/166973332Lelio R Paula01/2014
56002*5^104888-773314Lelio R Paula10/2014
5601(58695*2^243516-1)/98373308Lelio R Paula04/2015
5602(3^153648-2)/3342313809773299Lelio R Paula06/2012
560318^58376-525573278Enzo Doria03/2013
560411^70363+3273276Lelio R Paula02/2015
56052^243413+425773275Lelio R Paula05/2013
5606104824^5+5^10482473269Andrey Kulsha07/2010
56077^86689-6^8668973261Predrag Minovic09/2004
56082^243296+9019573240Lelio R Paula05/2013
5609p(15433)#/2-473218Robert Price12/2016
56102^243127+7135573189Lelio R Paula05/2013
56112^243116-24941973186Paul Bourdelais03/2013
5612(58695*2^243085-1)/1173180Lelio R Paula04/2015
561311^70262-9873171Lelio R Paula02/2015
5614(2^243034+47)/72270330373152Lelio R Paula07/2012
5615(2^242966+47)/4688773136Lelio R Paula07/2012
5616(43^44773-1)/4273134Robert Price04/2014
56176^93980-15835973131Mike Oakes02/2011
56186^93915+5373081Lelio R Paula01/2015
5619(74*10^73076+43)/973077Robert Price10/2015
5620(3^153125+2)/114495573054Lelio R Paula06/2012
56212^242632-11219973040Enzo Doria06/2014
5622V(351646)73029Serge Batalov03/2015
562318^58175-8573026Lelio R Paula01/2015
5624p(15395)#/2-473019Robert Price12/2016
5625(4^121271+3^121271)/773012Jean-Louis Charton03/2011
56268*6^93825-573011Lelio R Paula10/2014
5627(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
56286^93815+14373003Lelio R Paula01/2015
56296^93812+573000Wojciech Florek03/2006
563019^57078-6272989Lelio R Paula01/2015
5631(29*10^72985+91)/372986Robert Price03/2016
563211^70082-252072983Enzo Doria12/2012
56336^93773+13372970Lelio R Paula01/2015
56342^242328-5972948Lelio R Paula03/2012
56355^104358-1301672944Enzo Doria02/2013
5636(75*10^72941-57)/9972941Ray Chandler03/2011
563712^67585-9572937Lelio R Paula02/2015
56382^242230-11328572919Enzo Doria07/2014
5639(5*10^72916-11)/372917Erik Branger12/2013
56402^242220-11039972916Enzo Doria05/2014
56412^242205-11341372911Enzo Doria07/2014
5642(3^152809+3^76405+1)/772908Serge Batalov03/2014
56432^242175+7424372902Yves Minet03/2011
56442^242150+1765972895Lelio R Paula11/2009
564511^69982-234072879Enzo Doria12/2012
5646(23*2^242093+1)/1011772875Lelio R Paula08/2012
5647(67607*2^242043+1)/3326372863Lelio R Paula06/2014
56482^242032+8772859Lelio R Paula03/2012
56492^241968-11059572840Enzo Doria05/2014
5650(10^72821+71)/972821Robert Price11/2014
56512^241852-6487572805Lelio R Paula05/2013
5652F(348307)/2056289086590809372776Donovan Johnson07/2007
5653(67*10^72772+23)/972773Ray Chandler11/2010
5654(8*10^72759+67)/372760Robert Price01/2017
56552^241670+14572750Lelio R Paula03/2012
56565^104074+5272745Lelio R Paula08/2014
5657(3^152466-5)/72472742Lelio R Paula06/2012
565820^55908-4172738Lelio R Paula01/2015
5659(73*10^72735+53)/972736Robert Price10/2015
566010^72730+22401172731Patrick De Geest05/2013
566110^72730-9972730Robert Price05/2011
5662(11^69833+3^69833)/1472723Robert Price03/2013
5663(88*10^72711-43)/972712Robert Price11/2015
56643^152379+28072704Lelio R Paula01/2015
5665(25*10^72703-241)/972704Robert Price01/2017
5666(47*10^72696+133)/972697Robert Price04/2017
566717^59077-9072692Lelio R Paula01/2015
566865^40096+5872691Lelio R Paula01/2016
5669(29*2^241446-1)/24572682Lelio R Paula01/2014
567111^69783-3840000072672Enzo Doria01/2013
56702^241409-11290372672Enzo Doria06/2014
5672(3^152287+1)/472659Paul Bourdelais04/2008
56733^152249-5672642Lelio R Paula01/2015
567410^72631+3772632Robert Price01/2011
567510^72631-881372631Patrick De Geest05/2013
5676(19*2^241254+1)/10172624Lelio R Paula08/2012
5677(9^76103+8^76103)/1772620Robert Price12/2012
56782^241220-11233772615Enzo Doria06/2014
5679(82*10^72612+449)/972613Robert Price02/2017
56802^241169-1579372600Enzo Doria04/2013
56819*10^72595+1172596Robert Kinser01/2017
5682(25*2^241048+1)/8972563Lelio R Paula08/2012
5683(22*10^72560+17)/372561Robert Price09/2015
56842^241032-2372558Lelio R Paula02/2012
568534485*10^72550+2^241004-372555Gilbert Mozzo12/2012
56862^241004-372550M. Frind & P. Underwood07/2002
568797*10^72522-372524Robert Price01/2017
5688(68*10^72516+7)/372518Robert Price03/2016
5689(78557*2^240844+1)/6372505Lelio R Paula06/2014
569067^39701-6672497Norbert Schneider11/2014
5691(185*10^72484+7)/372486Robert Price02/2017
5693(293*27^50631-1736)/1372473Curtis Bright05/2015
5692103^36005-10272473Norbert Schneider10/2016
569415^61616+8872467Lelio R Paula01/2015
569545^43831+272462Lelio R Paula05/2013
56962^240692-49238972456Paul Bourdelais03/2013
5697(646*10^72446-7)/972448Robert Price07/2016
56989*6^93083+772434Lelio R Paula10/2014
56992^240617-364572433Lelio R Paula05/2013
570011^69531-2400072410Enzo Doria12/2012
5701(22699*2^240396+1)/5572370Lelio R Paula06/2014
57026^92995+1372365Lelio R Paula01/2015
5703(11*10^72362-149)/372363Robert Price01/2017
5704(2^240381+3)/5165572358Lelio R Paula05/2012
57056^92974-5572348Lelio R Paula01/2015
57062^240295+1172337Lelio R Paula02/2012
5707(14*10^72326-53)/372327Robert Price12/2016
570815^61493-4672322Lelio R Paula01/2015
5709lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
57115*10^72302+972303Dmitry Domanov11/2010
5710(9787*2^240179-1)/26572303Lelio R Paula04/2015
571211^69419-312072293Enzo Doria12/2012
571310^72267+3372268Robert Price01/2011
571410^72267-55394772267Patrick De Geest05/2013
571511^69389-138072262Enzo Doria12/2012
5716(16^60013-5^60013)/1172262Robert Price07/2013
57177^85507-3072262Lelio R Paula08/2014
5718(19*2^240026-1)/1572256Lelio R Paula02/2014
5719(3^151426-2)/66133772243Lelio R Paula06/2012
5720gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
57212^239863-11226772206Enzo Doria06/2014
57222^239853-11485372203Enzo Doria05/2015
5723(4*10^72174+149)/972174Robert Price03/2017
5725(2^239671+9)/29613172143Lelio R Paula05/2012
57242^239651-11066572143Enzo Doria05/2014
5726(29*2^239650-1)/330572140Lelio R Paula01/2014
5727241^30280+30280^24172128Norbert Schneider11/2014
5728(68*10^72120-23)/972121Robert Price10/2015
5729(9^75571+8^75571)/1772112Robert Price12/2012
5730(15*2^239530-1)/17372105Lelio R Paula01/2014
57312^239513-11251972101Enzo Doria06/2014
5732(10^72097+149)/372097Serge Batalov12/2014
57332^239442-655572080Lelio R Paula05/2012
57342*5^103106+372069Lelio R Paula10/2014
57352^239402-19772068Lelio R Paula02/2012
57362^239356-11187572054Enzo Doria05/2014
5737(38*10^72050-119)/972051Robert Price11/2016
57382^239339+1501572049Lelio R Paula01/2013
5739159^32728+272048Lelio R Paula05/2013
574015^61259-3872047Lelio R Paula01/2015
574192^36683-91^3668372038Robert Price08/2015
57422^239280+5461572031Lelio R Paula05/2012
5743(47*2^239267+1)/7772027Lelio R Paula04/2015
5744(85*10^72025-1)/372027Robert Price07/2017
57452^239236-9730572018Lelio R Paula05/2012
57462^239169+5971998Lelio R Paula02/2012
5748lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
5747(15*2^239171-1)/10630171994Lelio R Paula01/2014
5749(29^49211-1)/2871965Robert Price04/2012
5750V(344293)71953Serge Batalov03/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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