PRP Records

Probable Primes Top 10000

(193013 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 ?
5751(2^247759-1017)/331831171774574Lelio R Paula07/2012
57525^106682-2474568Lelio R Paula08/2014
5753474^27863+27863^47474556Norbert Schneider01/2017
5754(14*10^74540+79)/374541Robert Price11/2017
5755(35365^16384+1)/274524Lelio R Paula11/2011
57563^156161+266074508Lelio R Paula01/2015
57572^247474-5869574498Lelio R Paula05/2013
575811^71519-9074480Enzo Doria07/2012
5759(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5761(2^247394-7)/374473Lelio R Paula06/2012
576018^59328+1774473Lelio R Paula01/2015
57622^247379-18174469Lelio R Paula03/2012
5763(15*2^247370-1)/47974465Lelio R Paula01/2014
57642^247344+204774458Lelio R Paula05/2013
57652^247311-101774449Lelio R Paula05/2013
57662^247280+774439Lelio R Paula03/2012
5767(68*10^74434+13)/974435Ray Chandler11/2010
57683^156004-6274433Lelio R Paula01/2015
576936095!2-6474416Robert Price06/2015
57702^247165-374405M. Frind & P. Underwood07/2002
57712^247150+3276974400Lelio R Paula05/2013
577212^68911+7374368Lelio R Paula01/2015
57732^246999+7490374355Enzo Doria04/2016
57742^246989-11064374352Enzo Doria05/2014
577510^74350+27943974351Patrick De Geest07/2017
5778(10^74350+11)/374350Robert Price11/2014
577610^74350-40000000174350Robert Price07/2017
577710^74350-71624174350Patrick De Geest07/2017
577910^74335+1365974336Patrick De Geest05/2013
578010^74335-5374335Robert Price05/2011
57812^246906-121574327Lelio R Paula05/2013
57822^246848+11174309Lelio R Paula03/2012
57836^95490-1844374306Enzo Doria03/2013
578418^59188-236974298Enzo Doria03/2013
5785(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
57862^246744+4075574278Lelio R Paula05/2013
5787(29*10^74276+91)/374277Robert Price03/2016
57886^95441+16374268Lelio R Paula01/2015
5789V(390863)74258Serge Batalov03/2015
579010^74254+9174255Robert Price03/2011
5791(19*10^74253-1)/974254Ray Chandler02/2012
579210^74254-13056974254Patrick De Geest05/2013
5793771^25718+25718^77174250Norbert Schneider10/2016
57942^246618+42774240Henri Lifchitz02/2005
579588*10^74234+374236Robert Price11/2016
57968*10^74234-4974235Robert Price04/2016
57972^246578+1228574228Lelio R Paula05/2013
5798(3^155569-5)/274225Lelio R Paula06/2012
579913^66628+4674220Lelio R Paula01/2015
58002^246476-1729574197Lelio R Paula05/2013
5801(61*10^74189-1)/374191Robert Price11/2017
5802(15185*2^246432-1)/1374187Lelio R Paula04/2015
58035*2^246413-374179Lelio R Paula05/2014
58042^246386-2863574170Lelio R Paula05/2013
58052^246334-11124574154Enzo Doria05/2014
58063*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
580715^63045+8274147Lelio R Paula01/2015
580819255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
58092^246268-11050774135Enzo Doria05/2014
58103^155328+266074111Lelio R Paula01/2015
58112^246148-278624974098Enzo Doria03/2016
5812(16*10^74092-19)/374093Robert Price03/2016
58132^246115-11076774088Enzo Doria05/2014
58147^87666-6874087Lelio R Paula08/2014
581510^74079+114514191974080Marisa Kirisame03/2015
581610^74079+621974080Patrick De Geest03/2016
581710^74079-28270774079Patrick De Geest03/2016
5818129^35098+274078Lelio R Paula05/2013
58192^246025-11212374061Enzo Doria06/2014
5820(67*10^74045+17)/374047Robert Price02/2017
58212^245823+6683174001Marek Hubal02/2017
58225^105869+4274000Lelio R Paula08/2014
5823(21*2^245806+1)/63455573991Lelio R Paula08/2012
5824(22699*2^245762+1)/11973985Lelio R Paula06/2014
5825(3^155048-7)/26273975Lelio R Paula06/2012
58269998*2^245696+373966Donovan Johnson10/2004
582713^66400-8073966Lelio R Paula01/2015
5829(2^245704+9)/2573963Lelio R Paula07/2012
583011^71023-717073963Enzo Doria01/2013
58283*10^73962+1373963Robert Price08/2017
5831(31*2^245660-1)/11419573948Lelio R Paula01/2014
58322^245629-279781373942Eric Chen03/2016
58332^245557-15373921Lelio R Paula03/2012
5834(77*10^73917-59)/973918Robert Price11/2017
58352^245525+186988173911Enzo Doria06/2016
58362^245522+15973910Lelio R Paula03/2012
5837(13*10^73891-43)/373892Robert Price08/2017
583819^57783-5673891Lelio R Paula01/2015
58397*10^73888+7973889Robert Price02/2017
58406^94948+17428173884Mike Oakes02/2011
584111^70939-486073876Enzo Doria01/2013
58422^245372+5461573865Lelio R Paula05/2013
58432^245362-14373862Lelio R Paula03/2012
58447^87396+6^(87396-1)73859Robert Price03/2016
5845(22*10^73853-37)/373854Robert Price05/2017
58465^105646-1424673844Enzo Doria02/2013
58482^245290-4173840Lelio R Paula03/2012
58472^245290-9439573840Lelio R Paula05/2013
58498*5^105600-773813Lelio R Paula10/2014
58507*5^105573-473794Lelio R Paula10/2014
585118^58742-480573738Enzo Doria03/2013
585213^66179+6673720Lelio R Paula01/2015
5853(82*10^73714-1)/973715Robert Price12/2014
5854(29*2^244856-1)/18612173706Lelio R Paula01/2014
5855(13*2^244840-1)/279973702Lelio R Paula01/2014
5856(13*10^73701+17)/373702Robert Price06/2015
5857(2^244787-1017)/2841173684Lelio R Paula07/2012
5858(3^154421-4)/2373677Lelio R Paula06/2012
58598*7^87170+573669Lelio R Paula10/2014
5860(29*10^73659-113)/373660Robert Price11/2017
5861Phi(40100,-40100)73651Henri Lifchitz06/2013
5862(4*10^73647-19)/373648Robert Price06/2017
58632^244618-229773638Yves Minet10/2009
58643*5^105344+873633Lelio R Paula10/2014
58655^105334-1409673626Enzo Doria02/2013
5866(2^244584-7)/1323707424303373614Lelio R Paula07/2012
58672^244465-11018573592Enzo Doria05/2014
58682^244443+4075573585Lelio R Paula05/2013
58692^244404+384173573Yves Minet03/2011
58702^244372-11062773564Enzo Doria05/2014
5871(3*2^244255+1)/24573527Lelio R Paula08/2012
5872(11*2^244245+1)/2373525Lelio R Paula08/2012
5873(15185*2^244187-1)/611173509Lelio R Paula04/2015
5874(91^37507+1)/9273476Paul Bourdelais08/2017
587518^58521+6573460Lelio R Paula01/2015
587613^65940+3673454Lelio R Paula01/2015
58775^105050-1473427Lelio R Paula08/2014
5878(((((((((((((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
587915^62410-4673400Lelio R Paula01/2015
58802^243733+186970773371Enzo Doria05/2016
588111^70439-543073355Enzo Doria01/2013
58822^243676-8773354Lelio R Paula03/2012
5883(101*10^73346-17)/373348Robert Price08/2016
58842^243621-11318573338Enzo Doria07/2014
5885(5*2^243610-1)/166973332Lelio R Paula01/2014
58862*5^104888-773314Lelio R Paula10/2014
5887(58695*2^243516-1)/98373308Lelio R Paula04/2015
5888(3^153648-2)/3342313809773299Lelio R Paula06/2012
588918^58376-525573278Enzo Doria03/2013
589011^70363+3273276Lelio R Paula02/2015
58912^243413+425773275Lelio R Paula05/2013
5892104824^5+5^10482473269Andrey Kulsha07/2010
58937^86689-6^8668973261Predrag Minovic09/2004
58942^243296+9019573240Lelio R Paula05/2013
5895p(15433)#/2-473218Robert Price12/2016
5896(59*10^73217-77)/973218Robert Price11/2017
58972^243127+7135573189Lelio R Paula05/2013
58982^243116-24941973186Paul Bourdelais03/2013
5899(58695*2^243085-1)/1173180Lelio R Paula04/2015
590011^70262-9873171Lelio R Paula02/2015
5901(2^243034+47)/72270330373152Lelio R Paula07/2012
5902(2^242966+47)/4688773136Lelio R Paula07/2012
5903(43^44773-1)/4273134Robert Price04/2014
59046^93980-15835973131Mike Oakes02/2011
59056^93915+5373081Lelio R Paula01/2015
5906(5*10^73079+211)/973079Robert Price12/2017
5907(74*10^73076+43)/973077Robert Price10/2015
5908(3^153125+2)/114495573054Lelio R Paula06/2012
59092^242632-11219973040Enzo Doria06/2014
5910V(351646)73029Serge Batalov03/2015
591118^58175-8573026Lelio R Paula01/2015
5912p(15395)#/2-473019Robert Price12/2016
5913(4^121271+3^121271)/773012Jean-Louis Charton03/2011
59148*6^93825-573011Lelio R Paula10/2014
5916(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
5915(73^39181+1)/7473005Paul Bourdelais08/2017
59176^93815+14373003Lelio R Paula01/2015
59186^93812+573000Wojciech Florek03/2006
591919^57078-6272989Lelio R Paula01/2015
5920(29*10^72985+91)/372986Robert Price03/2016
592111^70082-252072983Enzo Doria12/2012
59226^93773+13372970Lelio R Paula01/2015
59232^242328-5972948Lelio R Paula03/2012
59245^104358-1301672944Enzo Doria02/2013
5925(75*10^72941-57)/9972941Ray Chandler03/2011
592612^67585-9572937Lelio R Paula02/2015
59272^242230-11328572919Enzo Doria07/2014
5928(5*10^72916-11)/372917Erik Branger12/2013
59292^242220-11039972916Enzo Doria05/2014
59302^242205-11341372911Enzo Doria07/2014
5931(3^152809+3^76405+1)/772908Serge Batalov03/2014
59322^242175+7424372902Yves Minet03/2011
59332^242150+1765972895Lelio R Paula11/2009
593411^69982-234072879Enzo Doria12/2012
5935(23*2^242093+1)/1011772875Lelio R Paula08/2012
5936(67607*2^242043+1)/3326372863Lelio R Paula06/2014
59372^242032+8772859Lelio R Paula03/2012
59382^241968-11059572840Enzo Doria05/2014
5939(10^72821+71)/972821Robert Price11/2014
59402^241852-6487572805Lelio R Paula05/2013
5941F(348307)/2056289086590809372776Donovan Johnson07/2007
5942(67*10^72772+23)/972773Ray Chandler11/2010
5943(8*10^72759+67)/372760Robert Price01/2017
59442^241670+14572750Lelio R Paula03/2012
59455^104074+5272745Lelio R Paula08/2014
5946(3^152466-5)/72472742Lelio R Paula06/2012
594720^55908-4172738Lelio R Paula01/2015
5948(73*10^72735+53)/972736Robert Price10/2015
594910^72730+22401172731Patrick De Geest05/2013
595010^72730-9972730Robert Price05/2011
59513*10^72723+6772724Robert Price11/2017
5952(11^69833+3^69833)/1472723Robert Price03/2013
5953(10^72723-79)/372723Robert Price10/2017
5954(88*10^72711-43)/972712Robert Price11/2015
59553^152379+28072704Lelio R Paula01/2015
5956(25*10^72703-241)/972704Robert Price01/2017
5957(47*10^72696+133)/972697Robert Price04/2017
595817^59077-9072692Lelio R Paula01/2015
595965^40096+5872691Lelio R Paula01/2016
5960(29*2^241446-1)/24572682Lelio R Paula01/2014
596211^69783-3840000072672Enzo Doria01/2013
59612^241409-11290372672Enzo Doria06/2014
5963(3^152287+1)/472659Paul Bourdelais04/2008
59643^152249-5672642Lelio R Paula01/2015
596510^72631+3772632Robert Price01/2011
596610^72631-881372631Patrick De Geest05/2013
5967(19*2^241254+1)/10172624Lelio R Paula08/2012
5968(9^76103+8^76103)/1772620Robert Price12/2012
59692^241220-11233772615Enzo Doria06/2014
5970(82*10^72612+449)/972613Robert Price02/2017
59712^241169-1579372600Enzo Doria04/2013
59729*10^72595+1172596Robert Kinser01/2017
5973(25*2^241048+1)/8972563Lelio R Paula08/2012
5974(22*10^72560+17)/372561Robert Price09/2015
59752^241032-2372558Lelio R Paula02/2012
597634485*10^72550+2^241004-372555Gilbert Mozzo12/2012
59772^241004-372550M. Frind & P. Underwood07/2002
597897*10^72522-372524Robert Price01/2017
5979(68*10^72516+7)/372518Robert Price03/2016
5980(78557*2^240844+1)/6372505Lelio R Paula06/2014
598167^39701-6672497Norbert Schneider11/2014
5982(185*10^72484+7)/372486Robert Price02/2017
5984(293*27^50631-1736)/1372473Curtis Bright05/2015
5983103^36005-10272473Norbert Schneider10/2016
598515^61616+8872467Lelio R Paula01/2015
598645^43831+272462Lelio R Paula05/2013
59872^240692-49238972456Paul Bourdelais03/2013
5988(646*10^72446-7)/972448Robert Price07/2016
59899*6^93083+772434Lelio R Paula10/2014
59902^240617-364572433Lelio R Paula05/2013
599111^69531-2400072410Enzo Doria12/2012
5992(22699*2^240396+1)/5572370Lelio R Paula06/2014
59936^92995+1372365Lelio R Paula01/2015
5994(11*10^72362-149)/372363Robert Price01/2017
5995(2^240381+3)/5165572358Lelio R Paula05/2012
59966^92974-5572348Lelio R Paula01/2015
59972^240295+1172337Lelio R Paula02/2012
5998(14*10^72326-53)/372327Robert Price12/2016
599915^61493-4672322Lelio R Paula01/2015
6000lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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