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 ?
52512*F(358297)-174880Henri Lifchitz12/2009
5252(22*10^74874-31)/974875Robert Price04/2015
525311^71892-7680000074868Enzo Doria01/2013
52549*5^107107-474866Lelio R Paula10/2014
52552^248678-71011174860Paul Bourdelais03/2013
525613^67194+1274851Lelio R Paula01/2015
5257(7*2^248634+1)/7174846Lelio R Paula08/2012
525811^71867-309074842Enzo Doria12/2012
52592^248609+26214574839Lelio R Paula05/2013
52603^156852+5074838Lelio R Paula01/2015
526118^59607-1174824Lelio R Paula01/2015
52622^248556-11050774823Enzo Doria05/2014
52637^88531-3674818Lelio R Paula01/2015
52644*3^156740-574785Lelio R Paula05/2014
5265(32*10^74773-41)/974774Robert Price05/2015
5266(29*2^248384-1)/1374772Lelio R Paula01/2014
526719401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
52682^248357-1279741374763Enzo Doria03/2016
526942^46057+4174762Lelio R Paula07/2012
527011^71784-300074756Enzo Doria12/2012
527119^58458+1874754Lelio R Paula01/2015
527212^69265-3574750Lelio R Paula02/2015
527311^71771-4800074742Enzo Doria12/2012
5274(2^248282-5)/5012974736Lelio R Paula06/2012
52752^248252-11010574732Enzo Doria04/2014
5276(7*10^74729+71)/374730Robert Price03/2016
52773^156614-5074724Lelio R Paula01/2015
5278(7*2^248213+1)/13574719Lelio R Paula07/2012
5279(2^248173+78557)/76774705Lelio R Paula07/2012
5280125^35622+12474697Norbert Schneider02/2015
5281(19*2^248099-1)/2974686Lelio R Paula01/2014
5282(86*10^74676-41)/974677Robert Price11/2015
528310^74670+3174671Robert Price01/2011
528410^74670-12246374670Patrick De Geest05/2013
52852^248036-6974667Lelio R Paula03/2012
528611^71698-600074666Enzo Doria12/2012
528758*(10^(3*24887)-1)/111-174661Robert Price10/2014
528814^65139-4574658Lelio R Paula01/2015
52896^95921-13374642Lelio R Paula01/2015
529011^71675+7874642Lelio R Paula02/2015
529118^59449-9174625Lelio R Paula01/2015
52926^95864-1604374597Enzo Doria02/2013
52935*7^88261+674590Lelio R Paula10/2014
52949*5^106710+474589Lelio R Paula10/2014
5295(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
5296(265*10^74579+17)/374581Robert Price05/2016
5297(2^247759-1017)/331831171774574Lelio R Paula07/2012
52985^106682-2474568Lelio R Paula08/2014
5299474^27863+27863^47474556Norbert Schneider01/2017
5300(35365^16384+1)/274524Lelio R Paula11/2011
53013^156161+266074508Lelio R Paula01/2015
53022^247474-5869574498Lelio R Paula05/2013
530311^71519-9074480Enzo Doria07/2012
5304(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5306(2^247394-7)/374473Lelio R Paula06/2012
530518^59328+1774473Lelio R Paula01/2015
53072^247379-18174469Lelio R Paula03/2012
5308(15*2^247370-1)/47974465Lelio R Paula01/2014
53092^247344+204774458Lelio R Paula05/2013
53102^247311-101774449Lelio R Paula05/2013
53112^247280+774439Lelio R Paula03/2012
5312(68*10^74434+13)/974435Ray Chandler11/2010
53133^156004-6274433Lelio R Paula01/2015
531436095!2-6474416Robert Price06/2015
53152^247165-374405M. Frind & P. Underwood07/2002
53162^247150+3276974400Lelio R Paula05/2013
531712^68911+7374368Lelio R Paula01/2015
53182^246999+7490374355Enzo Doria04/2016
53192^246989-11064374352Enzo Doria05/2014
5320(10^74350+11)/374350Robert Price11/2014
532110^74335+1365974336Patrick De Geest05/2013
532210^74335-5374335Robert Price05/2011
53232^246906-121574327Lelio R Paula05/2013
53242^246848+11174309Lelio R Paula03/2012
53256^95490-1844374306Enzo Doria03/2013
532618^59188-236974298Enzo Doria03/2013
5327(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
53282^246744+4075574278Lelio R Paula05/2013
5329(29*10^74276+91)/374277Robert Price03/2016
53306^95441+16374268Lelio R Paula01/2015
5331V(390863)74258Serge Batalov03/2015
533210^74254+9174255Robert Price03/2011
5333(19*10^74253-1)/974254Ray Chandler02/2012
533410^74254-13056974254Patrick De Geest05/2013
5335771^25718+25718^77174250Norbert Schneider10/2016
53362^246618+42774240Henri Lifchitz02/2005
533788*10^74234+374236Robert Price11/2016
53388*10^74234-4974235Robert Price04/2016
53392^246578+1228574228Lelio R Paula05/2013
5340(3^155569-5)/274225Lelio R Paula06/2012
534113^66628+4674220Lelio R Paula01/2015
53422^246476-1729574197Lelio R Paula05/2013
5343(15185*2^246432-1)/1374187Lelio R Paula04/2015
53445*2^246413-374179Lelio R Paula05/2014
53452^246386-2863574170Lelio R Paula05/2013
53462^246334-11124574154Enzo Doria05/2014
53473*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
534815^63045+8274147Lelio R Paula01/2015
534919255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
53502^246268-11050774135Enzo Doria05/2014
53513^155328+266074111Lelio R Paula01/2015
53522^246148-278624974098Enzo Doria03/2016
5353(16*10^74092-19)/374093Robert Price03/2016
53542^246115-11076774088Enzo Doria05/2014
53557^87666-6874087Lelio R Paula08/2014
535610^74079+114514191974080Marisa Kirisame03/2015
535710^74079+621974080Patrick De Geest03/2016
535810^74079-28270774079Patrick De Geest03/2016
5359129^35098+274078Lelio R Paula05/2013
53602^246025-11212374061Enzo Doria06/2014
5361(67*10^74045+17)/374047Robert Price02/2017
53622^245823+6683174001Marek Hubal02/2017
53635^105869+4274000Lelio R Paula08/2014
5364(21*2^245806+1)/63455573991Lelio R Paula08/2012
5365(22699*2^245762+1)/11973985Lelio R Paula06/2014
5366(3^155048-7)/26273975Lelio R Paula06/2012
53679998*2^245696+373966Donovan Johnson10/2004
536813^66400-8073966Lelio R Paula01/2015
5370(2^245704+9)/2573963Lelio R Paula07/2012
536911^71023-717073963Enzo Doria01/2013
5371(31*2^245660-1)/11419573948Lelio R Paula01/2014
53722^245629-279781373942Eric Chen03/2016
53732^245557-15373921Lelio R Paula03/2012
53742^245525+186988173911Enzo Doria06/2016
53752^245522+15973910Lelio R Paula03/2012
537619^57783-5673891Lelio R Paula01/2015
53777*10^73888+7973889Robert Price02/2017
53786^94948+17428173884Mike Oakes02/2011
537911^70939-486073876Enzo Doria01/2013
53802^245372+5461573865Lelio R Paula05/2013
53812^245362-14373862Lelio R Paula03/2012
53827^87396+6^(87396-1)73859Robert Price03/2016
53835^105646-1424673844Enzo Doria02/2013
53852^245290-4173840Lelio R Paula03/2012
53842^245290-9439573840Lelio R Paula05/2013
53868*5^105600-773813Lelio R Paula10/2014
53877*5^105573-473794Lelio R Paula10/2014
538818^58742-480573738Enzo Doria03/2013
538913^66179+6673720Lelio R Paula01/2015
5390(82*10^73714-1)/973715Robert Price12/2014
5391(29*2^244856-1)/18612173706Lelio R Paula01/2014
5392(13*2^244840-1)/279973702Lelio R Paula01/2014
5393(13*10^73701+17)/373702Robert Price06/2015
5394(2^244787-1017)/2841173684Lelio R Paula07/2012
5395(3^154421-4)/2373677Lelio R Paula06/2012
53968*7^87170+573669Lelio R Paula10/2014
5397Phi(40100,-40100)73651Henri Lifchitz06/2013
53982^244618-229773638Yves Minet10/2009
53993*5^105344+873633Lelio R Paula10/2014
54005^105334-1409673626Enzo Doria02/2013
5401(2^244584-7)/1323707424303373614Lelio R Paula07/2012
54022^244465-11018573592Enzo Doria05/2014
54032^244443+4075573585Lelio R Paula05/2013
54042^244404+384173573Yves Minet03/2011
54052^244372-11062773564Enzo Doria05/2014
5406(3*2^244255+1)/24573527Lelio R Paula08/2012
5407(11*2^244245+1)/2373525Lelio R Paula08/2012
5408(15185*2^244187-1)/611173509Lelio R Paula04/2015
540918^58521+6573460Lelio R Paula01/2015
541013^65940+3673454Lelio R Paula01/2015
54115^105050-1473427Lelio R Paula08/2014
5412(((((((((((((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
541315^62410-4673400Lelio R Paula01/2015
54142^243733+186970773371Enzo Doria05/2016
541511^70439-543073355Enzo Doria01/2013
54162^243676-8773354Lelio R Paula03/2012
5417(101*10^73346-17)/373348Robert Price08/2016
54182^243621-11318573338Enzo Doria07/2014
5419(5*2^243610-1)/166973332Lelio R Paula01/2014
54202*5^104888-773314Lelio R Paula10/2014
5421(58695*2^243516-1)/98373308Lelio R Paula04/2015
5422(3^153648-2)/3342313809773299Lelio R Paula06/2012
542318^58376-525573278Enzo Doria03/2013
542411^70363+3273276Lelio R Paula02/2015
54252^243413+425773275Lelio R Paula05/2013
5426104824^5+5^10482473269Andrey Kulsha07/2010
54277^86689-6^8668973261Predrag Minovic09/2004
54282^243296+9019573240Lelio R Paula05/2013
5429p(15433)#/2-473218Robert Price12/2016
54302^243127+7135573189Lelio R Paula05/2013
54312^243116-24941973186Paul Bourdelais03/2013
5432(58695*2^243085-1)/1173180Lelio R Paula04/2015
543311^70262-9873171Lelio R Paula02/2015
5434(2^243034+47)/72270330373152Lelio R Paula07/2012
5435(2^242966+47)/4688773136Lelio R Paula07/2012
5436(43^44773-1)/4273134Robert Price04/2014
54376^93980-15835973131Mike Oakes02/2011
54386^93915+5373081Lelio R Paula01/2015
5439(74*10^73076+43)/973077Robert Price10/2015
5440(3^153125+2)/114495573054Lelio R Paula06/2012
54412^242632-11219973040Enzo Doria06/2014
5442V(351646)73029Serge Batalov03/2015
544318^58175-8573026Lelio R Paula01/2015
5444p(15395)#/2-473019Robert Price12/2016
5445(4^121271+3^121271)/773012Jean-Louis Charton03/2011
54468*6^93825-573011Lelio R Paula10/2014
5447(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
54486^93815+14373003Lelio R Paula01/2015
54496^93812+573000Wojciech Florek03/2006
545019^57078-6272989Lelio R Paula01/2015
5451(29*10^72985+91)/372986Robert Price03/2016
545211^70082-252072983Enzo Doria12/2012
54536^93773+13372970Lelio R Paula01/2015
54542^242328-5972948Lelio R Paula03/2012
54555^104358-1301672944Enzo Doria02/2013
5456(75*10^72941-57)/9972941Ray Chandler03/2011
545712^67585-9572937Lelio R Paula02/2015
54582^242230-11328572919Enzo Doria07/2014
5459(5*10^72916-11)/372917Erik Branger12/2013
54602^242220-11039972916Enzo Doria05/2014
54612^242205-11341372911Enzo Doria07/2014
5462(3^152809+3^76405+1)/772908Serge Batalov03/2014
54632^242175+7424372902Yves Minet03/2011
54642^242150+1765972895Lelio R Paula11/2009
546511^69982-234072879Enzo Doria12/2012
5466(23*2^242093+1)/1011772875Lelio R Paula08/2012
5467(67607*2^242043+1)/3326372863Lelio R Paula06/2014
54682^242032+8772859Lelio R Paula03/2012
54692^241968-11059572840Enzo Doria05/2014
5470(10^72821+71)/972821Robert Price11/2014
54712^241852-6487572805Lelio R Paula05/2013
5472F(348307)/2056289086590809372776Donovan Johnson07/2007
5473(67*10^72772+23)/972773Ray Chandler11/2010
5474(8*10^72759+67)/372760Robert Price01/2017
54752^241670+14572750Lelio R Paula03/2012
54765^104074+5272745Lelio R Paula08/2014
5477(3^152466-5)/72472742Lelio R Paula06/2012
547820^55908-4172738Lelio R Paula01/2015
5479(73*10^72735+53)/972736Robert Price10/2015
548010^72730+22401172731Patrick De Geest05/2013
548110^72730-9972730Robert Price05/2011
5482(11^69833+3^69833)/1472723Robert Price03/2013
5483(88*10^72711-43)/972712Robert Price11/2015
54843^152379+28072704Lelio R Paula01/2015
5485(25*10^72703-241)/972704Robert Price01/2017
548617^59077-9072692Lelio R Paula01/2015
548765^40096+5872691Lelio R Paula01/2016
5488(29*2^241446-1)/24572682Lelio R Paula01/2014
549011^69783-3840000072672Enzo Doria01/2013
54892^241409-11290372672Enzo Doria06/2014
5491(3^152287+1)/472659Paul Bourdelais04/2008
54923^152249-5672642Lelio R Paula01/2015
549310^72631+3772632Robert Price01/2011
549410^72631-881372631Patrick De Geest05/2013
5495(19*2^241254+1)/10172624Lelio R Paula08/2012
5496(9^76103+8^76103)/1772620Robert Price12/2012
54972^241220-11233772615Enzo Doria06/2014
5498(82*10^72612+449)/972613Robert Price02/2017
54992^241169-1579372600Enzo Doria04/2013
55009*10^72595+1172596Robert Kinser01/2017


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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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