PRP Records

Probable Primes Top 10000

(181746 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 ?
55012^248816+111174902Lelio R Paula01/2011
5502V(388219)74890Serge Batalov03/2015
55032*F(358297)-174880Henri Lifchitz12/2009
5504(22*10^74874-31)/974875Robert Price04/2015
550511^71892-7680000074868Enzo Doria01/2013
55069*5^107107-474866Lelio R Paula10/2014
55072^248678-71011174860Paul Bourdelais03/2013
550813^67194+1274851Lelio R Paula01/2015
5509(7*2^248634+1)/7174846Lelio R Paula08/2012
551011^71867-309074842Enzo Doria12/2012
55112^248609+26214574839Lelio R Paula05/2013
55123^156852+5074838Lelio R Paula01/2015
551318^59607-1174824Lelio R Paula01/2015
55142^248556-11050774823Enzo Doria05/2014
55157^88531-3674818Lelio R Paula01/2015
5516p(15738)#/2+102474814Robert Price07/2017
55174*3^156740-574785Lelio R Paula05/2014
5518(32*10^74773-41)/974774Robert Price05/2015
5519(29*2^248384-1)/1374772Lelio R Paula01/2014
552019401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
55212^248357-1279741374763Enzo Doria03/2016
552242^46057+4174762Lelio R Paula07/2012
552311^71784-300074756Enzo Doria12/2012
552419^58458+1874754Lelio R Paula01/2015
552512^69265-3574750Lelio R Paula02/2015
552611^71771-4800074742Enzo Doria12/2012
5527(7*10^74741+197)/374742Robert Price07/2017
5528(2^248282-5)/5012974736Lelio R Paula06/2012
55292^248252-11010574732Enzo Doria04/2014
5530(7*10^74729+71)/374730Robert Price03/2016
55313^156614-5074724Lelio R Paula01/2015
5532(7*2^248213+1)/13574719Lelio R Paula07/2012
5533(2^248173+78557)/76774705Lelio R Paula07/2012
5534125^35622+12474697Norbert Schneider02/2015
5535(19*2^248099-1)/2974686Lelio R Paula01/2014
5536(86*10^74676-41)/974677Robert Price11/2015
553710^74670+3174671Robert Price01/2011
553810^74670-12246374670Patrick De Geest05/2013
55392^248036-6974667Lelio R Paula03/2012
554011^71698-600074666Enzo Doria12/2012
554158*(10^(3*24887)-1)/111-174661Robert Price10/2014
554214^65139-4574658Lelio R Paula01/2015
55436^95921-13374642Lelio R Paula01/2015
554411^71675+7874642Lelio R Paula02/2015
554518^59449-9174625Lelio R Paula01/2015
55466^95864-1604374597Enzo Doria02/2013
55475*7^88261+674590Lelio R Paula10/2014
55489*5^106710+474589Lelio R Paula10/2014
5549(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
5550(265*10^74579+17)/374581Robert Price05/2016
5551(2^247759-1017)/331831171774574Lelio R Paula07/2012
55525^106682-2474568Lelio R Paula08/2014
5553474^27863+27863^47474556Norbert Schneider01/2017
5554(35365^16384+1)/274524Lelio R Paula11/2011
55553^156161+266074508Lelio R Paula01/2015
55562^247474-5869574498Lelio R Paula05/2013
555711^71519-9074480Enzo Doria07/2012
5558(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5560(2^247394-7)/374473Lelio R Paula06/2012
555918^59328+1774473Lelio R Paula01/2015
55612^247379-18174469Lelio R Paula03/2012
5562(15*2^247370-1)/47974465Lelio R Paula01/2014
55632^247344+204774458Lelio R Paula05/2013
55642^247311-101774449Lelio R Paula05/2013
55652^247280+774439Lelio R Paula03/2012
5566(68*10^74434+13)/974435Ray Chandler11/2010
55673^156004-6274433Lelio R Paula01/2015
556836095!2-6474416Robert Price06/2015
55692^247165-374405M. Frind & P. Underwood07/2002
55702^247150+3276974400Lelio R Paula05/2013
557112^68911+7374368Lelio R Paula01/2015
55722^246999+7490374355Enzo Doria04/2016
55732^246989-11064374352Enzo Doria05/2014
557410^74350+27943974351Patrick De Geest07/2017
5577(10^74350+11)/374350Robert Price11/2014
557510^74350-40000000174350Robert Price07/2017
557610^74350-71624174350Patrick De Geest07/2017
557810^74335+1365974336Patrick De Geest05/2013
557910^74335-5374335Robert Price05/2011
55802^246906-121574327Lelio R Paula05/2013
55812^246848+11174309Lelio R Paula03/2012
55826^95490-1844374306Enzo Doria03/2013
558318^59188-236974298Enzo Doria03/2013
5584(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
55852^246744+4075574278Lelio R Paula05/2013
5586(29*10^74276+91)/374277Robert Price03/2016
55876^95441+16374268Lelio R Paula01/2015
5588V(390863)74258Serge Batalov03/2015
558910^74254+9174255Robert Price03/2011
5590(19*10^74253-1)/974254Ray Chandler02/2012
559110^74254-13056974254Patrick De Geest05/2013
5592771^25718+25718^77174250Norbert Schneider10/2016
55932^246618+42774240Henri Lifchitz02/2005
559488*10^74234+374236Robert Price11/2016
55958*10^74234-4974235Robert Price04/2016
55962^246578+1228574228Lelio R Paula05/2013
5597(3^155569-5)/274225Lelio R Paula06/2012
559813^66628+4674220Lelio R Paula01/2015
55992^246476-1729574197Lelio R Paula05/2013
5600(15185*2^246432-1)/1374187Lelio R Paula04/2015
56015*2^246413-374179Lelio R Paula05/2014
56022^246386-2863574170Lelio R Paula05/2013
56032^246334-11124574154Enzo Doria05/2014
56043*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
560515^63045+8274147Lelio R Paula01/2015
560619255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
56072^246268-11050774135Enzo Doria05/2014
56083^155328+266074111Lelio R Paula01/2015
56092^246148-278624974098Enzo Doria03/2016
5610(16*10^74092-19)/374093Robert Price03/2016
56112^246115-11076774088Enzo Doria05/2014
56127^87666-6874087Lelio R Paula08/2014
561310^74079+114514191974080Marisa Kirisame03/2015
561410^74079+621974080Patrick De Geest03/2016
561510^74079-28270774079Patrick De Geest03/2016
5616129^35098+274078Lelio R Paula05/2013
56172^246025-11212374061Enzo Doria06/2014
5618(67*10^74045+17)/374047Robert Price02/2017
56192^245823+6683174001Marek Hubal02/2017
56205^105869+4274000Lelio R Paula08/2014
5621(21*2^245806+1)/63455573991Lelio R Paula08/2012
5622(22699*2^245762+1)/11973985Lelio R Paula06/2014
5623(3^155048-7)/26273975Lelio R Paula06/2012
56249998*2^245696+373966Donovan Johnson10/2004
562513^66400-8073966Lelio R Paula01/2015
5626(2^245704+9)/2573963Lelio R Paula07/2012
562811^71023-717073963Enzo Doria01/2013
56273*10^73962+1373963Robert Price08/2017
5629(31*2^245660-1)/11419573948Lelio R Paula01/2014
56302^245629-279781373942Eric Chen03/2016
56312^245557-15373921Lelio R Paula03/2012
56322^245525+186988173911Enzo Doria06/2016
56332^245522+15973910Lelio R Paula03/2012
5634(13*10^73891-43)/373892Robert Price08/2017
563519^57783-5673891Lelio R Paula01/2015
56367*10^73888+7973889Robert Price02/2017
56376^94948+17428173884Mike Oakes02/2011
563811^70939-486073876Enzo Doria01/2013
56392^245372+5461573865Lelio R Paula05/2013
56402^245362-14373862Lelio R Paula03/2012
56417^87396+6^(87396-1)73859Robert Price03/2016
5642(22*10^73853-37)/373854Robert Price05/2017
56435^105646-1424673844Enzo Doria02/2013
56452^245290-4173840Lelio R Paula03/2012
56442^245290-9439573840Lelio R Paula05/2013
56468*5^105600-773813Lelio R Paula10/2014
56477*5^105573-473794Lelio R Paula10/2014
564818^58742-480573738Enzo Doria03/2013
564913^66179+6673720Lelio R Paula01/2015
5650(82*10^73714-1)/973715Robert Price12/2014
5651(29*2^244856-1)/18612173706Lelio R Paula01/2014
5652(13*2^244840-1)/279973702Lelio R Paula01/2014
5653(13*10^73701+17)/373702Robert Price06/2015
5654(2^244787-1017)/2841173684Lelio R Paula07/2012
5655(3^154421-4)/2373677Lelio R Paula06/2012
56568*7^87170+573669Lelio R Paula10/2014
5657Phi(40100,-40100)73651Henri Lifchitz06/2013
5658(4*10^73647-19)/373648Robert Price06/2017
56592^244618-229773638Yves Minet10/2009
56603*5^105344+873633Lelio R Paula10/2014
56615^105334-1409673626Enzo Doria02/2013
5662(2^244584-7)/1323707424303373614Lelio R Paula07/2012
56632^244465-11018573592Enzo Doria05/2014
56642^244443+4075573585Lelio R Paula05/2013
56652^244404+384173573Yves Minet03/2011
56662^244372-11062773564Enzo Doria05/2014
5667(3*2^244255+1)/24573527Lelio R Paula08/2012
5668(11*2^244245+1)/2373525Lelio R Paula08/2012
5669(15185*2^244187-1)/611173509Lelio R Paula04/2015
5670(91^37507+1)/9273476Paul Bourdelais08/2017
567118^58521+6573460Lelio R Paula01/2015
567213^65940+3673454Lelio R Paula01/2015
56735^105050-1473427Lelio R Paula08/2014
5674(((((((((((((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
567515^62410-4673400Lelio R Paula01/2015
56762^243733+186970773371Enzo Doria05/2016
567711^70439-543073355Enzo Doria01/2013
56782^243676-8773354Lelio R Paula03/2012
5679(101*10^73346-17)/373348Robert Price08/2016
56802^243621-11318573338Enzo Doria07/2014
5681(5*2^243610-1)/166973332Lelio R Paula01/2014
56822*5^104888-773314Lelio R Paula10/2014
5683(58695*2^243516-1)/98373308Lelio R Paula04/2015
5684(3^153648-2)/3342313809773299Lelio R Paula06/2012
568518^58376-525573278Enzo Doria03/2013
568611^70363+3273276Lelio R Paula02/2015
56872^243413+425773275Lelio R Paula05/2013
5688104824^5+5^10482473269Andrey Kulsha07/2010
56897^86689-6^8668973261Predrag Minovic09/2004
56902^243296+9019573240Lelio R Paula05/2013
5691p(15433)#/2-473218Robert Price12/2016
56922^243127+7135573189Lelio R Paula05/2013
56932^243116-24941973186Paul Bourdelais03/2013
5694(58695*2^243085-1)/1173180Lelio R Paula04/2015
569511^70262-9873171Lelio R Paula02/2015
5696(2^243034+47)/72270330373152Lelio R Paula07/2012
5697(2^242966+47)/4688773136Lelio R Paula07/2012
5698(43^44773-1)/4273134Robert Price04/2014
56996^93980-15835973131Mike Oakes02/2011
57006^93915+5373081Lelio R Paula01/2015
5701(74*10^73076+43)/973077Robert Price10/2015
5702(3^153125+2)/114495573054Lelio R Paula06/2012
57032^242632-11219973040Enzo Doria06/2014
5704V(351646)73029Serge Batalov03/2015
570518^58175-8573026Lelio R Paula01/2015
5706p(15395)#/2-473019Robert Price12/2016
5707(4^121271+3^121271)/773012Jean-Louis Charton03/2011
57088*6^93825-573011Lelio R Paula10/2014
5710(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
5709(73^39181+1)/7473005Paul Bourdelais08/2017
57116^93815+14373003Lelio R Paula01/2015
57126^93812+573000Wojciech Florek03/2006
571319^57078-6272989Lelio R Paula01/2015
5714(29*10^72985+91)/372986Robert Price03/2016
571511^70082-252072983Enzo Doria12/2012
57166^93773+13372970Lelio R Paula01/2015
57172^242328-5972948Lelio R Paula03/2012
57185^104358-1301672944Enzo Doria02/2013
5719(75*10^72941-57)/9972941Ray Chandler03/2011
572012^67585-9572937Lelio R Paula02/2015
57212^242230-11328572919Enzo Doria07/2014
5722(5*10^72916-11)/372917Erik Branger12/2013
57232^242220-11039972916Enzo Doria05/2014
57242^242205-11341372911Enzo Doria07/2014
5725(3^152809+3^76405+1)/772908Serge Batalov03/2014
57262^242175+7424372902Yves Minet03/2011
57272^242150+1765972895Lelio R Paula11/2009
572811^69982-234072879Enzo Doria12/2012
5729(23*2^242093+1)/1011772875Lelio R Paula08/2012
5730(67607*2^242043+1)/3326372863Lelio R Paula06/2014
57312^242032+8772859Lelio R Paula03/2012
57322^241968-11059572840Enzo Doria05/2014
5733(10^72821+71)/972821Robert Price11/2014
57342^241852-6487572805Lelio R Paula05/2013
5735F(348307)/2056289086590809372776Donovan Johnson07/2007
5736(67*10^72772+23)/972773Ray Chandler11/2010
5737(8*10^72759+67)/372760Robert Price01/2017
57382^241670+14572750Lelio R Paula03/2012
57395^104074+5272745Lelio R Paula08/2014
5740(3^152466-5)/72472742Lelio R Paula06/2012
574120^55908-4172738Lelio R Paula01/2015
5742(73*10^72735+53)/972736Robert Price10/2015
574310^72730+22401172731Patrick De Geest05/2013
574410^72730-9972730Robert Price05/2011
5745(11^69833+3^69833)/1472723Robert Price03/2013
5746(88*10^72711-43)/972712Robert Price11/2015
57473^152379+28072704Lelio R Paula01/2015
5748(25*10^72703-241)/972704Robert Price01/2017
5749(47*10^72696+133)/972697Robert Price04/2017
575017^59077-9072692Lelio R Paula01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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