PRP Records

Probable Primes Top 10000

(202622 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
30012^336958+79101435Lelio R Paula10/2009
30022^336942+169101430Lelio R Paula10/2009
3003(15185*2^336894-1)/7939101416Lelio R Paula05/2015
30042^336871+257463101409Tony Prest / Never Odd Or Even04/2016
30052^336871+318105101409Tony Prest / Never Odd Or Even04/2016
30062^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
30072^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
30082^336871+389273101409Tony Prest / Never Odd Or Even04/2016
30092^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
30102^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
30112^336871+586905101409Tony Prest / Never Odd Or Even04/2016
30122^336871+674571101409Tony Prest / Never Odd Or Even04/2016
30132^336871+707009101409Tony Prest / Never Odd Or Even04/2016
30142^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
30152^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
30162^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
30172^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
30182^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
30192^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
30202^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
30212^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3022(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3023(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3024(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3025(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
30262^336842+94065101400Lelio R Paula09/2016
3027(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3028(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3029(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3030(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3031(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3032(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3033(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
303410^101369+203811101370Patrick De Geest11/2016
303510^101369-99101369Lelio R Paula09/2016
3036(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
30372^336701-113563101358Enzo Doria08/2014
30382^336644-109023101340Enzo Doria04/2014
30392^336601-21081101327Enzo Doria06/2013
304020^77869+63101310Lelio R Paula09/2016
3041(13*2^336523-1)/19101304Lelio R Paula03/2014
30436^130179-137101299Lelio R Paula10/2016
3042(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3044(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3045(2^336448+9)/497405101276Lelio R Paula12/2013
30462^336369-19753101258Enzo Doria05/2013
30472^336350-344291101252Enzo Doria07/2015
30482^336243-108777101220Enzo Doria03/2014
3049(31*2^336189-1)/19101204Lelio R Paula03/2014
3050(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
30512^336150-20393101192Enzo Doria06/2013
30522^336112-1865249101180Enzo Doria03/2016
30532^336103-109015101178Enzo Doria04/2014
305413^90809-96101157Lelio R Paula10/2016
305519^79098-30101147Lelio R Paula10/2016
305619^79095+88101144Lelio R Paula10/2016
305715^85976+32101116Lelio R Paula10/2016
3058(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3059(4^167933+17)/3101106Robert Price02/2017
30602^335858+153101104Lelio R Paula10/2009
30616^129918-35101096Lelio R Paula10/2016
30623^211885-70101095Lelio R Paula09/2016
3063(29*2^335835-1)/550599101093Lelio R Paula03/2014
30642^335818-20033101092Enzo Doria06/2013
30652^335813-110083101090Enzo Doria04/2014
30662^335804+2155101088Lelio R Paula09/2016
30672^335784-16145101082Enzo Doria04/2013
306811^97051+62101069Lelio R Paula10/2016
3069(2^335691-3)/26515101049Lelio R Paula12/2013
30702^335658-94395101044Lelio R Paula09/2016
30712^335586+169101022Lelio R Paula10/2009
3072(56^57787-1)/55101021Paul Bourdelais08/2017
307347599!2+1024100991Robert Price02/2015
30742^335468-18629100986Enzo Doria05/2013
30752^335454-20961100982Enzo Doria06/2013
307610^100978+61100979Lelio R Paula09/2016
307710^100978-156437100978Patrick De Geest11/2016
3078(15*2^335417+1)/481100970Lelio R Paula12/2013
30792^335403-1859167100967Enzo Doria03/2016
30809*2^335364-5100956Lelio R Paula08/2014
30812^335349+72287100951Enzo Doria04/2016
30822^335329+16095100945Lelio R Paula09/2016
3083232823#+233663100937Makoto Morimoto10/2017
30842^335237-20893100917Enzo Doria06/2013
30852^335222-19337100912Enzo Doria05/2013
30862^335222-109985100912Enzo Doria04/2014
30872^335182-17237100900Enzo Doria05/2013
30882^335043-16737100858Enzo Doria05/2013
3089(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
30902^335038-20633100857Enzo Doria06/2013
30912^335031+1873373100855Enzo Doria06/2016
30923^211354-8816100842Enzo Doria05/2014
30932^334984-112757100841Enzo Doria06/2014
30952^334857+48527100803Lelio R Paula08/2011
309412^93406+29100803Lelio R Paula10/2016
3096(5*2^334825+1)/47100792Lelio R Paula12/2013
30972^334809-13100788Lelio R Paula04/2011
3098(82*10^100780-1)/9100781Robert Price12/2014
3099(2^334779+47)/5100778Lelio R Paula12/2013
31002^334751+2049100771Lelio R Paula09/2016
310113^90443-98100749Lelio R Paula10/2016
3102(24737*2^334628+1)/3100737Lelio R Paula07/2014
310315^85639-28100720Lelio R Paula10/2016
31042^334562+577294575100711Lelio R Paula09/2016
31054*3^211077-5100710Lelio R Paula08/2014
31062^334524+145100702Lelio R Paula07/2009
3107(1017*2^334391-1)/3535100662Lelio R Paula05/2015
31082^334294-113111100633Enzo Doria07/2014
31096^129308-17723100622Enzo Doria03/2013
31106^129305+95100619Lelio R Paula10/2016
31112^334244-1167100618Lelio R Paula09/2016
3112(21*2^334050+1)/935100558Lelio R Paula12/2013
3113(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3114(35*10^100542+1)/9100543Serge Batalov11/2010
311513^90251+24100535Lelio R Paula10/2016
31162^333963+789100533Lelio R Paula08/2011
31172^333919-1840087100520Enzo Doria06/2015
31182^333911+72623100518Enzo Doria04/2016
311918^80064-67100503Lelio R Paula10/2016
31205^143742-48100472Lelio R Paula10/2016
31212^333757-112123100471Enzo Doria06/2014
31222^333603-108861100425Enzo Doria03/2014
31239*7^118818-2100414Lelio R Paula11/2014
31242^333546-17097100408Enzo Doria05/2013
312517^81597+72100401Lelio R Paula10/2016
3126p(20559)#/2+8100384Robert Price01/2017
312711^96390-24100380Lelio R Paula10/2016
31284832563059*2^333333+30029100353Donovan Johnson01/2008
31292^333354+763100350Lelio R Paula08/2011
31302^333289-109483100330Enzo Doria04/2014
31312^333240-2790209100316Enzo Doria03/2016
3133(2^333227-2^166614+1)/510031111/2006
31322^333225+719100311Lelio R Paula08/2011
31342^333221-2785333100310Enzo Doria10/2015
313576^53332-75100308Norbert Schneider02/2015
31366^128892-17573100298Enzo Doria03/2013
31372^333105-113215100275Enzo Doria07/2014
3138(31*2^333102+1)/2375100272Lelio R Paula11/2013
313917^81476-74100253Lelio R Paula10/2016
314017^81417-16100180Theodore Burton11/2005
31412^332739-113215100165Enzo Doria07/2014
31422^332730-1865621100162Enzo Doria03/2016
314391^51127-2100160Lelio R Paula09/2013
314415^85159-32100155Lelio R Paula10/2016
31456^128661+97100118Lelio R Paula10/2016
314619^78285+40100108Lelio R Paula07/2016
31476^128640+5100102Lelio R Paula11/2014
31486^128565-127100044Lelio R Paula08/2016
31492^332309-133100035Lelio R Paula02/2011
31502^332307+731100035Lelio R Paula07/2011
31512^332301+12927100033Lelio R Paula04/2013
315212^92684-13100023Lelio R Paula07/2016
318825206!+p(4114)100001Henri Lifchitz09/2005
318925206!-p(5447)100001Henri Lifchitz10/2005
319025206!-p(12402)100001Henri Lifchitz04/2006
319125206!-p(16290)100001Henri Lifchitz09/2006
319225206!-p(19647)100001Henri Lifchitz02/2007
31932^332194+11473100001Henri Lifchitz03/2007
316410^100000+342909100001Milton L. Brown12/2007
319410^100000+346579100001Robert Price04/2012
319510^100000+829767100001Robert Price05/2012
319610^100000+871899100001Robert Price05/2012
319710^100000+1475997100001Robert Price07/2012
317810^100000+1751769100001Robert Price08/2012
317910^100000+2155489100001Robert Price10/2012
318010^100000+2483527100001Robert Price12/2012
318110^100000+2503087100001Robert Price12/2012
318210^100000+2686179100001Robert Price12/2012
318310^100000+2688933100001Robert Price12/2012
318410^100000+3667159100001Robert Price08/2013
316110^100000+3938473100001Robert Price05/2015
316210^100000+3979761100001Robert Price05/2015
316310^100000+4293973100001Robert Price09/2015
318510^100000+4858267100001Robert Price12/2015
318610^100000+5113299100001Robert Price02/2016
318710^100000+5169411100001Robert Price02/2016
315310^100000+5354043100001Robert Price05/2016
315410^100000+5717979100001Robert Price05/2016
315510^100000+6080631100001Robert Price07/2016
315610^100000+6308469100001Robert Price07/2016
315710^100000+6512023100001Robert Price08/2016
315810^100000+6596557100001Robert Price08/2016
315910^100000+7115409100001Robert Price10/2016
316010^100000+7235803100001Robert Price10/2016
316510^100000+7867333100001Robert Price12/2016
316610^100000+8743093100001Robert Price02/2017
316710^100000+8955391100001Robert Price03/2017
316810^100000+9180019100001Robert Price03/2017
316910^100000+9225987100001Robert Price04/2017
317010^100000+9265587100001Robert Price04/2017
317110^100000+9287049100001Robert Price04/2017
317210^100000+9425053100001Robert Price05/2017
317310^100000+9450769100001Robert Price05/2017
317410^100000+9528747100001Robert Smith05/2017
317510^100000+9548071100001Robert Price06/2017
317610^100000+10064287100001Robert Price08/2017
317710^100000+10229569100001Robert Price10/2017
319910^99999+309403100000Daniel Heuer01/2004
319810^100000-260199100000Patrick De Geest01/2010
320010^99999-5951199999Patrick De Geest07/2009
32012^332141-11307399985Enzo Doria07/2014
3202(3^209561+2)/72810125599978Lelio R Paula09/2013
32032^332085+186589799968Enzo Doria03/2016
3204(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
32052^332023+19199949Lelio R Paula02/2011
32062^331938+7114999924Enzo Doria04/2016
32072^331932-7879599922Lelio R Paula09/2016
32082^331921+77199919Lelio R Paula01/2013
3209(3^209419-2)/513275599912Lelio R Paula09/2013
32102^331860-11498999900Enzo Doria05/2015
32112^331746-1165599866Lelio R Paula09/2016
321211^95891-2899861Lelio R Paula08/2016
3213(2^331694-5)/1199849Lelio R Paula10/2013
3214(3^209246+7)/6499834Lelio R Paula09/2013
321515^84866-5299811Lelio R Paula08/2016
321613^89600+3099810Lelio R Paula08/2016
32175^142772-3899794Lelio R Paula08/2016
3218(23*2^331459+1)/47599778Lelio R Paula11/2013
32192^331416-331416+199767Robert Price10/2014
32202^331256-5799718Lelio R Paula12/2012
32212^331185+73799697Lelio R Paula01/2013
3222(4*10^99693+149)/999693Robert Price03/2017
32232^331154+188052799688Enzo Doria10/2016
3224(19^77951+1)/2099679Paul Bourdelais03/2010
32252^331110+187045999675Enzo Doria05/2016
32265*2^331075+799665Lelio R Paula08/2014
3227(16*10^99656-31)/399657Robert Price03/2016
32282^330968+34599632Lelio R Paula09/2016
32302*5^142528-799624Lelio R Paula11/2014
32292^330942+7732999624Enzo Doria05/2016
323114^86914-9999615Lelio R Paula08/2016
3232(19*2^330902+1)/7799611Lelio R Paula11/2013
32332^330845+7168799595Enzo Doria04/2016
3234(23*2^330770+1)/399573Lelio R Paula11/2013
32352^330735+841599562Lelio R Paula09/2016
32362^330720+7407199557Enzo Doria04/2016
323731^66738-299531Lelio R Paula09/2013
32387*3^208567+499513Lelio R Paula08/2014
3239(13*10^99508+47)/399509Robert Price01/2017
32402^330553+77999507Lelio R Paula01/2013
324115^84606-9499505Lelio R Paula08/2016
32426^127858+4799493Lelio R Paula08/2016
32435^142337+4899490Lelio R Paula08/2016
32447^117724-2099489Lelio R Paula08/2016
3245(29*10^99474-17)/399475Erik Branger09/2014
3246(9*2^330407-1)/799463Lelio R Paula03/2014
3247(68*10^99441+7)/399443Robert Price03/2016
324846^59791-45^5979199418Jean-Louis Charton01/2013
324923839^14802+14802^2383999417Hans Havermann02/2018
3250(2*10^99408+529)/999408Robert Price01/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!