PRP Records

Probable Primes Top 10000

(259919 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 (> 50000) Who ? When ?
2512^1116184+1883521336005Enzo Doria02/2017
2522^1114517+1880087335504Enzo Doria10/2016
253(3^700897+1)/4334413Paul Bourdelais04/2010
2542^1104408-114539332460Enzo Doria03/2015
2552^1101921+82085331712Enzo Doria10/2016
2562^1100655+683513331331Enzo Doria01/2017
257(10^330906+71)/9330906Serge Batalov07/2015
2582^1098346+482899330636Enzo Doria11/2016
2592^1095679+1878713329833Enzo Doria09/2016
2602^1094740-1851539329550Enzo Doria08/2015
2612^1091469-379369328565Enzo Doria03/2014
2622^1085750+582349326844Enzo Doria11/2016
2632^1083596+483061326195Enzo Doria12/2016
264(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
2652^1082908+583561325988Enzo Doria05/2017
26630^220411-29^220411325574Jean-Louis Charton10/2018
2672^1078242+1881649324584Enzo Doria11/2016
2682^1077737+1880117324432Enzo Doria10/2016
2692^1075425+1880117323736Enzo Doria10/2016
27010^322999+187071323000Stefano Morozzi03/2019
2712^1072146+1886869322749Enzo Doria04/2017
2722^1072118-7321953322740Enzo Doria02/2015
2732^1071026+1886869322411Enzo Doria04/2017
2742^1070539+1880633322265Enzo Doria10/2016
2752^1069293-1147195321890Enzo Doria05/2015
2762^1065968+1880941320889Enzo Doria10/2016
2772^1065897-1147195320867Enzo Doria05/2015
2782^1063427+1882103320124Enzo Doria12/2016
2792^1061095-1061095319422Henri Lifchitz10/2013
2802^1060950+653119319378Enzo Doria12/2016
2812^1060363+782753319202Enzo Doria11/2016
2822^1054736+483061317508Enzo Doria12/2016
2832^1053965+1879667317276Enzo Doria10/2016
2842^1052186-458165316740Enzo Doria03/2015
2852^1046613-114685315062Enzo Doria04/2015
2862^1045625-459373314765Enzo Doria06/2015
287(7*10^314564-61)/9314564Erik Branger09/2016
288(7^371669-1)/6314096Paul Bourdelais02/2010
2892^1041944+283051313657Enzo Doria12/2016
2902^1041153-114391313419Enzo Doria02/2015
2912^1038871+1866983312732Enzo Doria04/2016
2922^1037647+1881263312363Enzo Doria11/2016
2932^1037226+1879699312237Enzo Doria10/2016
2942^1036867+1865843312129Enzo Doria02/2016
2952^1036020-114539311874Enzo Doria02/2015
2962^1032240+1883431310736Enzo Doria01/2017
2972^1030352+1870021310167Enzo Doria06/2016
2982^1030046+1882843310075Enzo Doria11/2016
299(11^293831-1)/10305993Paul Bourdelais03/2010
3002^1015321-1015321305643Henri Lifchitz08/2013
3012^1014224-2791229305312Enzo Doria01/2016
3022^1010751-107709304267Enzo Doria03/2014
303(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
3042^1009577+1869587303913Enzo Doria06/2016
3058^336419-7^336419303817Jean-Louis Charton01/2008
3062^1008301+1869377303529Enzo Doria06/2016
307(2^1007838+5)/3303389Serge Batalov08/2015
3082^1005326+383059302634Enzo Doria12/2016
3092^1004929+1877567302514Enzo Doria08/2016
3102^1003494+1874899302082Enzo Doria06/2016
3112^1003046+60529301947Enzo Doria04/2016
3122^1000647+1881353301225Enzo Doria11/2016
3132^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
3142^999646+1874029300924Enzo Doria06/2016
31510^300476+3300477Ed Trice10/2012
31610^300476-530913300476Patrick De Geest03/2016
3172^998053+1879667300444Enzo Doria09/2016
318314738^9+9^314738300337Anatoly F. Selevich02/2011
3197^355039-6^355039300043Jean-Louis Charton05/2011
32010^300000+287389300001Patrick De Geest10/2019
32110^300000-83657300000Patrick De Geest10/2019
322numbpart(72526161452)299999Serge Batalov04/2017
3232^996182-114431299881Enzo Doria02/2015
3242^995214-2788361299590Enzo Doria12/2015
3252^994791-114319299462Enzo Doria01/2015
3262^994490-1863791299372Enzo Doria01/2016
3272^993322+1885729299020Enzo Doria03/2017
3282^992711-2788807298836Enzo Doria12/2015
3292^992525-114199298780Enzo Doria12/2014
3302^992329+1884707298721Enzo Doria02/2017
331(2^986191+1)/3296873Vincent Diepeveen06/2008
3322^985217-114553296580Enzo Doria03/2015
333(76^157649-1)/75296507Paul Bourdelais07/2019
3342^984131-1828009296253Enzo Doria01/2015
3352^983620+60451296100Phil Moore03/2008
3362^982721-2683295829Yves Minet02/2016
3372^981298-2788421295401Enzo Doria12/2015
3382^981163-2790967295360Enzo Doria12/2015
3392^979594+1865839294888Enzo Doria02/2016
3402^976760+1885021294035Enzo Doria02/2017
3412^974441+1878407293336Enzo Doria08/2016
3422^974180+1876831293258Enzo Doria07/2016
3432^974170+453319293255Enzo Doria01/2017
3442^972744-114419292826Enzo Doria03/2015
345CopelandErdos(292447)292447Mark Rodenkirch12/2015
3462^970911+1873373292274Enzo Doria07/2016
3472^970670+383059292201Enzo Doria12/2016
3482^970141-100363292042Enzo Doria02/2014
3492^969945+1874717291983Enzo Doria06/2016
3502^969384+1880701291814Enzo Doria10/2016
351(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
3522^962194+60139289650Enzo Doria02/2016
3532^959307-1861507288781Enzo Doria11/2015
3542^957372+283531288198Enzo Doria02/2017
3552^957192-1864049288144Enzo Doria01/2016
3562^956446+1875199287919Enzo Doria06/2016
357(17^233689+1)/18287542Paul Bourdelais09/2013
3582^955178+1883587287538Enzo Doria12/2016
3592^954001+1875257287183Enzo Doria07/2016
360(23891^65536+1)/2286932Serge Batalov03/2018
3612^952268+1878601286662Enzo Doria09/2016
3622^950801+81557286220Enzo Doria08/2016
363(11*2^948635-13)/15285568Renaud Lifchitz11/2011
364(54^164839+1)/55285565Paul Bourdelais07/2019
3652^948510+782569285530Enzo Doria10/2016
3662^948374-114137285490Enzo Doria01/2015
3672^947739+1872923285298Enzo Doria06/2016
3682^942533+82067283731Enzo Doria09/2016
3692^940950+1874989283255Enzo Doria06/2016
3702^940426-2786141283097Enzo Doria11/2015
3712^939881-114115282933Enzo Doria12/2014
37210^282493+632551282494Patrick De Geest02/2017
37410^282493-9^282493282493Jean-Louis Charton03/2007
37310^282493-132327282493Patrick De Geest02/2017
3753^591827-2^591827282374Mike Oakes08/2009
376Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
3772^936716-1835519281980Enzo Doria04/2015
3782^936588+79411281942Enzo Doria06/2016
3792^936047+1877423281779Enzo Doria08/2016
3802^935713+1869377281678Enzo Doria05/2016
3812^933082+1877059280886Enzo Doria08/2016
382(5*10^280710+1)/3280711Serge Batalov10/2014
383(42^172663+1)/43280274Paul Bourdelais07/2019
384(10^279978+11)/3279978Serge Batalov07/2015
3852^929524-1864829279815Enzo Doria01/2016
3862^929152+60181279703Enzo Doria02/2016
3872^928621-2787883279543Enzo Doria11/2015
388(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
3892^927429+1882277279184Enzo Doria12/2016
390(71^150697-1)/70278978Paul Bourdelais07/2019
391(33^183661-1)/32278891Paul Bourdelais12/2018
392(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
3932^925330-1301278553Yves Minet06/2015
394(21^210599+1)/22278457Paul Bourdelais08/2013
3952^923261-69175277930Enzo Doria11/2015
396757^96487-756^96487277796Jean-Louis Charton12/2012
397((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
398(5^396413-1)/4277081Paul Bourdelais06/2010
3992^920318+2792299277044Enzo Doria02/2016
4002^918596-2786939276525Enzo Doria11/2015
4012^916639+60563275936Enzo Doria04/2016
4022^916385-2786383275860Enzo Doria11/2015
4032^915928+82081275722Enzo Doria09/2016
4042^915576-114137275616Enzo Doria01/2015
4052^914828+1876741275391Enzo Doria07/2016
4062^914757-2203275370Yves Minet12/2015
4072^911900+1871245274510Enzo Doria05/2016
4082^910490+283429274085Enzo Doria01/2017
4092^909988-1862249273934Enzo Doria12/2015
4102^909297+1879157273726Enzo Doria08/2016
4112^909257-1864423273714Enzo Doria01/2016
4122^908579-1861747273510Enzo Doria12/2015
4132^907635-2791597273226Enzo Doria01/2016
414(53^158341+1)/54273022Paul Bourdelais07/2019
4152^906594-113201272912Enzo Doria08/2014
4162^904773+1872167272364Enzo Doria06/2016
4172^904149-1862473272176Enzo Doria12/2015
418(7*10^271757-61)/9271757Erik Branger03/2012
4192^902497+1880117271679Enzo Doria09/2016
4202^901858+77689271487Enzo Doria06/2016
4212^901372+1875301271341Enzo Doria06/2016
4222^899121-115033270663Enzo Doria07/2015
4232^898900+883021270596Enzo Doria12/2016
4242^898762-251511270555Enzo Doria12/2013
4252^898589+47270503Lelio R Paula03/2016
426187322*10^270343-187321270349Danilo Nitsche09/2013
42748358*10^270343-48357270348Danilo Nitsche09/2013
428(10^270343-1)/9270343Maksym Voznyy07/2007
4292^897867-3217270285Yves Minet12/2016
4302^897849-115273270280Enzo Doria07/2015
4312^896616-114179269909Enzo Doria12/2014
4322^894928+583561269401Enzo Doria04/2017
4332^894673-39343269324Enzo Doria08/2015
434F(1285607)268676Henri Lifchitz11/2008
4352^892112+187663268553Enzo Doria08/2016
436(10^268207+1)/11268206Paul Bourdelais02/2010
4372^890957-69583268205Enzo Doria12/2015
43832841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
4392^890122-351401267954Enzo Doria07/2015
440(19^209359-1)/18267718Paul Bourdelais08/2010
441(85^138647+1)/86267507Paul Bourdelais07/2019
4422^886324+77791266811Enzo Doria06/2016
4432^884714+1880527266326Enzo Doria10/2016
44411^255426+255426^11265999Serge Batalov05/2014
4452^883462-343421265949Enzo Doria07/2015
4462^883442+1875019265943Enzo Doria06/2016
4472^883333-291583265910Enzo Doria07/2015
4482^880411+1882673265031Enzo Doria12/2016
4492^879530-2788031264765Enzo Doria12/2015
4502^878118+2793079264340Enzo Doria02/2016
451(37^168527-1)/36264283Paul Bourdelais08/2019
4522^875748-461129263627Enzo Doria07/2015
4532^875181-2789923263456Enzo Doria12/2015
4542^875101-350083263432Enzo Doria08/2015
4552^874684+1883587263307Enzo Doria01/2017
4562^874616+1872211263286Enzo Doria05/2016
4572^874073+2792957263123Enzo Doria02/2016
4582^873628+1878751262989Enzo Doria08/2016
4592^873288-269262886Yves Minet01/2015
4602^871146-3173262242Yves Minet07/2016
4612^869601-163261776Yves Minet01/2015
4622^869326+282859261694Enzo Doria11/2016
4632^869035-114181261606Enzo Doria12/2014
4642^865715+80303260607Enzo Doria07/2016
4652^865048+1882411260406Enzo Doria12/2016
4662^864899-113871260361Enzo Doria10/2014
467(7*10^260198-61)/9260198Erik Branger11/2011
4682^864298-2788421260180Enzo Doria12/2015
4692^864039-2791357260102Enzo Doria01/2016
4702^863621-113833259976Enzo Doria10/2014
4712^862837+75767259740Enzo Doria05/2016
4722^862637-31259680Jorge Menendez05/2019
4732^862088+1874941259515Enzo Doria06/2016
4742^861987-134557259484Hans Havermann10/2018
4752^861516-1854029259343Enzo Doria09/2015
4762^860975-1853977259180Enzo Doria09/2015
4772^860625-1858843259074Enzo Doria10/2015
4782^860110+77689258919Enzo Doria05/2016
4792^859600+1880371258766Enzo Doria10/2016
4802^859433+494711258716Makoto Morimoto10/2013
481(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
482(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
4832^859240+1875271258658Enzo Doria06/2016
484Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
485(144^119671+1)/145258292Paul Bourdelais08/2019
486(11*2^857159-13)/15258031Renaud Lifchitz08/2011
4872^857016-633113257988Enzo Doria12/2013
4882^855732-113969257602Enzo Doria10/2014
4892^853682-3911256984Enzo Doria05/2014
49011^246668-90256879Enzo Doria12/2012
4912^851904-113939256449Enzo Doria10/2014
4922^851725-851725^2256395Henri Lifchitz03/2019
49311^246167-90256357Enzo Doria12/2012
4942^850700-569049256087Enzo Doria11/2013
49521^193601-20^193601255983Jean-Louis Charton02/2015
496(37^163193+1)/38255918Paul Bourdelais07/2019
4972^849177-114025255628Enzo Doria12/2014
4982^848502-3173255425Yves Minet07/2016
4992^848178-140291255328Enzo Doria01/2014
5002^847622-2441255160Yves Minet02/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!