PRP Records

Probable Primes Top 10000

(252675 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 (> 50000) Who ? When ?
2512^1054736+483061317508Enzo Doria12/2016
2522^1053965+1879667317276Enzo Doria10/2016
2532^1052186-458165316740Enzo Doria03/2015
2542^1046613-114685315062Enzo Doria04/2015
2552^1045625-459373314765Enzo Doria06/2015
256(7*10^314564-61)/9314564Erik Branger09/2016
257(7^371669-1)/6314096Paul Bourdelais02/2010
2582^1041944+283051313657Enzo Doria12/2016
2592^1041153-114391313419Enzo Doria02/2015
2602^1038871+1866983312732Enzo Doria04/2016
2612^1037647+1881263312363Enzo Doria11/2016
2622^1037226+1879699312237Enzo Doria10/2016
2632^1036867+1865843312129Enzo Doria02/2016
2642^1036020-114539311874Enzo Doria02/2015
2652^1032240+1883431310736Enzo Doria01/2017
2662^1030352+1870021310167Enzo Doria06/2016
2672^1030046+1882843310075Enzo Doria11/2016
268(11^293831-1)/10305993Paul Bourdelais03/2010
2692^1015321-1015321305643Henri Lifchitz08/2013
2702^1014224-2791229305312Enzo Doria01/2016
2712^1010751-107709304267Enzo Doria03/2014
272(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
2732^1009577+1869587303913Enzo Doria06/2016
2748^336419-7^336419303817Jean-Louis Charton01/2008
2752^1008301+1869377303529Enzo Doria06/2016
276(2^1007838+5)/3303389Serge Batalov08/2015
2772^1005326+383059302634Enzo Doria12/2016
2782^1004929+1877567302514Enzo Doria08/2016
2792^1003494+1874899302082Enzo Doria06/2016
2802^1003046+60529301947Enzo Doria04/2016
2812^1000647+1881353301225Enzo Doria11/2016
2822^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
2832^999646+1874029300924Enzo Doria06/2016
28410^300476+3300477Ed Trice10/2012
28510^300476-530913300476Patrick De Geest03/2016
2862^998053+1879667300444Enzo Doria09/2016
287314738^9+9^314738300337Anatoly F. Selevich02/2011
2887^355039-6^355039300043Jean-Louis Charton05/2011
289numbpart(72526161452)299999Serge Batalov04/2017
2902^996182-114431299881Enzo Doria02/2015
2912^995214-2788361299590Enzo Doria12/2015
2922^994791-114319299462Enzo Doria01/2015
2932^994490-1863791299372Enzo Doria01/2016
2942^993322+1885729299020Enzo Doria03/2017
2952^992711-2788807298836Enzo Doria12/2015
2962^992525-114199298780Enzo Doria12/2014
2972^992329+1884707298721Enzo Doria02/2017
298(2^986191+1)/3296873Vincent Diepeveen06/2008
2992^985217-114553296580Enzo Doria03/2015
3002^984131-1828009296253Enzo Doria01/2015
3012^983620+60451296100Phil Moore03/2008
3022^982721-2683295829Yves Minet02/2016
3032^981298-2788421295401Enzo Doria12/2015
3042^981163-2790967295360Enzo Doria12/2015
3052^979594+1865839294888Enzo Doria02/2016
3062^976760+1885021294035Enzo Doria02/2017
3072^974441+1878407293336Enzo Doria08/2016
3082^974180+1876831293258Enzo Doria07/2016
3092^974170+453319293255Enzo Doria01/2017
3102^972744-114419292826Enzo Doria03/2015
311CopelandErdos(292447)292447Mark Rodenkirch12/2015
3122^970911+1873373292274Enzo Doria07/2016
3132^970670+383059292201Enzo Doria12/2016
3142^970141-100363292042Enzo Doria02/2014
3152^969945+1874717291983Enzo Doria06/2016
3162^969384+1880701291814Enzo Doria10/2016
317(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
3182^962194+60139289650Enzo Doria02/2016
3192^959307-1861507288781Enzo Doria11/2015
3202^957372+283531288198Enzo Doria02/2017
3212^957192-1864049288144Enzo Doria01/2016
3222^956446+1875199287919Enzo Doria06/2016
323(17^233689+1)/18287542Paul Bourdelais09/2013
3242^955178+1883587287538Enzo Doria12/2016
3252^954001+1875257287183Enzo Doria07/2016
326(23891^65536+1)/2286932Serge Batalov03/2018
3272^952268+1878601286662Enzo Doria09/2016
3282^950801+81557286220Enzo Doria08/2016
329(11*2^948635-13)/15285568Renaud Lifchitz11/2011
3302^948510+782569285530Enzo Doria10/2016
3312^948374-114137285490Enzo Doria01/2015
3322^947739+1872923285298Enzo Doria06/2016
3332^942533+82067283731Enzo Doria09/2016
3342^940950+1874989283255Enzo Doria06/2016
3352^940426-2786141283097Enzo Doria11/2015
3362^939881-114115282933Enzo Doria12/2014
33710^282493+632551282494Patrick De Geest02/2017
33910^282493-9^282493282493Jean-Louis Charton03/2007
33810^282493-132327282493Patrick De Geest02/2017
3403^591827-2^591827282374Mike Oakes08/2009
341Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
3422^936716-1835519281980Enzo Doria04/2015
3432^936588+79411281942Enzo Doria06/2016
3442^936047+1877423281779Enzo Doria08/2016
3452^935713+1869377281678Enzo Doria05/2016
3462^933082+1877059280886Enzo Doria08/2016
347(5*10^280710+1)/3280711Serge Batalov10/2014
348(10^279978+11)/3279978Serge Batalov07/2015
3492^929524-1864829279815Enzo Doria01/2016
3502^929152+60181279703Enzo Doria02/2016
3512^928621-2787883279543Enzo Doria11/2015
352(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
3532^927429+1882277279184Enzo Doria12/2016
354(33^183661-1)/32278891Paul Bourdelais12/2018
355(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
3562^925330-1301278553Yves Minet06/2015
357(21^210599+1)/22278457Paul Bourdelais08/2013
3582^923261-69175277930Enzo Doria11/2015
359757^96487-756^96487277796Jean-Louis Charton12/2012
360((((((((((((((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
361(5^396413-1)/4277081Paul Bourdelais06/2010
3622^920318+2792299277044Enzo Doria02/2016
3632^918596-2786939276525Enzo Doria11/2015
3642^916639+60563275936Enzo Doria04/2016
3652^916385-2786383275860Enzo Doria11/2015
3662^915928+82081275722Enzo Doria09/2016
3672^915576-114137275616Enzo Doria01/2015
3682^914828+1876741275391Enzo Doria07/2016
3692^914757-2203275370Yves Minet12/2015
3702^911900+1871245274510Enzo Doria05/2016
3712^910490+283429274085Enzo Doria01/2017
3722^909988-1862249273934Enzo Doria12/2015
3732^909297+1879157273726Enzo Doria08/2016
3742^909257-1864423273714Enzo Doria01/2016
3752^908579-1861747273510Enzo Doria12/2015
3762^907635-2791597273226Enzo Doria01/2016
3772^906594-113201272912Enzo Doria08/2014
3782^904773+1872167272364Enzo Doria06/2016
3792^904149-1862473272176Enzo Doria12/2015
380(7*10^271757-61)/9271757Erik Branger03/2012
3812^902497+1880117271679Enzo Doria09/2016
3822^901858+77689271487Enzo Doria06/2016
3832^901372+1875301271341Enzo Doria06/2016
3842^899121-115033270663Enzo Doria07/2015
3852^898900+883021270596Enzo Doria12/2016
3862^898762-251511270555Enzo Doria12/2013
3872^898589+47270503Lelio R Paula03/2016
388187322*10^270343-187321270349Danilo Nitsche09/2013
38948358*10^270343-48357270348Danilo Nitsche09/2013
390(10^270343-1)/9270343Maksym Voznyy07/2007
3912^897867-3217270285Yves Minet12/2016
3922^897849-115273270280Enzo Doria07/2015
3932^896616-114179269909Enzo Doria12/2014
3942^894928+583561269401Enzo Doria04/2017
3952^894673-39343269324Enzo Doria08/2015
396F(1285607)268676Henri Lifchitz11/2008
3972^892112+187663268553Enzo Doria08/2016
398(10^268207+1)/11268206Paul Bourdelais02/2010
3992^890957-69583268205Enzo Doria12/2015
40032841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
4012^890122-351401267954Enzo Doria07/2015
402(19^209359-1)/18267718Paul Bourdelais08/2010
4032^886324+77791266811Enzo Doria06/2016
4042^884714+1880527266326Enzo Doria10/2016
40511^255426+255426^11265999Serge Batalov05/2014
4062^883462-343421265949Enzo Doria07/2015
4072^883442+1875019265943Enzo Doria06/2016
4082^883333-291583265910Enzo Doria07/2015
4092^880411+1882673265031Enzo Doria12/2016
4102^879530-2788031264765Enzo Doria12/2015
4112^878118+2793079264340Enzo Doria02/2016
4122^875748-461129263627Enzo Doria07/2015
4132^875181-2789923263456Enzo Doria12/2015
4142^875101-350083263432Enzo Doria08/2015
4152^874684+1883587263307Enzo Doria01/2017
4162^874616+1872211263286Enzo Doria05/2016
4172^874073+2792957263123Enzo Doria02/2016
4182^873628+1878751262989Enzo Doria08/2016
4192^873288-269262886Yves Minet01/2015
4202^871146-3173262242Yves Minet07/2016
4212^869601-163261776Yves Minet01/2015
4222^869326+282859261694Enzo Doria11/2016
4232^869035-114181261606Enzo Doria12/2014
4242^865715+80303260607Enzo Doria07/2016
4252^865048+1882411260406Enzo Doria12/2016
4262^864899-113871260361Enzo Doria10/2014
427(7*10^260198-61)/9260198Erik Branger11/2011
4282^864298-2788421260180Enzo Doria12/2015
4292^864039-2791357260102Enzo Doria01/2016
4302^863621-113833259976Enzo Doria10/2014
4312^862837+75767259740Enzo Doria05/2016
4322^862088+1874941259515Enzo Doria06/2016
4332^861987-134557259484Hans Havermann10/2018
4342^861516-1854029259343Enzo Doria09/2015
4352^860975-1853977259180Enzo Doria09/2015
4362^860625-1858843259074Enzo Doria10/2015
4372^860110+77689258919Enzo Doria05/2016
4382^859600+1880371258766Enzo Doria10/2016
4392^859433+494711258716Makoto Morimoto10/2013
440(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
4412^859240+1875271258658Enzo Doria06/2016
442Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
443(11*2^857159-13)/15258031Renaud Lifchitz08/2011
4442^857016-633113257988Enzo Doria12/2013
4452^855732-113969257602Enzo Doria10/2014
4462^853682-3911256984Enzo Doria05/2014
44711^246668-90256879Enzo Doria12/2012
4482^851904-113939256449Enzo Doria10/2014
4492^851725-851725^2256395Henri Lifchitz03/2019
45011^246167-90256357Enzo Doria12/2012
4512^850700-569049256087Enzo Doria11/2013
45221^193601-20^193601255983Jean-Louis Charton02/2015
4532^849177-114025255628Enzo Doria12/2014
4542^848502-3173255425Yves Minet07/2016
4552^848178-140291255328Enzo Doria01/2014
4562^847622-2441255160Yves Minet02/2016
4572^847291+182843255061Enzo Doria11/2016
4582^847174+1879429255025Enzo Doria09/2016
45924*29^174239+13361254809Curtis Bright04/2015
4602^845610-1868591254554Enzo Doria04/2016
4612^845484+81931254517Enzo Doria08/2016
4622^845402-114761254492Enzo Doria05/2015
4632^844334-2792441254170Enzo Doria02/2016
46411^243796-90253888Enzo Doria12/2012
46530^171733-29^171733253671Jean-Louis Charton10/2018
4662^842209+1876037253531Enzo Doria07/2016
4672^842123-59197253505Enzo Doria10/2015
4682^840716-2969253081Yves Minet05/2016
4692^840358-462491252973Enzo Doria08/2015
4702^840310+1878379252959Enzo Doria08/2016
47111^242579-60252620Enzo Doria10/2012
47245^152659+2252378Robert Price09/2015
4732^837725+1869377252181Enzo Doria05/2016
4742^837536-311039252124Enzo Doria06/2015
47521^190632-2252058Robert Price07/2015
4762^837242+1873297252035Enzo Doria06/2016
4772^836656-2787929251859Enzo Doria11/2015
4782^836380+1875541251776Enzo Doria07/2016
479(359^98327-1)/358251233Alexander Zhirkov11/2017
480tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
4812^832511-461197250611Enzo Doria07/2015
4822^832505+1881137250609Enzo Doria11/2016
4832^832363+583295250567Enzo Doria12/2016
4842^832244-403635250531Enzo Doria01/2014
4852^831157+1880657250204Enzo Doria11/2016
4862^831088-7200899250183Enzo Doria01/2015
4872^830956-1349250143Yves Minet07/2015
4882^830037+282317249867Enzo Doria09/2016
4892^829589-113653249732Enzo Doria09/2014
4902^828281-3193249338Yves Minet08/2016
4912^828064-2785619249273Enzo Doria10/2015
4922^827602+60409249134Enzo Doria03/2016
49310^249010+348861249011Patrick De Geest04/2016
49410^249010-21249010Serge Batalov12/2014
4952^826733+1882907248872Enzo Doria12/2016
4962^825682+1876549248556Enzo Doria07/2016
4972^824991-114121248348Enzo Doria12/2014
4982^824642-362727248242Enzo Doria12/2013
4992^824565-114265248219Enzo Doria01/2015
500(73*10^248145-1)/9248146Robert Price01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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