PRP Records

Probable Primes Top 10000

(252538 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 ?
251(7^371669-1)/6314096Paul Bourdelais02/2010
2522^1041944+283051313657Enzo Doria12/2016
2532^1041153-114391313419Enzo Doria02/2015
2542^1038871+1866983312732Enzo Doria04/2016
2552^1037647+1881263312363Enzo Doria11/2016
2562^1037226+1879699312237Enzo Doria10/2016
2572^1036867+1865843312129Enzo Doria02/2016
2582^1036020-114539311874Enzo Doria02/2015
2592^1032240+1883431310736Enzo Doria01/2017
2602^1030352+1870021310167Enzo Doria06/2016
2612^1030046+1882843310075Enzo Doria11/2016
262(11^293831-1)/10305993Paul Bourdelais03/2010
2632^1015321-1015321305643Henri Lifchitz08/2013
2642^1014224-2791229305312Enzo Doria01/2016
2652^1010751-107709304267Enzo Doria03/2014
266(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
2672^1009577+1869587303913Enzo Doria06/2016
2688^336419-7^336419303817Jean-Louis Charton01/2008
2692^1008301+1869377303529Enzo Doria06/2016
270(2^1007838+5)/3303389Serge Batalov08/2015
2712^1005326+383059302634Enzo Doria12/2016
2722^1004929+1877567302514Enzo Doria08/2016
2732^1003494+1874899302082Enzo Doria06/2016
2742^1003046+60529301947Enzo Doria04/2016
2752^1000647+1881353301225Enzo Doria11/2016
2762^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
2772^999646+1874029300924Enzo Doria06/2016
27810^300476+3300477Ed Trice10/2012
27910^300476-530913300476Patrick De Geest03/2016
2802^998053+1879667300444Enzo Doria09/2016
281314738^9+9^314738300337Anatoly F. Selevich02/2011
2827^355039-6^355039300043Jean-Louis Charton05/2011
283numbpart(72526161452)299999Serge Batalov04/2017
2842^996182-114431299881Enzo Doria02/2015
2852^995214-2788361299590Enzo Doria12/2015
2862^994791-114319299462Enzo Doria01/2015
2872^994490-1863791299372Enzo Doria01/2016
2882^993322+1885729299020Enzo Doria03/2017
2892^992711-2788807298836Enzo Doria12/2015
2902^992525-114199298780Enzo Doria12/2014
2912^992329+1884707298721Enzo Doria02/2017
292(2^986191+1)/3296873Vincent Diepeveen06/2008
2932^985217-114553296580Enzo Doria03/2015
2942^984131-1828009296253Enzo Doria01/2015
2952^983620+60451296100Phil Moore03/2008
2962^982721-2683295829Yves Minet02/2016
2972^981298-2788421295401Enzo Doria12/2015
2982^981163-2790967295360Enzo Doria12/2015
2992^979594+1865839294888Enzo Doria02/2016
3002^976760+1885021294035Enzo Doria02/2017
3012^974441+1878407293336Enzo Doria08/2016
3022^974180+1876831293258Enzo Doria07/2016
3032^974170+453319293255Enzo Doria01/2017
3042^972744-114419292826Enzo Doria03/2015
305CopelandErdos(292447)292447Mark Rodenkirch12/2015
3062^970911+1873373292274Enzo Doria07/2016
3072^970670+383059292201Enzo Doria12/2016
3082^970141-100363292042Enzo Doria02/2014
3092^969945+1874717291983Enzo Doria06/2016
3102^969384+1880701291814Enzo Doria10/2016
311(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
3122^962194+60139289650Enzo Doria02/2016
3132^959307-1861507288781Enzo Doria11/2015
3142^957372+283531288198Enzo Doria02/2017
3152^957192-1864049288144Enzo Doria01/2016
3162^956446+1875199287919Enzo Doria06/2016
317(17^233689+1)/18287542Paul Bourdelais09/2013
3182^955178+1883587287538Enzo Doria12/2016
3192^954001+1875257287183Enzo Doria07/2016
320(23891^65536+1)/2286932Serge Batalov03/2018
3212^952268+1878601286662Enzo Doria09/2016
3222^950801+81557286220Enzo Doria08/2016
323(11*2^948635-13)/15285568Renaud Lifchitz11/2011
3242^948510+782569285530Enzo Doria10/2016
3252^948374-114137285490Enzo Doria01/2015
3262^947739+1872923285298Enzo Doria06/2016
3272^942533+82067283731Enzo Doria09/2016
3282^940950+1874989283255Enzo Doria06/2016
3292^940426-2786141283097Enzo Doria11/2015
3302^939881-114115282933Enzo Doria12/2014
33110^282493+632551282494Patrick De Geest02/2017
33310^282493-9^282493282493Jean-Louis Charton03/2007
33210^282493-132327282493Patrick De Geest02/2017
3343^591827-2^591827282374Mike Oakes08/2009
335Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
3362^936716-1835519281980Enzo Doria04/2015
3372^936588+79411281942Enzo Doria06/2016
3382^936047+1877423281779Enzo Doria08/2016
3392^935713+1869377281678Enzo Doria05/2016
3402^933082+1877059280886Enzo Doria08/2016
341(5*10^280710+1)/3280711Serge Batalov10/2014
342(10^279978+11)/3279978Serge Batalov07/2015
3432^929524-1864829279815Enzo Doria01/2016
3442^929152+60181279703Enzo Doria02/2016
3452^928621-2787883279543Enzo Doria11/2015
346(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
3472^927429+1882277279184Enzo Doria12/2016
348(33^183661-1)/32278891Paul Bourdelais12/2018
349(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
3502^925330-1301278553Yves Minet06/2015
351(21^210599+1)/22278457Paul Bourdelais08/2013
3522^923261-69175277930Enzo Doria11/2015
353757^96487-756^96487277796Jean-Louis Charton12/2012
354((((((((((((((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
355(5^396413-1)/4277081Paul Bourdelais06/2010
3562^920318+2792299277044Enzo Doria02/2016
3572^918596-2786939276525Enzo Doria11/2015
3582^916639+60563275936Enzo Doria04/2016
3592^916385-2786383275860Enzo Doria11/2015
3602^915928+82081275722Enzo Doria09/2016
3612^915576-114137275616Enzo Doria01/2015
3622^914828+1876741275391Enzo Doria07/2016
3632^914757-2203275370Yves Minet12/2015
3642^911900+1871245274510Enzo Doria05/2016
3652^910490+283429274085Enzo Doria01/2017
3662^909988-1862249273934Enzo Doria12/2015
3672^909297+1879157273726Enzo Doria08/2016
3682^909257-1864423273714Enzo Doria01/2016
3692^908579-1861747273510Enzo Doria12/2015
3702^907635-2791597273226Enzo Doria01/2016
3712^906594-113201272912Enzo Doria08/2014
3722^904773+1872167272364Enzo Doria06/2016
3732^904149-1862473272176Enzo Doria12/2015
374(7*10^271757-61)/9271757Erik Branger03/2012
3752^902497+1880117271679Enzo Doria09/2016
3762^901858+77689271487Enzo Doria06/2016
3772^901372+1875301271341Enzo Doria06/2016
3782^899121-115033270663Enzo Doria07/2015
3792^898900+883021270596Enzo Doria12/2016
3802^898762-251511270555Enzo Doria12/2013
3812^898589+47270503Lelio R Paula03/2016
382187322*10^270343-187321270349Danilo Nitsche09/2013
38348358*10^270343-48357270348Danilo Nitsche09/2013
384(10^270343-1)/9270343Maksym Voznyy07/2007
3852^897867-3217270285Yves Minet12/2016
3862^897849-115273270280Enzo Doria07/2015
3872^896616-114179269909Enzo Doria12/2014
3882^894928+583561269401Enzo Doria04/2017
3892^894673-39343269324Enzo Doria08/2015
390F(1285607)268676Henri Lifchitz11/2008
3912^892112+187663268553Enzo Doria08/2016
392(10^268207+1)/11268206Paul Bourdelais02/2010
3932^890957-69583268205Enzo Doria12/2015
39432841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
3952^890122-351401267954Enzo Doria07/2015
396(19^209359-1)/18267718Paul Bourdelais08/2010
3972^886324+77791266811Enzo Doria06/2016
3982^884714+1880527266326Enzo Doria10/2016
39911^255426+255426^11265999Serge Batalov05/2014
4002^883462-343421265949Enzo Doria07/2015
4012^883442+1875019265943Enzo Doria06/2016
4022^883333-291583265910Enzo Doria07/2015
4032^880411+1882673265031Enzo Doria12/2016
4042^879530-2788031264765Enzo Doria12/2015
4052^878118+2793079264340Enzo Doria02/2016
4062^875748-461129263627Enzo Doria07/2015
4072^875181-2789923263456Enzo Doria12/2015
4082^875101-350083263432Enzo Doria08/2015
4092^874684+1883587263307Enzo Doria01/2017
4102^874616+1872211263286Enzo Doria05/2016
4112^874073+2792957263123Enzo Doria02/2016
4122^873628+1878751262989Enzo Doria08/2016
4132^873288-269262886Yves Minet01/2015
4142^871146-3173262242Yves Minet07/2016
4152^869601-163261776Yves Minet01/2015
4162^869326+282859261694Enzo Doria11/2016
4172^869035-114181261606Enzo Doria12/2014
4182^865715+80303260607Enzo Doria07/2016
4192^865048+1882411260406Enzo Doria12/2016
4202^864899-113871260361Enzo Doria10/2014
421(7*10^260198-61)/9260198Erik Branger11/2011
4222^864298-2788421260180Enzo Doria12/2015
4232^864039-2791357260102Enzo Doria01/2016
4242^863621-113833259976Enzo Doria10/2014
4252^862837+75767259740Enzo Doria05/2016
4262^862088+1874941259515Enzo Doria06/2016
4272^861987-134557259484Hans Havermann10/2018
4282^861516-1854029259343Enzo Doria09/2015
4292^860975-1853977259180Enzo Doria09/2015
4302^860625-1858843259074Enzo Doria10/2015
4312^860110+77689258919Enzo Doria05/2016
4322^859600+1880371258766Enzo Doria10/2016
4332^859433+494711258716Makoto Morimoto10/2013
434(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
4352^859240+1875271258658Enzo Doria06/2016
436Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
437(11*2^857159-13)/15258031Renaud Lifchitz08/2011
4382^857016-633113257988Enzo Doria12/2013
4392^855732-113969257602Enzo Doria10/2014
4402^853682-3911256984Enzo Doria05/2014
44111^246668-90256879Enzo Doria12/2012
4422^851904-113939256449Enzo Doria10/2014
44311^246167-90256357Enzo Doria12/2012
4442^850700-569049256087Enzo Doria11/2013
44521^193601-20^193601255983Jean-Louis Charton02/2015
4462^849177-114025255628Enzo Doria12/2014
4472^848502-3173255425Yves Minet07/2016
4482^848178-140291255328Enzo Doria01/2014
4492^847622-2441255160Yves Minet02/2016
4502^847291+182843255061Enzo Doria11/2016
4512^847174+1879429255025Enzo Doria09/2016
45224*29^174239+13361254809Curtis Bright04/2015
4532^845610-1868591254554Enzo Doria04/2016
4542^845484+81931254517Enzo Doria08/2016
4552^845402-114761254492Enzo Doria05/2015
4562^844334-2792441254170Enzo Doria02/2016
45711^243796-90253888Enzo Doria12/2012
45830^171733-29^171733253671Jean-Louis Charton10/2018
4592^842209+1876037253531Enzo Doria07/2016
4602^842123-59197253505Enzo Doria10/2015
4612^840716-2969253081Yves Minet05/2016
4622^840358-462491252973Enzo Doria08/2015
4632^840310+1878379252959Enzo Doria08/2016
46411^242579-60252620Enzo Doria10/2012
46545^152659+2252378Robert Price09/2015
4662^837725+1869377252181Enzo Doria05/2016
4672^837536-311039252124Enzo Doria06/2015
46821^190632-2252058Robert Price07/2015
4692^837242+1873297252035Enzo Doria06/2016
4702^836656-2787929251859Enzo Doria11/2015
4712^836380+1875541251776Enzo Doria07/2016
472(359^98327-1)/358251233Alexander Zhirkov11/2017
473tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
4742^832511-461197250611Enzo Doria07/2015
4752^832505+1881137250609Enzo Doria11/2016
4762^832363+583295250567Enzo Doria12/2016
4772^832244-403635250531Enzo Doria01/2014
4782^831157+1880657250204Enzo Doria11/2016
4792^831088-7200899250183Enzo Doria01/2015
4802^830956-1349250143Yves Minet07/2015
4812^830037+282317249867Enzo Doria09/2016
4822^829589-113653249732Enzo Doria09/2014
4832^828281-3193249338Yves Minet08/2016
4842^828064-2785619249273Enzo Doria10/2015
4852^827602+60409249134Enzo Doria03/2016
48610^249010+348861249011Patrick De Geest04/2016
48710^249010-21249010Serge Batalov12/2014
4882^826733+1882907248872Enzo Doria12/2016
4892^825682+1876549248556Enzo Doria07/2016
4902^824991-114121248348Enzo Doria12/2014
4912^824642-362727248242Enzo Doria12/2013
4922^824565-114265248219Enzo Doria01/2015
493(73*10^248145-1)/9248146Robert Price01/2015
494(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
495(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
4962^822296+76501247536Enzo Doria05/2016
4972^821590-114167247324Enzo Doria12/2014
4982^821512-2790659247300Enzo Doria12/2015
4992^820077+382847246868Enzo Doria11/2016
5002^820001+81269246845Enzo Doria07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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