PRP Records

Probable Primes Top 10000

(191107 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 ?
2512^981163-2790967295360Enzo Doria12/2015
2522^979594+1865839294888Enzo Doria02/2016
2532^976760+1885021294035Enzo Doria02/2017
2542^974441+1878407293336Enzo Doria08/2016
2552^974180+1876831293258Enzo Doria07/2016
2562^974170+453319293255Enzo Doria01/2017
2572^972744-114419292826Enzo Doria03/2015
258CopelandErdos(292447)292447Mark Rodenkirch12/2015
2592^970911+1873373292274Enzo Doria07/2016
2602^970670+383059292201Enzo Doria12/2016
2612^970141-100363292042Enzo Doria02/2014
2622^969945+1874717291983Enzo Doria06/2016
2632^969384+1880701291814Enzo Doria10/2016
264(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
2652^962194+60139289650Enzo Doria02/2016
2662^959307-1861507288781Enzo Doria11/2015
2672^957372+283531288198Enzo Doria02/2017
2682^957192-1864049288144Enzo Doria01/2016
2692^956446+1875199287919Enzo Doria06/2016
270(17^233689+1)/18287542Paul Bourdelais09/2013
2712^955178+1883587287538Enzo Doria12/2016
2722^954001+1875257287183Enzo Doria07/2016
2732^952268+1878601286662Enzo Doria09/2016
2742^950801+81557286220Enzo Doria08/2016
275(11*2^948635-13)/15285568Renaud Lifchitz11/2011
2762^948510+782569285530Enzo Doria10/2016
2772^948374-114137285490Enzo Doria01/2015
2782^947739+1872923285298Enzo Doria06/2016
2792^942533+82067283731Enzo Doria09/2016
2802^940950+1874989283255Enzo Doria06/2016
2812^940426-2786141283097Enzo Doria11/2015
2822^939881-114115282933Enzo Doria12/2014
28310^282493+632551282494Patrick De Geest02/2017
28510^282493-9^282493282493Jean-Louis Charton03/2007
28410^282493-132327282493Patrick De Geest02/2017
2863^591827-2^591827282374Mike Oakes08/2009
287Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
2882^936716-1835519281980Enzo Doria04/2015
2892^936588+79411281942Enzo Doria06/2016
2902^936047+1877423281779Enzo Doria08/2016
2912^935713+1869377281678Enzo Doria05/2016
2922^933082+1877059280886Enzo Doria08/2016
293(5*10^280710+1)/3280711Serge Batalov10/2014
294(10^279978+11)/3279978Serge Batalov07/2015
2952^929524-1864829279815Enzo Doria01/2016
2962^929152+60181279703Enzo Doria02/2016
2972^928621-2787883279543Enzo Doria11/2015
298(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
2992^927429+1882277279184Enzo Doria12/2016
300(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
3012^925330-1301278553Yves Minet06/2015
302(21^210599+1)/22278457Paul Bourdelais08/2013
3032^923261-69175277930Enzo Doria11/2015
304757^96487-756^96487277796Jean-Louis Charton12/2012
305((((((((((((((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
306(5^396413-1)/4277081Paul Bourdelais06/2010
3072^920318+2792299277044Enzo Doria02/2016
3082^918596-2786939276525Enzo Doria11/2015
3092^916639+60563275936Enzo Doria04/2016
3102^916385-2786383275860Enzo Doria11/2015
3112^915928+82081275722Enzo Doria09/2016
3122^915576-114137275616Enzo Doria01/2015
3132^914828+1876741275391Enzo Doria07/2016
3142^914757-2203275370Yves Minet12/2015
3152^911900+1871245274510Enzo Doria05/2016
3162^910490+283429274085Enzo Doria01/2017
3172^909988-1862249273934Enzo Doria12/2015
3182^909297+1879157273726Enzo Doria08/2016
3192^909257-1864423273714Enzo Doria01/2016
3202^908579-1861747273510Enzo Doria12/2015
3212^907635-2791597273226Enzo Doria01/2016
3222^906594-113201272912Enzo Doria08/2014
3232^904773+1872167272364Enzo Doria06/2016
3242^904149-1862473272176Enzo Doria12/2015
325(7*10^271757-61)/9271757Erik Branger03/2012
3262^902497+1880117271679Enzo Doria09/2016
3272^901858+77689271487Enzo Doria06/2016
3282^901372+1875301271341Enzo Doria06/2016
3292^899121-115033270663Enzo Doria07/2015
3302^898900+883021270596Enzo Doria12/2016
3312^898762-251511270555Enzo Doria12/2013
3322^898589+47270503Lelio R Paula03/2016
333187322*10^270343-187321270349Danilo Nitsche09/2013
33448358*10^270343-48357270348Danilo Nitsche09/2013
335(10^270343-1)/9270343Maksym Voznyy07/2007
3362^897867-3217270285Yves Minet12/2016
3372^897849-115273270280Enzo Doria07/2015
3382^896616-114179269909Enzo Doria12/2014
3392^894928+583561269401Enzo Doria04/2017
3402^894673-39343269324Enzo Doria08/2015
341F(1285607)268676Henri Lifchitz11/2008
3422^892112+187663268553Enzo Doria08/2016
343(10^268207+1)/11268206Paul Bourdelais02/2010
3442^890957-69583268205Enzo Doria12/2015
34532841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
3462^890122-351401267954Enzo Doria07/2015
347(19^209359-1)/18267718Paul Bourdelais08/2010
3482^886324+77791266811Enzo Doria06/2016
3492^884714+1880527266326Enzo Doria10/2016
35011^255426+255426^11265999Serge Batalov05/2014
3512^883462-343421265949Enzo Doria07/2015
3522^883442+1875019265943Enzo Doria06/2016
3532^883333-291583265910Enzo Doria07/2015
3542^880411+1882673265031Enzo Doria12/2016
3552^879530-2788031264765Enzo Doria12/2015
3562^878118+2793079264340Enzo Doria02/2016
3572^875748-461129263627Enzo Doria07/2015
3582^875181-2789923263456Enzo Doria12/2015
3592^875101-350083263432Enzo Doria08/2015
3602^874684+1883587263307Enzo Doria01/2017
3612^874616+1872211263286Enzo Doria05/2016
3622^874073+2792957263123Enzo Doria02/2016
3632^873628+1878751262989Enzo Doria08/2016
3642^873288-269262886Yves Minet01/2015
3652^871146-3173262242Yves Minet07/2016
3662^869601-163261776Yves Minet01/2015
3672^869326+282859261694Enzo Doria11/2016
3682^869035-114181261606Enzo Doria12/2014
3692^865715+80303260607Enzo Doria07/2016
3702^865048+1882411260406Enzo Doria12/2016
3712^864899-113871260361Enzo Doria10/2014
372(7*10^260198-61)/9260198Erik Branger11/2011
3732^864298-2788421260180Enzo Doria12/2015
3742^864039-2791357260102Enzo Doria01/2016
3752^863621-113833259976Enzo Doria10/2014
3762^862837+75767259740Enzo Doria05/2016
3772^862088+1874941259515Enzo Doria06/2016
3782^861516-1854029259343Enzo Doria09/2015
3792^860975-1853977259180Enzo Doria09/2015
3802^860625-1858843259074Enzo Doria10/2015
3812^860110+77689258919Enzo Doria05/2016
3822^859600+1880371258766Enzo Doria10/2016
3832^859433+494711258716Makoto Morimoto10/2013
384(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
3852^859240+1875271258658Enzo Doria06/2016
386Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
387(11*2^857159-13)/15258031Renaud Lifchitz08/2011
3882^857016-633113257988Enzo Doria12/2013
3892^855732-113969257602Enzo Doria10/2014
3902^853682-3911256984Enzo Doria05/2014
39111^246668-90256879Enzo Doria12/2012
3922^851904-113939256449Enzo Doria10/2014
39311^246167-90256357Enzo Doria12/2012
3942^850700-569049256087Enzo Doria11/2013
39521^193601-20^193601255983Jean-Louis Charton02/2015
3962^849177-114025255628Enzo Doria12/2014
3972^848502-3173255425Yves Minet07/2016
3982^848178-140291255328Enzo Doria01/2014
3992^847622-2441255160Yves Minet02/2016
4002^847291+182843255061Enzo Doria11/2016
4012^847174+1879429255025Enzo Doria09/2016
40224*29^174239+13361254809Curtis Bright04/2015
4032^845610-1868591254554Enzo Doria04/2016
4042^845484+81931254517Enzo Doria08/2016
4052^845402-114761254492Enzo Doria05/2015
4062^844334-2792441254170Enzo Doria02/2016
40711^243796-90253888Enzo Doria12/2012
4082^842209+1876037253531Enzo Doria07/2016
4092^842123-59197253505Enzo Doria10/2015
4102^840716-2969253081Yves Minet05/2016
4112^840358-462491252973Enzo Doria08/2015
4122^840310+1878379252959Enzo Doria08/2016
41311^242579-60252620Enzo Doria10/2012
41445^152659+2252378Robert Price09/2015
4152^837725+1869377252181Enzo Doria05/2016
4162^837536-311039252124Enzo Doria06/2015
41721^190632-2252058Robert Price07/2015
4182^837242+1873297252035Enzo Doria06/2016
4192^836656-2787929251859Enzo Doria11/2015
4202^836380+1875541251776Enzo Doria07/2016
421(359^98327-1)/358251233Alexander Zhirkov11/2017
422tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
4232^832511-461197250611Enzo Doria07/2015
4242^832505+1881137250609Enzo Doria11/2016
4252^832363+583295250567Enzo Doria12/2016
4262^832244-403635250531Enzo Doria01/2014
4272^831157+1880657250204Enzo Doria11/2016
4282^831088-7200899250183Enzo Doria01/2015
4292^830956-1349250143Yves Minet07/2015
4302^830037+282317249867Enzo Doria09/2016
4312^829589-113653249732Enzo Doria09/2014
4322^828281-3193249338Yves Minet08/2016
4332^828064-2785619249273Enzo Doria10/2015
4342^827602+60409249134Enzo Doria03/2016
43510^249010+348861249011Patrick De Geest04/2016
43610^249010-21249010Serge Batalov12/2014
4372^826733+1882907248872Enzo Doria12/2016
4382^825682+1876549248556Enzo Doria07/2016
4392^824991-114121248348Enzo Doria12/2014
4402^824642-362727248242Enzo Doria12/2013
4412^824565-114265248219Enzo Doria01/2015
442(73*10^248145-1)/9248146Robert Price01/2015
443(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
4442^822296+76501247536Enzo Doria05/2016
4452^821590-114167247324Enzo Doria12/2014
4462^821512-2790659247300Enzo Doria12/2015
4472^820077+382847246868Enzo Doria11/2016
4482^820001+81269246845Enzo Doria07/2016
4492^819463-59197246683Enzo Doria10/2015
4502^819296+80581246633Enzo Doria07/2016
4512^817160-350369245990Enzo Doria06/2015
45288093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
4532^815111-113857245373Enzo Doria10/2014
4542^814914-4001245314Yves Minet05/2017
455846^83761-845^83761245200Jean-Louis Charton12/2012
4562^814356-2790449245146Enzo Doria12/2015
4572^814276-459029245122Enzo Doria04/2015
4582^814023+180923245046Enzo Doria07/2016
459(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
4602^811842-113675244389Enzo Doria09/2014
4612^811132-2787929244176Enzo Doria11/2015
4622^809746-2790971243758Enzo Doria01/2016
4632^808767-3295243464Yves Minet12/2016
4642^808621-113809243420Enzo Doria09/2014
4652^807724+1879621243150Enzo Doria09/2016
4662^805843-113611242583Enzo Doria08/2014
4672^805745-459763242554Enzo Doria05/2015
4682^805353+782687242436Enzo Doria11/2016
4692^804277-417933242112Enzo Doria01/2014
4702^803468-269039241868Enzo Doria10/2013
4712^803172+80851241779Enzo Doria07/2016
4723^506233-2241535Robert Price11/2013
4732^802025-25999241434Enzo Doria10/2013
474(3^505823+3^252912+1)/7241339Serge Batalov03/2014
4752^801303+1872923241217Enzo Doria05/2016
4762^800579-1862947240999Enzo Doria12/2015
4772^798973-26283240515Enzo Doria10/2013
4782^798671-69487240424Enzo Doria12/2015
4792^797220+79831239988Enzo Doria06/2016
4802^796910-26001239894Enzo Doria10/2013
4812^796598+653119239800Enzo Doria12/2016
4822^796432-1859729239750Enzo Doria11/2015
4832^796002-1852211239621Enzo Doria08/2015
4842^795709+75767239533Enzo Doria04/2016
4852^795708+81721239532Enzo Doria08/2016
4862^795468-2786249239460Enzo Doria10/2015
4872^795442+80779239452Enzo Doria07/2016
4882^795075-1852057239342Enzo Doria08/2015
4892^794043+1875023239031Enzo Doria06/2016
4902^793347-69577238822Enzo Doria01/2016
4912^792988-344429238714Enzo Doria08/2015
4922^792700-2786369238627Enzo Doria11/2015
4932^792663-1844797238616Enzo Doria06/2015
4942^792605-291943238598Enzo Doria07/2015
495(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
4962^789373+1869377237625Enzo Doria05/2016
497((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
4982^788942+1866409237496Enzo Doria02/2016
4992^788844-114329237466Enzo Doria01/2015
5002^788705-1859713237424Enzo Doria11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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