PRP Records

Probable Primes Top 10000

(181746 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 ?
2512^969384+1880701291814Enzo Doria10/2016
252(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
2532^962194+60139289650Enzo Doria02/2016
2542^959307-1861507288781Enzo Doria11/2015
2552^957372+283531288198Enzo Doria02/2017
2562^957192-1864049288144Enzo Doria01/2016
2572^956446+1875199287919Enzo Doria06/2016
258(17^233689+1)/18287542Paul Bourdelais09/2013
2592^955178+1883587287538Enzo Doria12/2016
2602^954001+1875257287183Enzo Doria07/2016
2612^952268+1878601286662Enzo Doria09/2016
2622^950801+81557286220Enzo Doria08/2016
263(11*2^948635-13)/15285568Renaud Lifchitz11/2011
2642^948510+782569285530Enzo Doria10/2016
2652^948374-114137285490Enzo Doria01/2015
2662^947739+1872923285298Enzo Doria06/2016
2672^942533+82067283731Enzo Doria09/2016
2682^940950+1874989283255Enzo Doria06/2016
2692^940426-2786141283097Enzo Doria11/2015
2702^939881-114115282933Enzo Doria12/2014
27110^282493+632551282494Patrick De Geest02/2017
27310^282493-9^282493282493Jean-Louis Charton03/2007
27210^282493-132327282493Patrick De Geest02/2017
2743^591827-2^591827282374Mike Oakes08/2009
275Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
2762^936716-1835519281980Enzo Doria04/2015
2772^936588+79411281942Enzo Doria06/2016
2782^936047+1877423281779Enzo Doria08/2016
2792^935713+1869377281678Enzo Doria05/2016
2802^933082+1877059280886Enzo Doria08/2016
281(5*10^280710+1)/3280711Serge Batalov10/2014
282(10^279978+11)/3279978Serge Batalov07/2015
2832^929524-1864829279815Enzo Doria01/2016
2842^929152+60181279703Enzo Doria02/2016
2852^928621-2787883279543Enzo Doria11/2015
286(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
2872^927429+1882277279184Enzo Doria12/2016
288(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
2892^925330-1301278553Yves Minet06/2015
290(21^210599+1)/22278457Paul Bourdelais08/2013
2912^923261-69175277930Enzo Doria11/2015
292757^96487-756^96487277796Jean-Louis Charton12/2012
293((((((((((((((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
294(5^396413-1)/4277081Paul Bourdelais06/2010
2952^920318+2792299277044Enzo Doria02/2016
2962^918596-2786939276525Enzo Doria11/2015
2972^916639+60563275936Enzo Doria04/2016
2982^916385-2786383275860Enzo Doria11/2015
2992^915928+82081275722Enzo Doria09/2016
3002^915576-114137275616Enzo Doria01/2015
3012^914828+1876741275391Enzo Doria07/2016
3022^914757-2203275370Yves Minet12/2015
3032^911900+1871245274510Enzo Doria05/2016
3042^910490+283429274085Enzo Doria01/2017
3052^909988-1862249273934Enzo Doria12/2015
3062^909297+1879157273726Enzo Doria08/2016
3072^909257-1864423273714Enzo Doria01/2016
3082^908579-1861747273510Enzo Doria12/2015
3092^907635-2791597273226Enzo Doria01/2016
3102^906594-113201272912Enzo Doria08/2014
3112^904773+1872167272364Enzo Doria06/2016
3122^904149-1862473272176Enzo Doria12/2015
313(7*10^271757-61)/9271757Erik Branger03/2012
3142^902497+1880117271679Enzo Doria09/2016
3152^901858+77689271487Enzo Doria06/2016
3162^901372+1875301271341Enzo Doria06/2016
3172^899121-115033270663Enzo Doria07/2015
3182^898900+883021270596Enzo Doria12/2016
3192^898762-251511270555Enzo Doria12/2013
3202^898589+47270503Lelio R Paula03/2016
321187322*10^270343-187321270349Danilo Nitsche09/2013
32248358*10^270343-48357270348Danilo Nitsche09/2013
323(10^270343-1)/9270343Maksym Voznyy07/2007
3242^897867-3217270285Yves Minet12/2016
3252^897849-115273270280Enzo Doria07/2015
3262^896616-114179269909Enzo Doria12/2014
3272^894928+583561269401Enzo Doria04/2017
3282^894673-39343269324Enzo Doria08/2015
329F(1285607)268676Henri Lifchitz11/2008
3302^892112+187663268553Enzo Doria08/2016
331(10^268207+1)/11268206Paul Bourdelais02/2010
3322^890957-69583268205Enzo Doria12/2015
33332841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
3342^890122-351401267954Enzo Doria07/2015
335(19^209359-1)/18267718Paul Bourdelais08/2010
3362^886324+77791266811Enzo Doria06/2016
3372^884714+1880527266326Enzo Doria10/2016
33811^255426+255426^11265999Serge Batalov05/2014
3392^883462-343421265949Enzo Doria07/2015
3402^883442+1875019265943Enzo Doria06/2016
3412^883333-291583265910Enzo Doria07/2015
3422^880411+1882673265031Enzo Doria12/2016
3432^879530-2788031264765Enzo Doria12/2015
3442^878118+2793079264340Enzo Doria02/2016
3452^875748-461129263627Enzo Doria07/2015
3462^875181-2789923263456Enzo Doria12/2015
3472^875101-350083263432Enzo Doria08/2015
3482^874684+1883587263307Enzo Doria01/2017
3492^874616+1872211263286Enzo Doria05/2016
3502^874073+2792957263123Enzo Doria02/2016
3512^873628+1878751262989Enzo Doria08/2016
3522^873288-269262886Yves Minet01/2015
3532^871146-3173262242Yves Minet07/2016
3542^869601-163261776Yves Minet01/2015
3552^869326+282859261694Enzo Doria11/2016
3562^869035-114181261606Enzo Doria12/2014
3572^865715+80303260607Enzo Doria07/2016
3582^865048+1882411260406Enzo Doria12/2016
3592^864899-113871260361Enzo Doria10/2014
360(7*10^260198-61)/9260198Erik Branger11/2011
3612^864298-2788421260180Enzo Doria12/2015
3622^864039-2791357260102Enzo Doria01/2016
3632^863621-113833259976Enzo Doria10/2014
3642^862837+75767259740Enzo Doria05/2016
3652^862088+1874941259515Enzo Doria06/2016
3662^861516-1854029259343Enzo Doria09/2015
3672^860975-1853977259180Enzo Doria09/2015
3682^860625-1858843259074Enzo Doria10/2015
3692^860110+77689258919Enzo Doria05/2016
3702^859600+1880371258766Enzo Doria10/2016
3712^859433+494711258716Makoto Morimoto10/2013
372(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
3732^859240+1875271258658Enzo Doria06/2016
374Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
375(11*2^857159-13)/15258031Renaud Lifchitz08/2011
3762^857016-633113257988Enzo Doria12/2013
3772^855732-113969257602Enzo Doria10/2014
3782^853682-3911256984Enzo Doria05/2014
37911^246668-90256879Enzo Doria12/2012
3802^851904-113939256449Enzo Doria10/2014
38111^246167-90256357Enzo Doria12/2012
3822^850700-569049256087Enzo Doria11/2013
38321^193601-20^193601255983Jean-Louis Charton02/2015
3842^849177-114025255628Enzo Doria12/2014
3852^848502-3173255425Yves Minet07/2016
3862^848178-140291255328Enzo Doria01/2014
3872^847622-2441255160Yves Minet02/2016
3882^847291+182843255061Enzo Doria11/2016
3892^847174+1879429255025Enzo Doria09/2016
39024*29^174239+13361254809Curtis Bright04/2015
3912^845610-1868591254554Enzo Doria04/2016
3922^845484+81931254517Enzo Doria08/2016
3932^845402-114761254492Enzo Doria05/2015
3942^844334-2792441254170Enzo Doria02/2016
39511^243796-90253888Enzo Doria12/2012
3962^842209+1876037253531Enzo Doria07/2016
3972^842123-59197253505Enzo Doria10/2015
3982^840716-2969253081Yves Minet05/2016
3992^840358-462491252973Enzo Doria08/2015
4002^840310+1878379252959Enzo Doria08/2016
40111^242579-60252620Enzo Doria10/2012
40245^152659+2252378Robert Price09/2015
4032^837725+1869377252181Enzo Doria05/2016
4042^837536-311039252124Enzo Doria06/2015
40521^190632-2252058Robert Price07/2015
4062^837242+1873297252035Enzo Doria06/2016
4072^836656-2787929251859Enzo Doria11/2015
4082^836380+1875541251776Enzo Doria07/2016
409tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
4102^832511-461197250611Enzo Doria07/2015
4112^832505+1881137250609Enzo Doria11/2016
4122^832363+583295250567Enzo Doria12/2016
4132^832244-403635250531Enzo Doria01/2014
4142^831157+1880657250204Enzo Doria11/2016
4152^831088-7200899250183Enzo Doria01/2015
4162^830956-1349250143Yves Minet07/2015
4172^830037+282317249867Enzo Doria09/2016
4182^829589-113653249732Enzo Doria09/2014
4192^828281-3193249338Yves Minet08/2016
4202^828064-2785619249273Enzo Doria10/2015
4212^827602+60409249134Enzo Doria03/2016
42210^249010+348861249011Patrick De Geest04/2016
42310^249010-21249010Serge Batalov12/2014
4242^826733+1882907248872Enzo Doria12/2016
4252^825682+1876549248556Enzo Doria07/2016
4262^824991-114121248348Enzo Doria12/2014
4272^824642-362727248242Enzo Doria12/2013
4282^824565-114265248219Enzo Doria01/2015
429(73*10^248145-1)/9248146Robert Price01/2015
430(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
4312^822296+76501247536Enzo Doria05/2016
4322^821590-114167247324Enzo Doria12/2014
4332^821512-2790659247300Enzo Doria12/2015
4342^820077+382847246868Enzo Doria11/2016
4352^820001+81269246845Enzo Doria07/2016
4362^819463-59197246683Enzo Doria10/2015
4372^819296+80581246633Enzo Doria07/2016
4382^817160-350369245990Enzo Doria06/2015
4392^815111-113857245373Enzo Doria10/2014
4402^814914-4001245314Yves Minet05/2017
441846^83761-845^83761245200Jean-Louis Charton12/2012
4422^814356-2790449245146Enzo Doria12/2015
4432^814276-459029245122Enzo Doria04/2015
4442^814023+180923245046Enzo Doria07/2016
445(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
4462^811842-113675244389Enzo Doria09/2014
4472^811132-2787929244176Enzo Doria11/2015
4482^809746-2790971243758Enzo Doria01/2016
4492^808767-3295243464Yves Minet12/2016
4502^808621-113809243420Enzo Doria09/2014
4512^807724+1879621243150Enzo Doria09/2016
4522^805843-113611242583Enzo Doria08/2014
4532^805745-459763242554Enzo Doria05/2015
4542^805353+782687242436Enzo Doria11/2016
4552^804277-417933242112Enzo Doria01/2014
4562^803468-269039241868Enzo Doria10/2013
4572^803172+80851241779Enzo Doria07/2016
4583^506233-2241535Robert Price11/2013
4592^802025-25999241434Enzo Doria10/2013
460(3^505823+3^252912+1)/7241339Serge Batalov03/2014
4612^801303+1872923241217Enzo Doria05/2016
4622^800579-1862947240999Enzo Doria12/2015
4632^798973-26283240515Enzo Doria10/2013
4642^798671-69487240424Enzo Doria12/2015
4652^797220+79831239988Enzo Doria06/2016
4662^796910-26001239894Enzo Doria10/2013
4672^796598+653119239800Enzo Doria12/2016
4682^796432-1859729239750Enzo Doria11/2015
4692^796002-1852211239621Enzo Doria08/2015
4702^795709+75767239533Enzo Doria04/2016
4712^795708+81721239532Enzo Doria08/2016
4722^795468-2786249239460Enzo Doria10/2015
4732^795442+80779239452Enzo Doria07/2016
4742^795075-1852057239342Enzo Doria08/2015
4752^794043+1875023239031Enzo Doria06/2016
4762^793347-69577238822Enzo Doria01/2016
4772^792988-344429238714Enzo Doria08/2015
4782^792700-2786369238627Enzo Doria11/2015
4792^792663-1844797238616Enzo Doria06/2015
4802^792605-291943238598Enzo Doria07/2015
481(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
4822^789373+1869377237625Enzo Doria05/2016
483((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
4842^788942+1866409237496Enzo Doria02/2016
4852^788844-114329237466Enzo Doria01/2015
4862^788705-1859713237424Enzo Doria11/2015
4872^786180+1871971236664Enzo Doria05/2016
48811^227092-90236492Enzo Doria11/2012
4892^785260+1866361236387Enzo Doria02/2016
4902^785220+1880611236375Enzo Doria10/2016
49119^184650-2236122Robert Price10/2014
49210^236059+216513236060Patrick De Geest04/2016
49310^236059-20909236059Robert Price09/2015
4942^782634-113981235597Enzo Doria11/2014
4952^782423+1879733235533Enzo Doria09/2016
4962^781682-2789543235310Enzo Doria12/2015
4972^780408-113453234927Enzo Doria08/2014
4982^780368-1864829234915Enzo Doria01/2016
4992^779593-1836559234681Enzo Doria05/2015
500(5^335429+1)/6234455Paul Bourdelais08/2010


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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