PRP Records

Probable Primes Top 10000

(172213 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 ?
2512^925330-1301278553Yves Minet06/2015
252(21^210599+1)/22278457Paul Bourdelais08/2013
2532^923261-69175277930Enzo Doria11/2015
254757^96487-756^96487277796Jean-Louis Charton12/2012
255((((((((((((((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
256(5^396413-1)/4277081Paul Bourdelais06/2010
2572^920318+2792299277044Enzo Doria02/2016
2582^918596-2786939276525Enzo Doria11/2015
2592^916639+60563275936Enzo Doria04/2016
2602^916385-2786383275860Enzo Doria11/2015
2612^915928+82081275722Enzo Doria09/2016
2622^915576-114137275616Enzo Doria01/2015
2632^914828+1876741275391Enzo Doria07/2016
2642^914757-2203275370Yves Minet12/2015
2652^911900+1871245274510Enzo Doria05/2016
2662^910490+283429274085Enzo Doria01/2017
2672^909988-1862249273934Enzo Doria12/2015
2682^909297+1879157273726Enzo Doria08/2016
2692^909257-1864423273714Enzo Doria01/2016
2702^908579-1861747273510Enzo Doria12/2015
2712^907635-2791597273226Enzo Doria01/2016
2722^906594-113201272912Enzo Doria08/2014
2732^904773+1872167272364Enzo Doria06/2016
2742^904149-1862473272176Enzo Doria12/2015
275(7*10^271757-61)/9271757Erik Branger03/2012
2762^902497+1880117271679Enzo Doria09/2016
2772^901858+77689271487Enzo Doria06/2016
2782^901372+1875301271341Enzo Doria06/2016
2792^899121-115033270663Enzo Doria07/2015
2802^898900+883021270596Enzo Doria12/2016
2812^898762-251511270555Enzo Doria12/2013
2822^898589+47270503Lelio R Paula03/2016
283187322*10^270343-187321270349Danilo Nitsche09/2013
28448358*10^270343-48357270348Danilo Nitsche09/2013
285(10^270343-1)/9270343Maksym Voznyy07/2007
2862^897867-3217270285Yves Minet12/2016
2872^897849-115273270280Enzo Doria07/2015
2882^896616-114179269909Enzo Doria12/2014
2892^894673-39343269324Enzo Doria08/2015
290F(1285607)268676Henri Lifchitz11/2008
2912^892112+187663268553Enzo Doria08/2016
292(10^268207+1)/11268206Paul Bourdelais02/2010
2932^890957-69583268205Enzo Doria12/2015
2942^890122-351401267954Enzo Doria07/2015
295(19^209359-1)/18267718Paul Bourdelais08/2010
2962^886324+77791266811Enzo Doria06/2016
2972^884714+1880527266326Enzo Doria10/2016
29811^255426+255426^11265999Serge Batalov05/2014
2992^883462-343421265949Enzo Doria07/2015
3002^883442+1875019265943Enzo Doria06/2016
3012^883333-291583265910Enzo Doria07/2015
3022^880411+1882673265031Enzo Doria12/2016
3032^879530-2788031264765Enzo Doria12/2015
3042^878118+2793079264340Enzo Doria02/2016
3052^875748-461129263627Enzo Doria07/2015
3062^875181-2789923263456Enzo Doria12/2015
3072^875101-350083263432Enzo Doria08/2015
3082^874684+1883587263307Enzo Doria01/2017
3092^874616+1872211263286Enzo Doria05/2016
3102^874073+2792957263123Enzo Doria02/2016
3112^873628+1878751262989Enzo Doria08/2016
3122^873288-269262886Yves Minet01/2015
3132^871146-3173262242Yves Minet07/2016
3142^869601-163261776Yves Minet01/2015
3152^869326+282859261694Enzo Doria11/2016
3162^869035-114181261606Enzo Doria12/2014
3172^865715+80303260607Enzo Doria07/2016
3182^865048+1882411260406Enzo Doria12/2016
3192^864899-113871260361Enzo Doria10/2014
320(7*10^260198-61)/9260198Erik Branger11/2011
3212^864298-2788421260180Enzo Doria12/2015
3222^864039-2791357260102Enzo Doria01/2016
3232^863621-113833259976Enzo Doria10/2014
3242^862837+75767259740Enzo Doria05/2016
3252^862088+1874941259515Enzo Doria06/2016
3262^861516-1854029259343Enzo Doria09/2015
3272^860975-1853977259180Enzo Doria09/2015
3282^860625-1858843259074Enzo Doria10/2015
3292^860110+77689258919Enzo Doria05/2016
3302^859600+1880371258766Enzo Doria10/2016
3312^859433+494711258716Makoto Morimoto10/2013
332(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
3332^859240+1875271258658Enzo Doria06/2016
334Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
335(11*2^857159-13)/15258031Renaud Lifchitz08/2011
3362^857016-633113257988Enzo Doria12/2013
3372^855732-113969257602Enzo Doria10/2014
3382^853682-3911256984Enzo Doria05/2014
33911^246668-90256879Enzo Doria12/2012
3402^851904-113939256449Enzo Doria10/2014
34111^246167-90256357Enzo Doria12/2012
3422^850700-569049256087Enzo Doria11/2013
34321^193601-20^193601255983Jean-Louis Charton02/2015
3442^849177-114025255628Enzo Doria12/2014
3452^848502-3173255425Yves Minet07/2016
3462^848178-140291255328Enzo Doria01/2014
3472^847622-2441255160Yves Minet02/2016
3482^847291+182843255061Enzo Doria11/2016
3492^847174+1879429255025Enzo Doria09/2016
35024*29^174239+13361254809Curtis Bright04/2015
3512^845610-1868591254554Enzo Doria04/2016
3522^845484+81931254517Enzo Doria08/2016
3532^845402-114761254492Enzo Doria05/2015
3542^844334-2792441254170Enzo Doria02/2016
35511^243796-90253888Enzo Doria12/2012
3562^842209+1876037253531Enzo Doria07/2016
3572^842123-59197253505Enzo Doria10/2015
3582^840716-2969253081Yves Minet05/2016
3592^840358-462491252973Enzo Doria08/2015
3602^840310+1878379252959Enzo Doria08/2016
36111^242579-60252620Enzo Doria10/2012
36245^152659+2252378Robert Price09/2015
3632^837725+1869377252181Enzo Doria05/2016
3642^837536-311039252124Enzo Doria06/2015
36521^190632-2252058Robert Price07/2015
3662^837242+1873297252035Enzo Doria06/2016
3672^836656-2787929251859Enzo Doria11/2015
3682^836380+1875541251776Enzo Doria07/2016
369tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
3702^832511-461197250611Enzo Doria07/2015
3712^832505+1881137250609Enzo Doria11/2016
3722^832363+583295250567Enzo Doria12/2016
3732^832244-403635250531Enzo Doria01/2014
3742^831157+1880657250204Enzo Doria11/2016
3752^831088-7200899250183Enzo Doria01/2015
3762^830956-1349250143Yves Minet07/2015
3772^830037+282317249867Enzo Doria09/2016
3782^829589-113653249732Enzo Doria09/2014
3792^828281-3193249338Yves Minet08/2016
3802^828064-2785619249273Enzo Doria10/2015
3812^827602+60409249134Enzo Doria03/2016
38210^249010+348861249011Patrick De Geest04/2016
38310^249010-21249010Serge Batalov12/2014
3842^826733+1882907248872Enzo Doria12/2016
3852^825682+1876549248556Enzo Doria07/2016
3862^824991-114121248348Enzo Doria12/2014
3872^824642-362727248242Enzo Doria12/2013
3882^824565-114265248219Enzo Doria01/2015
389(73*10^248145-1)/9248146Robert Price01/2015
390(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
3912^822296+76501247536Enzo Doria05/2016
3922^821590-114167247324Enzo Doria12/2014
3932^821512-2790659247300Enzo Doria12/2015
3942^820077+382847246868Enzo Doria11/2016
3952^820001+81269246845Enzo Doria07/2016
3962^819463-59197246683Enzo Doria10/2015
3972^819296+80581246633Enzo Doria07/2016
3982^817160-350369245990Enzo Doria06/2015
3992^815111-113857245373Enzo Doria10/2014
400846^83761-845^83761245200Jean-Louis Charton12/2012
4012^814356-2790449245146Enzo Doria12/2015
4022^814276-459029245122Enzo Doria04/2015
4032^814023+180923245046Enzo Doria07/2016
404(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
4052^811842-113675244389Enzo Doria09/2014
4062^811132-2787929244176Enzo Doria11/2015
4072^809746-2790971243758Enzo Doria01/2016
4082^808767-3295243464Yves Minet12/2016
4092^808621-113809243420Enzo Doria09/2014
4102^807724+1879621243150Enzo Doria09/2016
4112^805843-113611242583Enzo Doria08/2014
4122^805745-459763242554Enzo Doria05/2015
4132^805353+782687242436Enzo Doria11/2016
4142^804277-417933242112Enzo Doria01/2014
4152^803468-269039241868Enzo Doria10/2013
4162^803172+80851241779Enzo Doria07/2016
4173^506233-2241535Robert Price11/2013
4182^802025-25999241434Enzo Doria10/2013
419(3^505823+3^252912+1)/7241339Serge Batalov03/2014
4202^801303+1872923241217Enzo Doria05/2016
4212^800579-1862947240999Enzo Doria12/2015
4222^798973-26283240515Enzo Doria10/2013
4232^798671-69487240424Enzo Doria12/2015
4242^797220+79831239988Enzo Doria06/2016
4252^796910-26001239894Enzo Doria10/2013
4262^796598+653119239800Enzo Doria12/2016
4272^796432-1859729239750Enzo Doria11/2015
4282^796002-1852211239621Enzo Doria08/2015
4292^795709+75767239533Enzo Doria04/2016
4302^795708+81721239532Enzo Doria08/2016
4312^795468-2786249239460Enzo Doria10/2015
4322^795442+80779239452Enzo Doria07/2016
4332^795075-1852057239342Enzo Doria08/2015
4342^794043+1875023239031Enzo Doria06/2016
4352^793347-69577238822Enzo Doria01/2016
4362^792988-344429238714Enzo Doria08/2015
4372^792700-2786369238627Enzo Doria11/2015
4382^792663-1844797238616Enzo Doria06/2015
4392^792605-291943238598Enzo Doria07/2015
440(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
4412^789373+1869377237625Enzo Doria05/2016
442((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
4432^788942+1866409237496Enzo Doria02/2016
4442^788844-114329237466Enzo Doria01/2015
4452^788705-1859713237424Enzo Doria11/2015
4462^786180+1871971236664Enzo Doria05/2016
44711^227092-90236492Enzo Doria11/2012
4482^785260+1866361236387Enzo Doria02/2016
4492^785220+1880611236375Enzo Doria10/2016
45019^184650-2236122Robert Price10/2014
45110^236059+216513236060Patrick De Geest04/2016
45210^236059-20909236059Robert Price09/2015
4532^782634-113981235597Enzo Doria11/2014
4542^782423+1879733235533Enzo Doria09/2016
4552^781682-2789543235310Enzo Doria12/2015
4562^780408-113453234927Enzo Doria08/2014
4572^780368-1864829234915Enzo Doria01/2016
4582^779593-1836559234681Enzo Doria05/2015
459(5^335429+1)/6234455Paul Bourdelais08/2010
4602^778395-113617234321Enzo Doria08/2014
4612^776245-2792353233674Enzo Doria02/2016
4622^776060-114029233618Enzo Doria11/2014
4632^775987-2789557233596Enzo Doria12/2015
4642^775672+1866721233501Enzo Doria03/2016
465(11^223999+1)/12233270Paul Bourdelais02/2010
46621^176191-20^176191232964Jean-Louis Charton01/2015
4672^773679-113425232901Enzo Doria08/2014
46810^232599+192489232600Patrick De Geest12/2013
46910^232599-3232599Markus Tervooren10/2010
4702^772552-458879232562Enzo Doria04/2015
4712^772214+1874899232460Enzo Doria06/2016
4722^771994-1862771232394Enzo Doria12/2015
4732^771889+1876037232362Enzo Doria07/2016
4742^771660+1866511232293Enzo Doria02/2016
4755^332150-18188232163Enzo Doria06/2014
4763^485977-2^485977231870Mike Oakes09/2009
4772^770082-114161231818Enzo Doria01/2015
478(20^177967+1)/21231540Paul Bourdelais05/2013
4792^767622-9221231078Lelio R Paula01/2016
4802^767344+1880311230994Enzo Doria09/2016
481(3^483611-1)/2230741Paul Bourdelais02/2010
482(10^230706+179)/9230706Serge Batalov12/2014
4832^766309+1875257230682Enzo Doria06/2016
4842^765635+1879883230480Enzo Doria09/2016
4852^764348-113697230092Enzo Doria09/2014
4862^764131+78863230027Enzo Doria05/2016
4872^763701+60197229897Enzo Doria03/2016
4882^762841-25905229639Enzo Doria10/2013
4892^761117-113569229120Enzo Doria08/2014
4902^757985-2790013228177Enzo Doria12/2015
4912^757038-1862081227892Enzo Doria12/2015
4922^756839+95849227832Makoto Morimoto10/2013
493(2^756839+6989)/756091227826Makoto Morimoto09/2016
4942^756773-112723227812Enzo Doria07/2014
495524309#+616367227431Makoto Morimoto02/2016
4962^755097-114193227307Enzo Doria12/2014
4972^754473-2791513227120Enzo Doria01/2016
4982^751426-764321226202Enzo Doria12/2013
499(18^180181-1)/17226176Andy Steward04/2007
5002^750740-3225996Paul Bourdelais03/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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