PRP Records

Probable Primes Top 10000

(177649 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 ?
2512^950801+81557286220Enzo Doria08/2016
252(11*2^948635-13)/15285568Renaud Lifchitz11/2011
2532^948510+782569285530Enzo Doria10/2016
2542^948374-114137285490Enzo Doria01/2015
2552^947739+1872923285298Enzo Doria06/2016
2562^942533+82067283731Enzo Doria09/2016
2572^940950+1874989283255Enzo Doria06/2016
2582^940426-2786141283097Enzo Doria11/2015
2592^939881-114115282933Enzo Doria12/2014
26010^282493+632551282494Patrick De Geest02/2017
26210^282493-9^282493282493Jean-Louis Charton03/2007
26110^282493-132327282493Patrick De Geest02/2017
2633^591827-2^591827282374Mike Oakes08/2009
264Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
2652^936716-1835519281980Enzo Doria04/2015
2662^936588+79411281942Enzo Doria06/2016
2672^936047+1877423281779Enzo Doria08/2016
2682^935713+1869377281678Enzo Doria05/2016
2692^933082+1877059280886Enzo Doria08/2016
270(5*10^280710+1)/3280711Serge Batalov10/2014
271(10^279978+11)/3279978Serge Batalov07/2015
2722^929524-1864829279815Enzo Doria01/2016
2732^929152+60181279703Enzo Doria02/2016
2742^928621-2787883279543Enzo Doria11/2015
275(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
2762^927429+1882277279184Enzo Doria12/2016
277(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
2782^925330-1301278553Yves Minet06/2015
279(21^210599+1)/22278457Paul Bourdelais08/2013
2802^923261-69175277930Enzo Doria11/2015
281757^96487-756^96487277796Jean-Louis Charton12/2012
282((((((((((((((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
283(5^396413-1)/4277081Paul Bourdelais06/2010
2842^920318+2792299277044Enzo Doria02/2016
2852^918596-2786939276525Enzo Doria11/2015
2862^916639+60563275936Enzo Doria04/2016
2872^916385-2786383275860Enzo Doria11/2015
2882^915928+82081275722Enzo Doria09/2016
2892^915576-114137275616Enzo Doria01/2015
2902^914828+1876741275391Enzo Doria07/2016
2912^914757-2203275370Yves Minet12/2015
2922^911900+1871245274510Enzo Doria05/2016
2932^910490+283429274085Enzo Doria01/2017
2942^909988-1862249273934Enzo Doria12/2015
2952^909297+1879157273726Enzo Doria08/2016
2962^909257-1864423273714Enzo Doria01/2016
2972^908579-1861747273510Enzo Doria12/2015
2982^907635-2791597273226Enzo Doria01/2016
2992^906594-113201272912Enzo Doria08/2014
3002^904773+1872167272364Enzo Doria06/2016
3012^904149-1862473272176Enzo Doria12/2015
302(7*10^271757-61)/9271757Erik Branger03/2012
3032^902497+1880117271679Enzo Doria09/2016
3042^901858+77689271487Enzo Doria06/2016
3052^901372+1875301271341Enzo Doria06/2016
3062^899121-115033270663Enzo Doria07/2015
3072^898900+883021270596Enzo Doria12/2016
3082^898762-251511270555Enzo Doria12/2013
3092^898589+47270503Lelio R Paula03/2016
310187322*10^270343-187321270349Danilo Nitsche09/2013
31148358*10^270343-48357270348Danilo Nitsche09/2013
312(10^270343-1)/9270343Maksym Voznyy07/2007
3132^897867-3217270285Yves Minet12/2016
3142^897849-115273270280Enzo Doria07/2015
3152^896616-114179269909Enzo Doria12/2014
3162^894928+583561269401Enzo Doria04/2017
3172^894673-39343269324Enzo Doria08/2015
318F(1285607)268676Henri Lifchitz11/2008
3192^892112+187663268553Enzo Doria08/2016
320(10^268207+1)/11268206Paul Bourdelais02/2010
3212^890957-69583268205Enzo Doria12/2015
3222^890122-351401267954Enzo Doria07/2015
323(19^209359-1)/18267718Paul Bourdelais08/2010
3242^886324+77791266811Enzo Doria06/2016
3252^884714+1880527266326Enzo Doria10/2016
32611^255426+255426^11265999Serge Batalov05/2014
3272^883462-343421265949Enzo Doria07/2015
3282^883442+1875019265943Enzo Doria06/2016
3292^883333-291583265910Enzo Doria07/2015
3302^880411+1882673265031Enzo Doria12/2016
3312^879530-2788031264765Enzo Doria12/2015
3322^878118+2793079264340Enzo Doria02/2016
3332^875748-461129263627Enzo Doria07/2015
3342^875181-2789923263456Enzo Doria12/2015
3352^875101-350083263432Enzo Doria08/2015
3362^874684+1883587263307Enzo Doria01/2017
3372^874616+1872211263286Enzo Doria05/2016
3382^874073+2792957263123Enzo Doria02/2016
3392^873628+1878751262989Enzo Doria08/2016
3402^873288-269262886Yves Minet01/2015
3412^871146-3173262242Yves Minet07/2016
3422^869601-163261776Yves Minet01/2015
3432^869326+282859261694Enzo Doria11/2016
3442^869035-114181261606Enzo Doria12/2014
3452^865715+80303260607Enzo Doria07/2016
3462^865048+1882411260406Enzo Doria12/2016
3472^864899-113871260361Enzo Doria10/2014
348(7*10^260198-61)/9260198Erik Branger11/2011
3492^864298-2788421260180Enzo Doria12/2015
3502^864039-2791357260102Enzo Doria01/2016
3512^863621-113833259976Enzo Doria10/2014
3522^862837+75767259740Enzo Doria05/2016
3532^862088+1874941259515Enzo Doria06/2016
3542^861516-1854029259343Enzo Doria09/2015
3552^860975-1853977259180Enzo Doria09/2015
3562^860625-1858843259074Enzo Doria10/2015
3572^860110+77689258919Enzo Doria05/2016
3582^859600+1880371258766Enzo Doria10/2016
3592^859433+494711258716Makoto Morimoto10/2013
360(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
3612^859240+1875271258658Enzo Doria06/2016
362Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
363(11*2^857159-13)/15258031Renaud Lifchitz08/2011
3642^857016-633113257988Enzo Doria12/2013
3652^855732-113969257602Enzo Doria10/2014
3662^853682-3911256984Enzo Doria05/2014
36711^246668-90256879Enzo Doria12/2012
3682^851904-113939256449Enzo Doria10/2014
36911^246167-90256357Enzo Doria12/2012
3702^850700-569049256087Enzo Doria11/2013
37121^193601-20^193601255983Jean-Louis Charton02/2015
3722^849177-114025255628Enzo Doria12/2014
3732^848502-3173255425Yves Minet07/2016
3742^848178-140291255328Enzo Doria01/2014
3752^847622-2441255160Yves Minet02/2016
3762^847291+182843255061Enzo Doria11/2016
3772^847174+1879429255025Enzo Doria09/2016
37824*29^174239+13361254809Curtis Bright04/2015
3792^845610-1868591254554Enzo Doria04/2016
3802^845484+81931254517Enzo Doria08/2016
3812^845402-114761254492Enzo Doria05/2015
3822^844334-2792441254170Enzo Doria02/2016
38311^243796-90253888Enzo Doria12/2012
3842^842209+1876037253531Enzo Doria07/2016
3852^842123-59197253505Enzo Doria10/2015
3862^840716-2969253081Yves Minet05/2016
3872^840358-462491252973Enzo Doria08/2015
3882^840310+1878379252959Enzo Doria08/2016
38911^242579-60252620Enzo Doria10/2012
39045^152659+2252378Robert Price09/2015
3912^837725+1869377252181Enzo Doria05/2016
3922^837536-311039252124Enzo Doria06/2015
39321^190632-2252058Robert Price07/2015
3942^837242+1873297252035Enzo Doria06/2016
3952^836656-2787929251859Enzo Doria11/2015
3962^836380+1875541251776Enzo Doria07/2016
397tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
3982^832511-461197250611Enzo Doria07/2015
3992^832505+1881137250609Enzo Doria11/2016
4002^832363+583295250567Enzo Doria12/2016
4012^832244-403635250531Enzo Doria01/2014
4022^831157+1880657250204Enzo Doria11/2016
4032^831088-7200899250183Enzo Doria01/2015
4042^830956-1349250143Yves Minet07/2015
4052^830037+282317249867Enzo Doria09/2016
4062^829589-113653249732Enzo Doria09/2014
4072^828281-3193249338Yves Minet08/2016
4082^828064-2785619249273Enzo Doria10/2015
4092^827602+60409249134Enzo Doria03/2016
41010^249010+348861249011Patrick De Geest04/2016
41110^249010-21249010Serge Batalov12/2014
4122^826733+1882907248872Enzo Doria12/2016
4132^825682+1876549248556Enzo Doria07/2016
4142^824991-114121248348Enzo Doria12/2014
4152^824642-362727248242Enzo Doria12/2013
4162^824565-114265248219Enzo Doria01/2015
417(73*10^248145-1)/9248146Robert Price01/2015
418(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
4192^822296+76501247536Enzo Doria05/2016
4202^821590-114167247324Enzo Doria12/2014
4212^821512-2790659247300Enzo Doria12/2015
4222^820077+382847246868Enzo Doria11/2016
4232^820001+81269246845Enzo Doria07/2016
4242^819463-59197246683Enzo Doria10/2015
4252^819296+80581246633Enzo Doria07/2016
4262^817160-350369245990Enzo Doria06/2015
4272^815111-113857245373Enzo Doria10/2014
4282^814914-4001245314Yves Minet05/2017
429846^83761-845^83761245200Jean-Louis Charton12/2012
4302^814356-2790449245146Enzo Doria12/2015
4312^814276-459029245122Enzo Doria04/2015
4322^814023+180923245046Enzo Doria07/2016
433(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
4342^811842-113675244389Enzo Doria09/2014
4352^811132-2787929244176Enzo Doria11/2015
4362^809746-2790971243758Enzo Doria01/2016
4372^808767-3295243464Yves Minet12/2016
4382^808621-113809243420Enzo Doria09/2014
4392^807724+1879621243150Enzo Doria09/2016
4402^805843-113611242583Enzo Doria08/2014
4412^805745-459763242554Enzo Doria05/2015
4422^805353+782687242436Enzo Doria11/2016
4432^804277-417933242112Enzo Doria01/2014
4442^803468-269039241868Enzo Doria10/2013
4452^803172+80851241779Enzo Doria07/2016
4463^506233-2241535Robert Price11/2013
4472^802025-25999241434Enzo Doria10/2013
448(3^505823+3^252912+1)/7241339Serge Batalov03/2014
4492^801303+1872923241217Enzo Doria05/2016
4502^800579-1862947240999Enzo Doria12/2015
4512^798973-26283240515Enzo Doria10/2013
4522^798671-69487240424Enzo Doria12/2015
4532^797220+79831239988Enzo Doria06/2016
4542^796910-26001239894Enzo Doria10/2013
4552^796598+653119239800Enzo Doria12/2016
4562^796432-1859729239750Enzo Doria11/2015
4572^796002-1852211239621Enzo Doria08/2015
4582^795709+75767239533Enzo Doria04/2016
4592^795708+81721239532Enzo Doria08/2016
4602^795468-2786249239460Enzo Doria10/2015
4612^795442+80779239452Enzo Doria07/2016
4622^795075-1852057239342Enzo Doria08/2015
4632^794043+1875023239031Enzo Doria06/2016
4642^793347-69577238822Enzo Doria01/2016
4652^792988-344429238714Enzo Doria08/2015
4662^792700-2786369238627Enzo Doria11/2015
4672^792663-1844797238616Enzo Doria06/2015
4682^792605-291943238598Enzo Doria07/2015
469(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
4702^789373+1869377237625Enzo Doria05/2016
471((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
4722^788942+1866409237496Enzo Doria02/2016
4732^788844-114329237466Enzo Doria01/2015
4742^788705-1859713237424Enzo Doria11/2015
4752^786180+1871971236664Enzo Doria05/2016
47611^227092-90236492Enzo Doria11/2012
4772^785260+1866361236387Enzo Doria02/2016
4782^785220+1880611236375Enzo Doria10/2016
47919^184650-2236122Robert Price10/2014
48010^236059+216513236060Patrick De Geest04/2016
48110^236059-20909236059Robert Price09/2015
4822^782634-113981235597Enzo Doria11/2014
4832^782423+1879733235533Enzo Doria09/2016
4842^781682-2789543235310Enzo Doria12/2015
4852^780408-113453234927Enzo Doria08/2014
4862^780368-1864829234915Enzo Doria01/2016
4872^779593-1836559234681Enzo Doria05/2015
488(5^335429+1)/6234455Paul Bourdelais08/2010
4892^778395-113617234321Enzo Doria08/2014
4902^776245-2792353233674Enzo Doria02/2016
4912^776060-114029233618Enzo Doria11/2014
4922^775987-2789557233596Enzo Doria12/2015
4932^775672+1866721233501Enzo Doria03/2016
494(11^223999+1)/12233270Paul Bourdelais02/2010
4952^774118+1885789233033Enzo Doria04/2017
49621^176191-20^176191232964Jean-Louis Charton01/2015
4972^773679-113425232901Enzo Doria08/2014
49810^232599+192489232600Patrick De Geest12/2013
49910^232599-3232599Markus Tervooren10/2010
5002^772552-458879232562Enzo Doria04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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