PRP Records

Probable Primes Top 10000

(290751 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 ?
22512^502769+1877567151349Enzo Doria08/2016
22522^502576-4019151291Yves Minet10/2011
22535*10^151257+41151258Robert Price03/2019
22542^502290-2792501151205Enzo Doria02/2016
22552^502181+1868417151172Enzo Doria04/2016
22566*10^151063-77151064Robert Price09/2021
22572^501781-1850503151052Enzo Doria08/2015
2258(5*10^151007+37)/3151008Robert Price03/2018
22592^501627-991151005Yves Minet02/2014
22602^501577-115333150990Enzo Doria07/2015
22618*10^150975+3150976Robert Price08/2015
22622^501512-113669150971Enzo Doria09/2014
2263(83*10^150908+493)/9150909Robert Price12/2021
22642*10^150818+83150819Robert Price12/2021
2265(12^139739+1)/13150803Paul Bourdelais09/2011
2266(31^101111-1)/30150792Alexander Zhirkov11/2010
22672^500899-500899150786Henri Lifchitz04/2005
22682^500832+1876801150766Enzo Doria07/2016
2269(23*10^150763-59)/9150764Robert Price05/2018
22702^500699+1884953150726Enzo Doria02/2017
2271(13*10^150675-37)/3150676Robert Price01/2019
2272(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
22732^500337-71101150617Enzo Doria04/2016
2274(74*10^150616+133)/9150617Robert Price06/2019
22754*10^150577+91150578Robert Price08/2018
22762^500160+80071150564Enzo Doria06/2016
2277(2^500120+5)/9150551Lelio R Paula12/2017
2278(43*10^150515-421)/9150516Robert Price01/2019
2279(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
2280(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
22812^499861-29503150474Enzo Doria08/2015
22822^499653-113533150411Enzo Doria08/2014
2283(14*10^150391-191)/3150392Robert Price10/2020
22842^499534-221150375Yves Minet06/2012
2285(28*10^150294+41)/3150295Robert Price07/2021
22862^499225+49727150282Enzo Doria09/2016
2287(695*10^150274+7)/9150276Robert Price12/2021
22882^499054-29261150231Enzo Doria07/2015
2289(844*10^150196-7)/9150198Robert Price05/2021
22902^498907-933075150186Paul Bourdelais06/2021
2291(2^498898-7)/9150183Lelio R Paula10/2015
22923*10^150182+17150183Robert Price07/2018
22935*10^150175+63150176Robert Price09/2020
2294(77*10^150128+67)/9150129Robert Price12/2021
22952^498623+1866983150101Enzo Doria03/2016
2296(25*10^150050-403)/9150051Robert Price12/2020
2297numbpart(18140942830)150033Serge Batalov04/2017
229810^150029+4381150030Patrick De Geest05/2016
229910^150029-41150029Serge Batalov12/2014
230010^150000+1158603150001Patrick De Geest09/2018
230110^150000-245703150000Patrick De Geest09/2018
2302(38*10^149999+691)/9150000Robert Price10/2018
23032^498238-53149985Lelio R Paula12/2017
230445728^1905+1905^45728149984Hans Havermann10/2020
23055*10^149907+23149908Robert Price03/2019
230639347^6442+6442^39347149874Hans Havermann09/2020
23072^497850+81049149868Enzo Doria07/2016
230837228^10575+10575^37228149816Hans Havermann10/2020
2309(5*2^497673+1)/2743149812Lelio R Paula10/2015
2310(5*2^497671+1)/373703149810Lelio R Paula10/2015
2311(2*10^149803-143)/3149803Robert Price03/2018
231233845^26604+26604^33845149763Hans Havermann09/2020
23132^497434-2784191149743Enzo Doria10/2015
2314(865*10^149737-1)/9149739Robert Price04/2020
231510^149695-7000001149695Robert Price06/2021
231638237^8214+8214^38237149681Hans Havermann09/2020
2317(23*10^149655+19)/3149656Robert Price07/2019
23182^497068-113579149633Enzo Doria08/2014
23192^497037+73727149624Enzo Doria04/2016
232011*10^149618+3149620Robert Price07/2021
232134942^19067+19067^34942149562Hans Havermann09/2020
232233696^27449+27449^33696149561Hans Havermann09/2020
23232^496773+77747149544Enzo Doria05/2016
2324(7*10^149483-493)/9149483Robert Price04/2021
2325(206*10^149459+7)/3149461Robert Price07/2020
232634589^20940+20940^34589149459Hans Havermann09/2020
23272^496477-113485149455Enzo Doria08/2014
2328((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
23292^496270-49451149393Enzo Doria10/2015
23302^496238-1865081149383Enzo Doria01/2016
233133831^26030+26030^33831149380Hans Havermann09/2020
233234131^23780+23780^34131149365Hans Havermann09/2020
2333(5*10^149335-53)/3149336Robert Price09/2020
23342^495968-1853699149302Enzo Doria09/2015
23352^495935-4117149292Yves Minet02/2018
233635816^14709+14709^35816149267Hans Havermann09/2020
2337(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
23382^495712-396765149225Enzo Doria07/2013
2339(21*2^495676-1)/4835149211Lelio R Paula10/2015
23402^495420+1880701149137Enzo Doria10/2016
23412^495337-1847293149112Enzo Doria07/2015
2342(2^495193-7)/5149068Lelio R Paula10/2015
23432^495163+111546435149059Paul Bourdelais10/2021
234433282^30097+30097^33282149055Hans Havermann09/2020
234537384^9705+9705^37384149050Hans Havermann09/2020
234634808^19143+19143^34808149049Hans Havermann09/2020
2347413^56963-412^56963149013Jean-Louis Charton08/2012
234847^89113-46^89113149006Robert Price10/2012
23492^494916+87855148985Lelio R Paula01/2016
23506*10^148982+73148983Robert Price04/2019
235110^148934+1530019148935Patrick De Geest02/2021
235210^148934-1000000001148934Robert Price11/2020
235310^148934-512057148934Patrick De Geest02/2021
235439000^6571+6571^39000148888Hans Havermann10/2020
23552^494586-2791991148886Enzo Doria02/2016
23568*10^148860-3148861Ray Chandler04/2011
235738262^7769+7769^38262148854Hans Havermann10/2020
235810^148816-500001148816Robert Price03/2022
2359(53*10^148811-287)/9148812Robert Price02/2022
23602^494333-286183148810Enzo Doria06/2015
23612^494144-264119148753Enzo Doria05/2014
23626*10^148734+47148735Robert Price06/2022
236336502^11823+11823^36502148663Hans Havermann11/2020
2364(5*2^493838-1)/3721148658Lelio R Paula10/2015
236564239^206+206^64239148641Hans Havermann10/2020
2366(23*2^493761-1)/555148636Lelio R Paula10/2015
2367(23*10^148627-137)/3148628Robert Price08/2021
2368(151*10^148601-1)/3148603Robert Price03/2020
23692^493636+82081148600Enzo Doria09/2016
2370((((((((((((((34251^2-2)^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)^2-2148593Serge Batalov07/2016
2371177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
2372(2*10^148460-23)/3148460Robert Price04/2018
2373(28*10^148445+101)/3148446Robert Price09/2020
237436203^12556+12556^36203148391Hans Havermann10/2020
237533912^23749+23749^33912148387Hans Havermann10/2020
2376(8*10^148328+1)/9148328Serge Batalov05/2010
237734294^21117+21117^34294148309Hans Havermann10/2020
2378(71*10^148306-539)/9148307Robert Price07/2019
237938042^7875+7875^38042148222Hans Havermann10/2020
23805^211959-12874148153Enzo Doria05/2014
238134142^21831+21831^34142148145Hans Havermann10/2020
238210^148112+34059148113Patrick De Geest05/2021
238310^148112-70000001148112Robert Price03/2021
238410^148112-106593148112Patrick De Geest05/2021
238536303^12016+12016^36303148108Hans Havermann10/2020
2386(77*10^148089-149)/9148090Robert Price03/2022
2387(16*10^148071+41)/3148072Robert Price03/2019
2388187^65175-2148068Lelio R Paula11/2017
23892^491851+1871453148062Enzo Doria05/2016
2390(68*10^148060-257)/9148061Robert Price07/2019
2391(151*10^148020-1)/3148022Robert Price03/2020
239239153^6032+6032^39153148017Hans Havermann10/2020
239336798^10507+10507^36798147983Hans Havermann12/2020
2394(26*10^147973-23)/3147974Robert Price12/2019
23952^491521-1865323147963Enzo Doria02/2016
2396(2^491476+7)/71147948Lelio R Paula10/2015
23972*10^147928+47147929Robert Price12/2021
23982^491391-7807147924Lelio R Paula01/2013
239939736^5279+5279^39736147920Hans Havermann11/2020
24002^491370-113297147918Enzo Doria07/2014
2401(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
240244368^2155+2155^44368147899Hans Havermann12/2020
2403(17*10^147890+79)/3147891Robert Price04/2019
240494*10^147871-3147873Robert Price05/2020
240510^147843+620967147844Patrick De Geest05/2021
240610^147843-50000000001147843Robert Price12/2020
240710^147843-182891147843Patrick De Geest05/2021
240835805^13346+13346^35805147709Hans Havermann11/2020
24092^490672+255255147707Paul Bourdelais10/2021
24102^490660-17147704Lelio R Paula12/2017
2411(229*10^147699-1)/3147701Robert Price07/2020
241240656^4289+4289^40656147678Hans Havermann11/2020
24132^490550+1179439147671Enzo Doria06/2016
2414(23*10^147649-59)/9147650Robert Price05/2018
24152^490303+2793653147596Enzo Doria03/2016
24162^490266+255255147585Paul Bourdelais10/2021
2417199^64181-2147543Lelio R Paula11/2017
241832849^30958+30958^32849147518Hans Havermann11/2020
24192^489871-286987147466Enzo Doria07/2015
24202^489864-351899147464Enzo Doria07/2015
2421175^65724-2147422Lelio R Paula11/2017
24222^489712+1874851147419Enzo Doria06/2016
242334473^18830+18830^34473147367Hans Havermann11/2020
242463^81896-2147359Lelio R Paula10/2017
242534580^18237+18237^34580147344Hans Havermann11/2020
2426(11*10^147313-107)/3147314Robert Price09/2018
2427(397*10^147310+17)/9147312Robert Price03/2022
24282^489305-59815147296Enzo Doria10/2015
2429(2^489280-7)/6381147285Lelio R Paula09/2015
24302*10^147264-61147265Robert Price10/2021
24312*10^147260+29147261Robert Price02/2021
243233556^24457+24457^33556147258Hans Havermann11/2020
24332^489125+80357147242Enzo Doria06/2016
243432835^30452+30452^32835147220Hans Havermann12/2020
2435(19*10^147213-97)/3147214Robert Price10/2021
2436(148*10^147139-1)/3147141Robert Price03/2020
243734338^19255+19255^34338147123Hans Havermann11/2020
24382^488648-112799147098Enzo Doria07/2014
24392^488627-350317147092Enzo Doria06/2015
244033432^25075+25075^33432147076Hans Havermann12/2020
2441(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
24422^488280-2165146987Yves Minet07/2014
24432^488278+45146987Lelio R Paula12/2017
24442^487927-39146881Lelio R Paula12/2017
2445(7*10^146860-13)/3146861Robert Price07/2018
2446(26*10^146856-77)/3146857Robert Price11/2019
244732948^28611+28611^32948146834Hans Havermann11/2020
244842596^2799+2799^42596146829Hans Havermann12/2020
24492^487726-1863341146821Enzo Doria12/2015
245043838^2229+2229^43838146775Hans Havermann11/2020
245135005^15594+15594^35005146775Hans Havermann11/2020
2452(167*10^146764+7)/3146766Robert Price04/2021
245353^85114+85114146761Kellen Shenton05/2022
2454(59*10^146738+157)/9146739Robert Price12/2021
2455((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
245632963^28234+28234^32963146711Hans Havermann12/2020
2457(22*10^146661-19)/3146662Robert Price04/2019
245833958^20825+20825^33958146651Hans Havermann12/2020
24592^487121-39523146639Enzo Doria09/2015
246061063^252+252^61063146637Hans Havermann12/2020
2461(7*2^486967+1)/39146591Lelio R Paula09/2015
246234099^19900+19900^34099146587Hans Havermann11/2020
24632^486893-79146570Yves Minet09/2017
246436818^9567+9567^36818146565Hans Havermann12/2020
24652^486840+1879141146554Enzo Doria08/2016
24662^486774-87146534Lelio R Paula12/2017
246738655^6176+6176^38655146530Hans Havermann11/2020
24688*10^146522-81146523Robert Price02/2021
246932820^29059+29059^32820146485Hans Havermann12/2020
247037261^8530+8530^37261146472Hans Havermann12/2020
247166953^154+154^66953146462Hans Havermann12/2020
247296^73877-95^73877146445Robert Price10/2015
24738*10^146421+81146422Robert Price08/2019
247433153^26090+26090^33153146420Hans Havermann11/2020
2475(52^85259+1)/53146304Paul Bourdelais09/2017
2476179^64935+2146290Lelio R Paula10/2017
247732595^30758+30758^32595146285Hans Havermann11/2020
247834972^15157+15157^34972146205Hans Havermann12/2020
2479(16*10^146200+131)/3146201Robert Price03/2022
2480(19*10^146181-49)/3146182Robert Price05/2019
24812^485531-114621146160Enzo Doria05/2015
24822^485473-933075146142Paul Bourdelais06/2021
2483(2^485461-9)/4249146135Lelio R Paula09/2015
24842^485389+81887146117Enzo Doria08/2016
248532554^30773+30773^32554146108Hans Havermann11/2020
2486(10^146063+71)/9146063Serge Batalov07/2015
24872*10^146051-63146052Robert Price01/2022
2488(2^485119+7)/2745146032Lelio R Paula09/2015
2489(22*10^146029+257)/9146030Robert Price06/2018
24907*10^145982-53145983Robert Price06/2020
24912^484743+1872923145923Enzo Doria05/2016
249233140^25287+25287^33140145913Hans Havermann01/2021
249337875^7112+7112^37875145895Hans Havermann01/2021
249432862^27473+27473^32862145872Hans Havermann01/2021
249532836^27587+27587^32836145815Hans Havermann01/2021
24962^484341+1879157145802Enzo Doria08/2016
24972*10^145784-91145785Robert Price04/2020
24982^484271-51145781Lelio R Paula11/2017
2499(188*10^145750-11)/3145752Robert Price02/2022
250070^78989-69^78989145743Robert Price01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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