PRP Records

Probable Primes Top 10000

(288323 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 ?
20017*10^154038-57154039Robert Price06/2020
20022^511658-114371154025Enzo Doria02/2015
2003(57^87719+1)/58154022Paul Bourdelais11/2017
20042^511580-1846679154001Enzo Doria07/2015
2005(259*10^153998-1)/3154000Robert Price12/2020
20062^511541-113713153990Enzo Doria09/2014
200749958^32768+49957^32768153965Kellen Shenton11/2020
200810^153935+970801153936Patrick De Geest05/2021
200910^153935-1000001153935Robert Price08/2020
2010(16*10^153868-73)/3153869Robert Price07/2020
20119*10^153851-67153852Robert Price11/2020
20122^511077-112723153850Enzo Doria06/2014
201369^83653-68^83653153826Robert Price12/2013
20142^510963-113707153816Enzo Doria09/2014
2015(154*10^153810-1)/9153812Serge Batalov12/2014
2016(181*25^109991-75077)/8153763Curtis Bright05/2015
20172*10^153746-3153747Robert Price07/2015
20182^510626+1179379153714Enzo Doria05/2016
2019(7*10^153664+113)/3153665Robert Price02/2018
20202^510420+81121153652Enzo Doria07/2016
2021(197*7^181761-1)/2153608Karsten Bonath05/2017
20222^509894-459161153494Enzo Doria05/2015
20232^509841+71657153478Enzo Doria04/2016
20249*10^153446+41153447Robert Price08/2020
20252^509533-1846723153385Enzo Doria07/2015
20262^509468-39989153366Enzo Doria09/2015
202770^83117-69^83117153360Robert Price01/2014
2028(112*10^153025-1)/3153027Serge Batalov12/2014
2029(19*10^153010+131)/3153011Robert Price06/2020
20302^508174-1855151152976Enzo Doria09/2015
2031181^67757-2152974Lelio R Paula12/2017
20322^508160-1864829152972Enzo Doria01/2016
203310^152960+412563152961Patrick De Geest05/2021
203410^152960-50000000001152960Robert Price12/2020
203510^152960-423749152960Patrick De Geest05/2021
2036(71*10^152933-143)/9152934Robert Price10/2021
20372^507857-1848199152881Enzo Doria07/2015
20382^507638-115361152815Enzo Doria07/2015
20392^507551-114025152789Enzo Doria11/2014
2040(6^196337+1)/7152780Paul Bourdelais02/2010
2041(22*10^152670-13)/9152671Robert Price06/2018
20422^506451-22339152457Enzo Doria07/2013
20432^505995-113185152320Enzo Doria07/2014
2044(4*10^152253+149)/9152253Robert Price04/2018
2045578^55117-577^55117152230Jean-Louis Charton08/2012
20462^505431-505431152150Henri Lifchitz04/2005
2047(203*10^152143+1)/3152145Robert Price03/2020
20482^505053+73097152037Enzo Doria04/2016
204922*10^151998+3152000Robert Price01/2020
2050(238*10^151979-1)/3151981Robert Price04/2020
2051(2^504793-7)/46765151954Lelio R Paula12/2017
2052350377#+797581151937Nicolas PALAU08/2017
20532^504618-343991151906Enzo Doria07/2015
20542^504212-461939151783Enzo Doria07/2015
20557*10^151772-41151773Robert Price08/2021
20562^504054-2231151736Yves Minet10/2011
2057(28*10^151682+191)/3151683Robert Price02/2020
20582^503475-933075151562Paul Bourdelais06/2021
20592^503361-39883151527Enzo Doria09/2015
20602^503225+382667151486Enzo Doria10/2016
2061(844*10^151396-7)/9151398Robert Price05/2021
2062(26*10^151391-503)/9151392Robert Price07/2018
20632^502769+1877567151349Enzo Doria08/2016
20642^502576-4019151291Yves Minet10/2011
20655*10^151257+41151258Robert Price03/2019
20662^502290-2792501151205Enzo Doria02/2016
20672^502181+1868417151172Enzo Doria04/2016
20686*10^151063-77151064Robert Price09/2021
20692^501781-1850503151052Enzo Doria08/2015
2070(5*10^151007+37)/3151008Robert Price03/2018
20712^501627-991151005Yves Minet02/2014
20722^501577-115333150990Enzo Doria07/2015
20738*10^150975+3150976Robert Price08/2015
20742^501512-113669150971Enzo Doria09/2014
2075(12^139739+1)/13150803Paul Bourdelais09/2011
2076(31^101111-1)/30150792Alexander Zhirkov11/2010
20772^500899-500899150786Henri Lifchitz04/2005
20782^500832+1876801150766Enzo Doria07/2016
2079(23*10^150763-59)/9150764Robert Price05/2018
20802^500699+1884953150726Enzo Doria02/2017
2081(13*10^150675-37)/3150676Robert Price01/2019
2082(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
20832^500337-71101150617Enzo Doria04/2016
2084(74*10^150616+133)/9150617Robert Price06/2019
20854*10^150577+91150578Robert Price08/2018
20862^500160+80071150564Enzo Doria06/2016
2087(2^500120+5)/9150551Lelio R Paula12/2017
2088(43*10^150515-421)/9150516Robert Price01/2019
2089(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
2090(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
20912^499861-29503150474Enzo Doria08/2015
20922^499653-113533150411Enzo Doria08/2014
2093(14*10^150391-191)/3150392Robert Price10/2020
20942^499534-221150375Yves Minet06/2012
2095(28*10^150294+41)/3150295Robert Price07/2021
20962^499225+49727150282Enzo Doria09/2016
20972^499054-29261150231Enzo Doria07/2015
2098(844*10^150196-7)/9150198Robert Price05/2021
20992^498907-933075150186Paul Bourdelais06/2021
2100(2^498898-7)/9150183Lelio R Paula10/2015
21013*10^150182+17150183Robert Price07/2018
21025*10^150175+63150176Robert Price09/2020
21032^498623+1866983150101Enzo Doria03/2016
2104(25*10^150050-403)/9150051Robert Price12/2020
2105numbpart(18140942830)150033Serge Batalov04/2017
210610^150029+4381150030Patrick De Geest05/2016
210710^150029-41150029Serge Batalov12/2014
210810^150000+1158603150001Patrick De Geest09/2018
210910^150000-245703150000Patrick De Geest09/2018
2110(38*10^149999+691)/9150000Robert Price10/2018
21112^498238-53149985Lelio R Paula12/2017
211245728^1905+1905^45728149984Hans Havermann10/2020
21135*10^149907+23149908Robert Price03/2019
211439347^6442+6442^39347149874Hans Havermann09/2020
21152^497850+81049149868Enzo Doria07/2016
211637228^10575+10575^37228149816Hans Havermann10/2020
2117(5*2^497673+1)/2743149812Lelio R Paula10/2015
2118(5*2^497671+1)/373703149810Lelio R Paula10/2015
2119(2*10^149803-143)/3149803Robert Price03/2018
212033845^26604+26604^33845149763Hans Havermann09/2020
21212^497434-2784191149743Enzo Doria10/2015
2122(865*10^149737-1)/9149739Robert Price04/2020
212310^149695-7000001149695Robert Price06/2021
212438237^8214+8214^38237149681Hans Havermann09/2020
2125(23*10^149655+19)/3149656Robert Price07/2019
21262^497068-113579149633Enzo Doria08/2014
21272^497037+73727149624Enzo Doria04/2016
212811*10^149618+3149620Robert Price07/2021
212934942^19067+19067^34942149562Hans Havermann09/2020
213033696^27449+27449^33696149561Hans Havermann09/2020
21312^496773+77747149544Enzo Doria05/2016
2132(7*10^149483-493)/9149483Robert Price04/2021
2133(206*10^149459+7)/3149461Robert Price07/2020
213434589^20940+20940^34589149459Hans Havermann09/2020
21352^496477-113485149455Enzo Doria08/2014
2136((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
21372^496270-49451149393Enzo Doria10/2015
21382^496238-1865081149383Enzo Doria01/2016
213933831^26030+26030^33831149380Hans Havermann09/2020
214034131^23780+23780^34131149365Hans Havermann09/2020
2141(5*10^149335-53)/3149336Robert Price09/2020
21422^495968-1853699149302Enzo Doria09/2015
21432^495935-4117149292Yves Minet02/2018
214435816^14709+14709^35816149267Hans Havermann09/2020
2145(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
21462^495712-396765149225Enzo Doria07/2013
2147(21*2^495676-1)/4835149211Lelio R Paula10/2015
21482^495420+1880701149137Enzo Doria10/2016
21492^495337-1847293149112Enzo Doria07/2015
2150(2^495193-7)/5149068Lelio R Paula10/2015
215133282^30097+30097^33282149055Hans Havermann09/2020
215237384^9705+9705^37384149050Hans Havermann09/2020
215334808^19143+19143^34808149049Hans Havermann09/2020
2154413^56963-412^56963149013Jean-Louis Charton08/2012
215547^89113-46^89113149006Robert Price10/2012
21562^494916+87855148985Lelio R Paula01/2016
21576*10^148982+73148983Robert Price04/2019
215810^148934+1530019148935Patrick De Geest02/2021
215910^148934-1000000001148934Robert Price11/2020
216010^148934-512057148934Patrick De Geest02/2021
216139000^6571+6571^39000148888Hans Havermann10/2020
21622^494586-2791991148886Enzo Doria02/2016
21638*10^148860-3148861Ray Chandler04/2011
216438262^7769+7769^38262148854Hans Havermann10/2020
21652^494333-286183148810Enzo Doria06/2015
21662^494144-264119148753Enzo Doria05/2014
216736502^11823+11823^36502148663Hans Havermann11/2020
2168(5*2^493838-1)/3721148658Lelio R Paula10/2015
216964239^206+206^64239148641Hans Havermann10/2020
2170(23*2^493761-1)/555148636Lelio R Paula10/2015
2171(23*10^148627-137)/3148628Robert Price08/2021
2172(151*10^148601-1)/3148603Robert Price03/2020
21732^493636+82081148600Enzo Doria09/2016
2174((((((((((((((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
2175177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
2176(2*10^148460-23)/3148460Robert Price04/2018
2177(28*10^148445+101)/3148446Robert Price09/2020
217836203^12556+12556^36203148391Hans Havermann10/2020
217933912^23749+23749^33912148387Hans Havermann10/2020
2180(8*10^148328+1)/9148328Serge Batalov05/2010
218134294^21117+21117^34294148309Hans Havermann10/2020
2182(71*10^148306-539)/9148307Robert Price07/2019
218338042^7875+7875^38042148222Hans Havermann10/2020
21845^211959-12874148153Enzo Doria05/2014
218534142^21831+21831^34142148145Hans Havermann10/2020
218610^148112+34059148113Patrick De Geest05/2021
218710^148112-70000001148112Robert Price03/2021
218810^148112-106593148112Patrick De Geest05/2021
218936303^12016+12016^36303148108Hans Havermann10/2020
2190(16*10^148071+41)/3148072Robert Price03/2019
2191187^65175-2148068Lelio R Paula11/2017
21922^491851+1871453148062Enzo Doria05/2016
2193(68*10^148060-257)/9148061Robert Price07/2019
2194(151*10^148020-1)/3148022Robert Price03/2020
219539153^6032+6032^39153148017Hans Havermann10/2020
219636798^10507+10507^36798147983Hans Havermann12/2020
2197(26*10^147973-23)/3147974Robert Price12/2019
21982^491521-1865323147963Enzo Doria02/2016
2199(2^491476+7)/71147948Lelio R Paula10/2015
22002^491391-7807147924Lelio R Paula01/2013
220139736^5279+5279^39736147920Hans Havermann11/2020
22022^491370-113297147918Enzo Doria07/2014
2203(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
220444368^2155+2155^44368147899Hans Havermann12/2020
2205(17*10^147890+79)/3147891Robert Price04/2019
220694*10^147871-3147873Robert Price05/2020
220710^147843+620967147844Patrick De Geest05/2021
220810^147843-50000000001147843Robert Price12/2020
220910^147843-182891147843Patrick De Geest05/2021
221035805^13346+13346^35805147709Hans Havermann11/2020
22112^490660-17147704Lelio R Paula12/2017
2212(229*10^147699-1)/3147701Robert Price07/2020
221340656^4289+4289^40656147678Hans Havermann11/2020
22142^490550+1179439147671Enzo Doria06/2016
2215(23*10^147649-59)/9147650Robert Price05/2018
22162^490303+2793653147596Enzo Doria03/2016
2217199^64181-2147543Lelio R Paula11/2017
221832849^30958+30958^32849147518Hans Havermann11/2020
22192^489871-286987147466Enzo Doria07/2015
22202^489864-351899147464Enzo Doria07/2015
2221175^65724-2147422Lelio R Paula11/2017
22222^489712+1874851147419Enzo Doria06/2016
222334473^18830+18830^34473147367Hans Havermann11/2020
222463^81896-2147359Lelio R Paula10/2017
222534580^18237+18237^34580147344Hans Havermann11/2020
2226(11*10^147313-107)/3147314Robert Price09/2018
22272^489305-59815147296Enzo Doria10/2015
2228(2^489280-7)/6381147285Lelio R Paula09/2015
22292*10^147264-61147265Robert Price10/2021
22302*10^147260+29147261Robert Price02/2021
223133556^24457+24457^33556147258Hans Havermann11/2020
22322^489125+80357147242Enzo Doria06/2016
223332835^30452+30452^32835147220Hans Havermann12/2020
2234(148*10^147139-1)/3147141Robert Price03/2020
223534338^19255+19255^34338147123Hans Havermann11/2020
22362^488648-112799147098Enzo Doria07/2014
22372^488627-350317147092Enzo Doria06/2015
223833432^25075+25075^33432147076Hans Havermann12/2020
2239(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
22402^488280-2165146987Yves Minet07/2014
22412^488278+45146987Lelio R Paula12/2017
22422^487927-39146881Lelio R Paula12/2017
2243(7*10^146860-13)/3146861Robert Price07/2018
2244(26*10^146856-77)/3146857Robert Price11/2019
224532948^28611+28611^32948146834Hans Havermann11/2020
224642596^2799+2799^42596146829Hans Havermann12/2020
22472^487726-1863341146821Enzo Doria12/2015
224843838^2229+2229^43838146775Hans Havermann11/2020
224935005^15594+15594^35005146775Hans Havermann11/2020
2250(167*10^146764+7)/3146766Robert Price04/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 23 2021 10:56 (Time in France)

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