PRP Records

Probable Primes Top 10000

(277054 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 ?
1751(14*10^154773+37)/3154774Robert Price12/2018
17526*10^154742-31154743Robert Price07/2020
17532^513437+1879337154560Enzo Doria09/2016
17542^513306-113201154521Enzo Doria07/2014
1755(10^154494-13)/3154494Robert Price12/2017
17562^513042-113787154442Enzo Doria09/2014
1757(151*10^154434-7)/9154436Robert Price01/2020
17582^512628-114053154317Enzo Doria11/2014
17592^512529-49783154287Enzo Doria10/2015
1760(355573#+6991)/(6991*2031599)154285Makoto Morimoto06/2019
17612^512315-115297154223Enzo Doria06/2015
17622^512168+79561154178Enzo Doria06/2016
17634*10^154078-57154079Robert Price10/2018
1764(355049#+1859)/(11*13*10148891*62587751)154051Makoto Morimoto06/2019
17657*10^154038-57154039Robert Price06/2020
17662^511658-114371154025Enzo Doria02/2015
1767(57^87719+1)/58154022Paul Bourdelais11/2017
17682^511580-1846679154001Enzo Doria07/2015
1769(259*10^153998-1)/3154000Robert Price12/2020
17702^511541-113713153990Enzo Doria09/2014
177149958^32768+49957^32768153965Kellen Shenton11/2020
177210^153935-1000001153935Robert Price08/2020
1773(16*10^153868-73)/3153869Robert Price07/2020
17749*10^153851-67153852Robert Price11/2020
17752^511077-112723153850Enzo Doria06/2014
177669^83653-68^83653153826Robert Price12/2013
17772^510963-113707153816Enzo Doria09/2014
1778(154*10^153810-1)/9153812Serge Batalov12/2014
1779(181*25^109991-75077)/8153763Curtis Bright05/2015
17802*10^153746-3153747Robert Price07/2015
17812^510626+1179379153714Enzo Doria05/2016
1782(7*10^153664+113)/3153665Robert Price02/2018
17832^510420+81121153652Enzo Doria07/2016
1784(197*7^181761-1)/2153608Karsten Bonath05/2017
17852^509894-459161153494Enzo Doria05/2015
17862^509841+71657153478Enzo Doria04/2016
17879*10^153446+41153447Robert Price08/2020
17882^509533-1846723153385Enzo Doria07/2015
17892^509468-39989153366Enzo Doria09/2015
179070^83117-69^83117153360Robert Price01/2014
1791(112*10^153025-1)/3153027Serge Batalov12/2014
1792(19*10^153010+131)/3153011Robert Price06/2020
17932^508174-1855151152976Enzo Doria09/2015
1794181^67757-2152974Lelio R Paula12/2017
17952^508160-1864829152972Enzo Doria01/2016
179610^152960-50000000001152960Robert Price12/2020
17972^507857-1848199152881Enzo Doria07/2015
17982^507638-115361152815Enzo Doria07/2015
17992^507551-114025152789Enzo Doria11/2014
1800(6^196337+1)/7152780Paul Bourdelais02/2010
1801(22*10^152670-13)/9152671Robert Price06/2018
18022^506451-22339152457Enzo Doria07/2013
18032^505995-113185152320Enzo Doria07/2014
1804(4*10^152253+149)/9152253Robert Price04/2018
1805578^55117-577^55117152230Jean-Louis Charton08/2012
18062^505431-505431152150Henri Lifchitz04/2005
1807(203*10^152143+1)/3152145Robert Price03/2020
18082^505053+73097152037Enzo Doria04/2016
180922*10^151998+3152000Robert Price01/2020
1810(238*10^151979-1)/3151981Robert Price04/2020
1811(2^504793-7)/46765151954Lelio R Paula12/2017
1812350377#+797581151937Nicolas PALAU08/2017
18132^504618-343991151906Enzo Doria07/2015
18142^504212-461939151783Enzo Doria07/2015
18152^504054-2231151736Yves Minet10/2011
1816(28*10^151682+191)/3151683Robert Price02/2020
18172^503361-39883151527Enzo Doria09/2015
18182^503225+382667151486Enzo Doria10/2016
1819(26*10^151391-503)/9151392Robert Price07/2018
18202^502769+1877567151349Enzo Doria08/2016
18212^502576-4019151291Yves Minet10/2011
18225*10^151257+41151258Robert Price03/2019
18232^502290-2792501151205Enzo Doria02/2016
18242^502181+1868417151172Enzo Doria04/2016
18252^501781-1850503151052Enzo Doria08/2015
1826(5*10^151007+37)/3151008Robert Price03/2018
18272^501627-991151005Yves Minet02/2014
18282^501577-115333150990Enzo Doria07/2015
18298*10^150975+3150976Robert Price08/2015
18302^501512-113669150971Enzo Doria09/2014
1831(12^139739+1)/13150803Paul Bourdelais09/2011
1832(31^101111-1)/30150792Alexander Zhirkov11/2010
18332^500899-500899150786Henri Lifchitz04/2005
18342^500832+1876801150766Enzo Doria07/2016
1835(23*10^150763-59)/9150764Robert Price05/2018
18362^500699+1884953150726Enzo Doria02/2017
1837(13*10^150675-37)/3150676Robert Price01/2019
1838(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
18402^500337-71101150617Enzo Doria04/2016
1839(74*10^150616+133)/9150617Robert Price06/2019
18414*10^150577+91150578Robert Price08/2018
18422^500160+80071150564Enzo Doria06/2016
1843(2^500120+5)/9150551Lelio R Paula12/2017
1844(43*10^150515-421)/9150516Robert Price01/2019
1846(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
1845(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
18472^499861-29503150474Enzo Doria08/2015
18482^499653-113533150411Enzo Doria08/2014
1849(14*10^150391-191)/3150392Robert Price10/2020
18502^499534-221150375Yves Minet06/2012
18512^499225+49727150282Enzo Doria09/2016
18522^499054-29261150231Enzo Doria07/2015
1853(2^498898-7)/9150183Lelio R Paula10/2015
18543*10^150182+17150183Robert Price07/2018
18555*10^150175+63150176Robert Price09/2020
18562^498623+1866983150101Enzo Doria03/2016
1857(25*10^150050-403)/9150051Robert Price12/2020
1858numbpart(18140942830)150033Serge Batalov04/2017
185910^150029+4381150030Patrick De Geest05/2016
186010^150029-41150029Serge Batalov12/2014
186110^150000+1158603150001Patrick De Geest09/2018
186210^150000-245703150000Patrick De Geest09/2018
1863(38*10^149999+691)/9150000Robert Price10/2018
18642^498238-53149985Lelio R Paula12/2017
186545728^1905+1905^45728149984Hans Havermann10/2020
18665*10^149907+23149908Robert Price03/2019
186739347^6442+6442^39347149874Hans Havermann09/2020
18682^497850+81049149868Enzo Doria07/2016
186937228^10575+10575^37228149816Hans Havermann10/2020
1870(5*2^497673+1)/2743149812Lelio R Paula10/2015
1871(5*2^497671+1)/373703149810Lelio R Paula10/2015
1872(2*10^149803-143)/3149803Robert Price03/2018
187333845^26604+26604^33845149763Hans Havermann09/2020
18742^497434-2784191149743Enzo Doria10/2015
1875(865*10^149737-1)/9149739Robert Price04/2020
187638237^8214+8214^38237149681Hans Havermann09/2020
1877(23*10^149655+19)/3149656Robert Price07/2019
18782^497068-113579149633Enzo Doria08/2014
18792^497037+73727149624Enzo Doria04/2016
188034942^19067+19067^34942149562Hans Havermann09/2020
188133696^27449+27449^33696149561Hans Havermann09/2020
18822^496773+77747149544Enzo Doria05/2016
1883(206*10^149459+7)/3149461Robert Price07/2020
188434589^20940+20940^34589149459Hans Havermann09/2020
18852^496477-113485149455Enzo Doria08/2014
1886((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
18872^496270-49451149393Enzo Doria10/2015
18882^496238-1865081149383Enzo Doria01/2016
188933831^26030+26030^33831149380Hans Havermann09/2020
189034131^23780+23780^34131149365Hans Havermann09/2020
1891(5*10^149335-53)/3149336Robert Price09/2020
18922^495968-1853699149302Enzo Doria09/2015
18932^495935-4117149292Yves Minet02/2018
189435816^14709+14709^35816149267Hans Havermann09/2020
18952^495712-396765149225Enzo Doria07/2013
1896(21*2^495676-1)/4835149211Lelio R Paula10/2015
18972^495420+1880701149137Enzo Doria10/2016
18982^495337-1847293149112Enzo Doria07/2015
1899(2^495193-7)/5149068Lelio R Paula10/2015
190033282^30097+30097^33282149055Hans Havermann09/2020
190137384^9705+9705^37384149050Hans Havermann09/2020
190234808^19143+19143^34808149049Hans Havermann09/2020
1903413^56963-412^56963149013Jean-Louis Charton08/2012
190447^89113-46^89113149006Robert Price10/2012
19052^494916+87855148985Lelio R Paula01/2016
19066*10^148982+73148983Robert Price04/2019
190710^148934-1000000001148934Robert Price11/2020
190839000^6571+6571^39000148888Hans Havermann10/2020
19092^494586-2791991148886Enzo Doria02/2016
19108*10^148860-3148861Ray Chandler04/2011
191138262^7769+7769^38262148854Hans Havermann10/2020
19122^494333-286183148810Enzo Doria06/2015
19132^494144-264119148753Enzo Doria05/2014
191436502^11823+11823^36502148663Hans Havermann11/2020
1915(5*2^493838-1)/3721148658Lelio R Paula10/2015
191664239^206+206^64239148641Hans Havermann10/2020
1917(23*2^493761-1)/555148636Lelio R Paula10/2015
1918(151*10^148601-1)/3148603Robert Price03/2020
19192^493636+82081148600Enzo Doria09/2016
1920((((((((((((((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
1921177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
1922(2*10^148460-23)/3148460Robert Price04/2018
1923(28*10^148445+101)/3148446Robert Price09/2020
192436203^12556+12556^36203148391Hans Havermann10/2020
192533912^23749+23749^33912148387Hans Havermann10/2020
1926(8*10^148328+1)/9148328Serge Batalov05/2010
192734294^21117+21117^34294148309Hans Havermann10/2020
1928(71*10^148306-539)/9148307Robert Price07/2019
192938042^7875+7875^38042148222Hans Havermann10/2020
19305^211959-12874148153Enzo Doria05/2014
193134142^21831+21831^34142148145Hans Havermann10/2020
193236303^12016+12016^36303148108Hans Havermann10/2020
1933(16*10^148071+41)/3148072Robert Price03/2019
1934187^65175-2148068Lelio R Paula11/2017
19352^491851+1871453148062Enzo Doria05/2016
1936(68*10^148060-257)/9148061Robert Price07/2019
1937(151*10^148020-1)/3148022Robert Price03/2020
193839153^6032+6032^39153148017Hans Havermann10/2020
193936798^10507+10507^36798147983Hans Havermann12/2020
1940(26*10^147973-23)/3147974Robert Price12/2019
19412^491521-1865323147963Enzo Doria02/2016
1942(2^491476+7)/71147948Lelio R Paula10/2015
19432^491391-7807147924Lelio R Paula01/2013
194439736^5279+5279^39736147920Hans Havermann11/2020
19452^491370-113297147918Enzo Doria07/2014
1946(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
194744368^2155+2155^44368147899Hans Havermann12/2020
1948(17*10^147890+79)/3147891Robert Price04/2019
194994*10^147871-3147873Robert Price05/2020
195010^147843-50000000001147843Robert Price12/2020
195135805^13346+13346^35805147709Hans Havermann11/2020
19522^490660-17147704Lelio R Paula12/2017
1953(229*10^147699-1)/3147701Robert Price07/2020
195440656^4289+4289^40656147678Hans Havermann11/2020
19552^490550+1179439147671Enzo Doria06/2016
1956(23*10^147649-59)/9147650Robert Price05/2018
19572^490303+2793653147596Enzo Doria03/2016
1958199^64181-2147543Lelio R Paula11/2017
195932849^30958+30958^32849147518Hans Havermann11/2020
19602^489871-286987147466Enzo Doria07/2015
19612^489864-351899147464Enzo Doria07/2015
1962175^65724-2147422Lelio R Paula11/2017
19632^489712+1874851147419Enzo Doria06/2016
196434473^18830+18830^34473147367Hans Havermann11/2020
196563^81896-2147359Lelio R Paula10/2017
196634580^18237+18237^34580147344Hans Havermann11/2020
1967(11*10^147313-107)/3147314Robert Price09/2018
19682^489305-59815147296Enzo Doria10/2015
1969(2^489280-7)/6381147285Lelio R Paula09/2015
197033556^24457+24457^33556147258Hans Havermann11/2020
19712^489125+80357147242Enzo Doria06/2016
197232835^30452+30452^32835147220Hans Havermann12/2020
1973(148*10^147139-1)/3147141Robert Price03/2020
197434338^19255+19255^34338147123Hans Havermann11/2020
19752^488648-112799147098Enzo Doria07/2014
19762^488627-350317147092Enzo Doria06/2015
197733432^25075+25075^33432147076Hans Havermann12/2020
1978(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
19792^488280-2165146987Yves Minet07/2014
19802^488278+45146987Lelio R Paula12/2017
19812^487927-39146881Lelio R Paula12/2017
1982(7*10^146860-13)/3146861Robert Price07/2018
1983(26*10^146856-77)/3146857Robert Price11/2019
198432948^28611+28611^32948146834Hans Havermann11/2020
198542596^2799+2799^42596146829Hans Havermann12/2020
19862^487726-1863341146821Enzo Doria12/2015
198743838^2229+2229^43838146775Hans Havermann11/2020
198835005^15594+15594^35005146775Hans Havermann11/2020
1989((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
199032963^28234+28234^32963146711Hans Havermann12/2020
1991(22*10^146661-19)/3146662Robert Price04/2019
199233958^20825+20825^33958146651Hans Havermann12/2020
19932^487121-39523146639Enzo Doria09/2015
199461063^252+252^61063146637Hans Havermann12/2020
1995(7*2^486967+1)/39146591Lelio R Paula09/2015
199634099^19900+19900^34099146587Hans Havermann11/2020
19972^486893-79146570Yves Minet09/2017
199836818^9567+9567^36818146565Hans Havermann12/2020
19992^486840+1879141146554Enzo Doria08/2016
20002^486774-87146534Lelio R Paula12/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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