PRP Records

Probable Primes Top 10000

(301668 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 ?
400127868^33759-33759^27868150063Frank Doornink06/2024
4002(25*10^150050-403)/9150051Robert Price12/2020
4003numbpart(18140942830)150033Serge Batalov04/2017
400410^150029+4381150030Patrick De Geest05/2016
400510^150029-41150029Serge Batalov12/2014
400633185^33185+618^618150028Serge Batalov04/2024
40079*34^97952+529150013Eric Chen08/2023
400810^150000+1158603150001Patrick De Geest09/2018
400910^150000-245703150000Patrick De Geest09/2018
4010(38*10^149999+691)/9150000Robert Price10/2018
40112043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
4012(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
40132^498238-53149985Lelio R Paula12/2017
401445728^1905+1905^45728149984Hans Havermann10/2020
4015(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
40165*10^149907+23149908Robert Price03/2019
401732^99585-829149891Eric Chen11/2023
401839347^6442+6442^39347149874Hans Havermann09/2020
40192^497850+81049149868Enzo Doria07/2016
4020V(1075416)149830Serge Batalov07/2024
402137228^10575+10575^37228149816Hans Havermann10/2020
4022(5*2^497673+1)/2743149812Lelio R Paula10/2015
4023(5*2^497671+1)/373703149810Lelio R Paula10/2015
4024(2*10^149803-143)/3149803Robert Price03/2018
402533845^26604+26604^33845149763Hans Havermann09/2020
40262^497434-2784191149743Enzo Doria10/2015
4027(865*10^149737-1)/9149739Robert Price04/2020
402810^149695-7000001149695Robert Price06/2021
402938237^8214+8214^38237149681Hans Havermann09/2020
4030Phi(745791,2)/1491583149664Anonymous03/2025
4031(497167*2^497167-1)/70975149664Anonymous04/2025
4032(23*10^149655+19)/3149656Robert Price07/2019
40332^497068-113579149633Enzo Doria08/2014
40342^497037+73727149624Enzo Doria04/2016
403511*10^149618+3149620Robert Price07/2021
403634942^19067+19067^34942149562Hans Havermann09/2020
403733696^27449+27449^33696149561Hans Havermann09/2020
40382^496773+77747149544Enzo Doria05/2016
403929937^33400-33400^29937149506Frank Doornink06/2024
4040(7*10^149483-493)/9149483Robert Price04/2021
4041(206*10^149459+7)/3149461Robert Price07/2020
404234589^20940+20940^34589149459Hans Havermann09/2020
40432^496477-113485149455Enzo Doria08/2014
4044(496423*2^496423-1)/223573149439Anonymous04/2025
40453*2^496411-5149436Jon Grantham07/2023
4046((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
40472^496270-49451149393Enzo Doria10/2015
40482^496238-1865081149383Enzo Doria01/2016
404933831^26030+26030^33831149380Hans Havermann09/2020
405034131^23780+23780^34131149365Hans Havermann09/2020
4051(5*10^149335-53)/3149336Robert Price09/2020
405226043^33818-33818^26043149330Frank Doornink03/2024
40532^495968-1853699149302Enzo Doria09/2015
40542^495935-4117149292Yves Minet02/2018
40555*2^495930+3149291Jon Grantham07/2023
405635816^14709+14709^35816149267Hans Havermann09/2020
4057(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
405810^149240-40000001149240Robert Price07/2022
405910^149240-10809149240Alfred Reich08/2024
40602^495712-396765149225Enzo Doria07/2013
4061(21*2^495676-1)/4835149211Lelio R Paula10/2015
40622^495420+1880701149137Enzo Doria10/2016
406325646^33823-33823^25646149127Frank Doornink02/2024
40642^495337-1847293149112Enzo Doria07/2015
4065(2^495193-7)/5149068Lelio R Paula10/2015
40662^495163+111546435149059Paul Bourdelais10/2021
406733282^30097+30097^33282149055Hans Havermann09/2020
406837384^9705+9705^37384149050Hans Havermann09/2020
406934808^19143+19143^34808149049Hans Havermann09/2020
4070413^56963-412^56963149013Jean-Louis Charton08/2012
407130657^33212-33212^30657149007Frank Doornink06/2024
407247^89113-46^89113149006Robert Price10/2012
4073V(891190)148997Serge Batalov07/2024
40742^494916+87855148985Lelio R Paula01/2016
40756*10^148982+73148983Robert Price04/2019
40763^312155-4148936Anonymous02/2023
407710^148934+1530019148935Patrick De Geest02/2021
407810^148934-1000000001148934Robert Price11/2020
407910^148934-512057148934Patrick De Geest02/2021
408039000^6571+6571^39000148888Hans Havermann10/2020
40812^494586-2791991148886Enzo Doria02/2016
40828*10^148860-3148861Ray Chandler04/2011
408338262^7769+7769^38262148854Hans Havermann10/2020
408410^148816-500001148816Robert Price03/2022
4085(53*10^148811-287)/9148812Robert Price02/2022
40862^494333-286183148810Enzo Doria06/2015
40872^494144-264119148753Enzo Doria05/2014
40886*10^148734+47148735Robert Price06/2022
408928724^33353-33353^28724148696Frank Doornink06/2024
409036502^11823+11823^36502148663Hans Havermann11/2020
4091(5*2^493838-1)/3721148658Lelio R Paula10/2015
409264239^206+206^64239148641Hans Havermann10/2020
4093(23*2^493761-1)/555148636Lelio R Paula10/2015
4094(23*10^148627-137)/3148628Robert Price08/2021
4095(151*10^148601-1)/3148603Robert Price03/2020
40962^493636+82081148600Enzo Doria09/2016
4097((((((((((((((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
409827134^33509-33509^27134148563Frank Doornink01/2024
4099177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
4100(2*10^148460-23)/3148460Robert Price04/2018
4101(28*10^148445+101)/3148446Robert Price09/2020
41022^493065+225148428Henri Lifchitz11/2024
410336203^12556+12556^36203148391Hans Havermann10/2020
410433912^23749+23749^33912148387Hans Havermann10/2020
4105(8*10^148328+1)/9148328Serge Batalov05/2010
410634294^21117+21117^34294148309Hans Havermann10/2020
4107(71*10^148306-539)/9148307Robert Price07/2019
410830814^33039-33039^30814148304Frank Doornink06/2024
410938042^7875+7875^38042148222Hans Havermann10/2020
41105^211959-12874148153Enzo Doria05/2014
411134142^21831+21831^34142148145Hans Havermann10/2020
411210^148112+34059148113Patrick De Geest05/2021
411310^148112-70000001148112Robert Price03/2021
411410^148112-106593148112Patrick De Geest05/2021
411536303^12016+12016^36303148108Hans Havermann10/2020
4116(77*10^148089-149)/9148090Robert Price03/2022
4117(16*10^148071+41)/3148072Robert Price03/2019
4118187^65175-2148068Lelio R Paula11/2017
41192^491851+1871453148062Enzo Doria05/2016
4120(68*10^148060-257)/9148061Robert Price07/2019
4121(151*10^148020-1)/3148022Robert Price03/2020
412239153^6032+6032^39153148017Hans Havermann10/2020
412336798^10507+10507^36798147983Hans Havermann12/2020
4124(26*10^147973-23)/3147974Robert Price12/2019
41252^491521-1865323147963Enzo Doria02/2016
4126(2^491476+7)/71147948Lelio R Paula10/2015
41272*10^147928+47147929Robert Price12/2021
41282^491391-7807147924Lelio R Paula01/2013
41292^491384+236221147922Enzo Doria05/2025
413039736^5279+5279^39736147920Hans Havermann11/2020
41312^491370-113297147918Enzo Doria07/2014
4132(3^707753)%F(707753)147912Henri Lifchitz06/2025
4133(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
413444368^2155+2155^44368147899Hans Havermann12/2020
4135(17*10^147890+79)/3147891Robert Price04/2019
413694*10^147871-3147873Robert Price05/2020
413710^147843+620967147844Patrick De Geest05/2021
413810^147843-50000000001147843Robert Price12/2020
413910^147843-182891147843Patrick De Geest05/2021
414035805^13346+13346^35805147709Hans Havermann11/2020
41412^490672+255255147707Paul Bourdelais10/2021
41422^490660-17147704Lelio R Paula12/2017
4143(229*10^147699-1)/3147701Robert Price07/2020
414440656^4289+4289^40656147678Hans Havermann11/2020
4145(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
41462^490550+1179439147671Enzo Doria06/2016
414727249^33292-33292^27249147662Frank Doornink06/2024
4148(23*10^147649-59)/9147650Robert Price05/2018
41492^490303+2793653147596Enzo Doria03/2016
41502^490266+255255147585Paul Bourdelais10/2021
4151199^64181-2147543Lelio R Paula11/2017
415232849^30958+30958^32849147518Hans Havermann11/2020
41532^489871-286987147466Enzo Doria07/2015
41542^489864-351899147464Enzo Doria07/2015
4155175^65724-2147422Lelio R Paula11/2017
41562^489712+1874851147419Enzo Doria06/2016
415734473^18830+18830^34473147367Hans Havermann11/2020
415863^81896-2147359Lelio R Paula10/2017
415934580^18237+18237^34580147344Hans Havermann11/2020
4160(11*10^147313-107)/3147314Robert Price09/2018
4161(397*10^147310+17)/9147312Robert Price03/2022
41622^489305-59815147296Enzo Doria10/2015
4163(2^489280-7)/6381147285Lelio R Paula09/2015
41642*10^147264-61147265Robert Price10/2021
41652*10^147260+29147261Robert Price02/2021
416633556^24457+24457^33556147258Hans Havermann11/2020
416712^136450-11147255Riley Fisher12/2024
41682^489125+80357147242Enzo Doria06/2016
416910^147240-40000001147240Robert Price07/2022
417010^147240-371331147240Alfred Reich09/2024
417110^147240-464727147240Alfred Reich09/2024
417232835^30452+30452^32835147220Hans Havermann12/2020
4173(19*10^147213-97)/3147214Robert Price10/2021
417427123^33190-33190^27123147143Frank Doornink01/2024
4175(148*10^147139-1)/3147141Robert Price03/2020
417634338^19255+19255^34338147123Hans Havermann11/2020
41772^488648-112799147098Enzo Doria07/2014
41782^488627-350317147092Enzo Doria06/2015
417933432^25075+25075^33432147076Hans Havermann12/2020
4180(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
41812^488280-2165146987Yves Minet07/2014
41822^488278+45146987Lelio R Paula12/2017
4183(3^834646)/(2^834646)146974Henri Lifchitz06/2025
418432568^32568+32561^32561146973Henri Lifchitz08/2024
41852^487927-39146881Lelio R Paula12/2017
4186(7*10^146860-13)/3146861Robert Price07/2018
4187(26*10^146856-77)/3146857Robert Price11/2019
418832948^28611+28611^32948146834Hans Havermann11/2020
418942596^2799+2799^42596146829Hans Havermann12/2020
41902^487726-1863341146821Enzo Doria12/2015
419143838^2229+2229^43838146775Hans Havermann11/2020
419235005^15594+15594^35005146775Hans Havermann11/2020
4193(167*10^146764+7)/3146766Robert Price04/2021
419453^85114+85114146761Kellen Shenton05/2022
4195(59*10^146738+157)/9146739Robert Price12/2021
4196((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
419732963^28234+28234^32963146711Hans Havermann12/2020
4198(22*10^146661-19)/3146662Robert Price04/2019
419933958^20825+20825^33958146651Hans Havermann12/2020
420026289^33178-33178^26289146640Frank Doornink03/2024
42012^487121-39523146639Enzo Doria09/2015
420261063^252+252^61063146637Hans Havermann12/2020
4203(7*2^486967+1)/39146591Lelio R Paula09/2015
420434099^19900+19900^34099146587Hans Havermann11/2020
42052^486893-79146570Yves Minet09/2017
420636818^9567+9567^36818146565Hans Havermann12/2020
42072^486840+1879141146554Enzo Doria08/2016
42082^486774-87146534Lelio R Paula12/2017
420938655^6176+6176^38655146530Hans Havermann11/2020
42108*10^146522-81146523Robert Price02/2021
421132820^29059+29059^32820146485Hans Havermann12/2020
421237261^8530+8530^37261146472Hans Havermann12/2020
421366953^154+154^66953146462Hans Havermann12/2020
421496^73877-95^73877146445Robert Price10/2015
42158*10^146421+81146422Robert Price08/2019
421633153^26090+26090^33153146420Hans Havermann11/2020
42172^486275+23961146384Enzo Doria10/2023
4218(12^135607-1)/18437127731146335Paul Vanderveen06/2025
4219(52^85259+1)/53146304Paul Bourdelais09/2017
4220179^64935+2146290Lelio R Paula10/2017
422132595^30758+30758^32595146285Hans Havermann11/2020
422234972^15157+15157^34972146205Hans Havermann12/2020
4223(16*10^146200+131)/3146201Robert Price03/2022
4224(19*10^146181-49)/3146182Robert Price05/2019
42252^485531-114621146160Enzo Doria05/2015
42262^485473-933075146142Paul Bourdelais06/2021
4227(2^485461-9)/4249146135Lelio R Paula09/2015
4228(22*10^146130-193)/9146131Robert Price07/2022
42292^485389+81887146117Enzo Doria08/2016
423032554^30773+30773^32554146108Hans Havermann11/2020
423128075^32844-32844^28075146101Frank Doornink06/2024
4232(10^146063+71)/9146063Serge Batalov07/2015
42332*10^146051-63146052Robert Price01/2022
4234(2^485119+7)/2745146032Lelio R Paula09/2015
4235(22*10^146029+257)/9146030Robert Price06/2018
42367*10^145982-53145983Robert Price06/2020
42372^484743+1872923145923Enzo Doria05/2016
423833140^25287+25287^33140145913Hans Havermann01/2021
423937875^7112+7112^37875145895Hans Havermann01/2021
424030542^32529-32529^30542145890Frank Doornink06/2024
424132862^27473+27473^32862145872Hans Havermann01/2021
4242V(1046652)/2093303145817Serge Batalov07/2024
424332836^27587+27587^32836145815Hans Havermann01/2021
42442^484341+1879157145802Enzo Doria08/2016
42452*10^145784-91145785Robert Price04/2020
42462^484271-51145781Lelio R Paula11/2017
4247(188*10^145750-11)/3145752Robert Price02/2022
424870^78989-69^78989145743Robert Price01/2014
424951^85334+2145714Robert Price07/2015
425010^2^72843+72843^2^10145687Henri Lifchitz03/2025


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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