PRP Records

Probable Primes Top 10000

(300940 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 ?
375138237^8214+8214^38237149681Hans Havermann09/2020
3752(23*10^149655+19)/3149656Robert Price07/2019
37532^497068-113579149633Enzo Doria08/2014
37542^497037+73727149624Enzo Doria04/2016
375511*10^149618+3149620Robert Price07/2021
375634942^19067+19067^34942149562Hans Havermann09/2020
375733696^27449+27449^33696149561Hans Havermann09/2020
37582^496773+77747149544Enzo Doria05/2016
375929937^33400-33400^29937149506Frank Doornink06/2024
3760(7*10^149483-493)/9149483Robert Price04/2021
3761(206*10^149459+7)/3149461Robert Price07/2020
376234589^20940+20940^34589149459Hans Havermann09/2020
37632^496477-113485149455Enzo Doria08/2014
37643*2^496411-5149436Jon Grantham07/2023
3765((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
37662^496270-49451149393Enzo Doria10/2015
37672^496238-1865081149383Enzo Doria01/2016
376833831^26030+26030^33831149380Hans Havermann09/2020
376934131^23780+23780^34131149365Hans Havermann09/2020
3770(5*10^149335-53)/3149336Robert Price09/2020
377126043^33818-33818^26043149330Frank Doornink03/2024
37722^495968-1853699149302Enzo Doria09/2015
37732^495935-4117149292Yves Minet02/2018
37745*2^495930+3149291Jon Grantham07/2023
377535816^14709+14709^35816149267Hans Havermann09/2020
3776(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
377710^149240-40000001149240Robert Price07/2022
377810^149240-10809149240Alfred Reich08/2024
37792^495712-396765149225Enzo Doria07/2013
3780(21*2^495676-1)/4835149211Lelio R Paula10/2015
37812^495420+1880701149137Enzo Doria10/2016
378225646^33823-33823^25646149127Frank Doornink02/2024
37832^495337-1847293149112Enzo Doria07/2015
3784(2^495193-7)/5149068Lelio R Paula10/2015
37852^495163+111546435149059Paul Bourdelais10/2021
378633282^30097+30097^33282149055Hans Havermann09/2020
378737384^9705+9705^37384149050Hans Havermann09/2020
378834808^19143+19143^34808149049Hans Havermann09/2020
3789413^56963-412^56963149013Jean-Louis Charton08/2012
379030657^33212-33212^30657149007Frank Doornink06/2024
379147^89113-46^89113149006Robert Price10/2012
3792V(891190)148997Serge Batalov07/2024
37932^494916+87855148985Lelio R Paula01/2016
37946*10^148982+73148983Robert Price04/2019
37953^312155-4148936Anonymous02/2023
379610^148934+1530019148935Patrick De Geest02/2021
379710^148934-1000000001148934Robert Price11/2020
379810^148934-512057148934Patrick De Geest02/2021
379939000^6571+6571^39000148888Hans Havermann10/2020
38002^494586-2791991148886Enzo Doria02/2016
38018*10^148860-3148861Ray Chandler04/2011
380238262^7769+7769^38262148854Hans Havermann10/2020
380310^148816-500001148816Robert Price03/2022
3804(53*10^148811-287)/9148812Robert Price02/2022
38052^494333-286183148810Enzo Doria06/2015
38062^494144-264119148753Enzo Doria05/2014
38076*10^148734+47148735Robert Price06/2022
380828724^33353-33353^28724148696Frank Doornink06/2024
380936502^11823+11823^36502148663Hans Havermann11/2020
3810(5*2^493838-1)/3721148658Lelio R Paula10/2015
381164239^206+206^64239148641Hans Havermann10/2020
3812(23*2^493761-1)/555148636Lelio R Paula10/2015
3813(23*10^148627-137)/3148628Robert Price08/2021
3814(151*10^148601-1)/3148603Robert Price03/2020
38152^493636+82081148600Enzo Doria09/2016
3816((((((((((((((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
381727134^33509-33509^27134148563Frank Doornink01/2024
3818177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
3819(2*10^148460-23)/3148460Robert Price04/2018
3820(28*10^148445+101)/3148446Robert Price09/2020
38212^493065+225148428Henri Lifchitz11/2024
382236203^12556+12556^36203148391Hans Havermann10/2020
382333912^23749+23749^33912148387Hans Havermann10/2020
3824(8*10^148328+1)/9148328Serge Batalov05/2010
382534294^21117+21117^34294148309Hans Havermann10/2020
3826(71*10^148306-539)/9148307Robert Price07/2019
382730814^33039-33039^30814148304Frank Doornink06/2024
382838042^7875+7875^38042148222Hans Havermann10/2020
38295^211959-12874148153Enzo Doria05/2014
383034142^21831+21831^34142148145Hans Havermann10/2020
383110^148112+34059148113Patrick De Geest05/2021
383210^148112-70000001148112Robert Price03/2021
383310^148112-106593148112Patrick De Geest05/2021
383436303^12016+12016^36303148108Hans Havermann10/2020
3835(77*10^148089-149)/9148090Robert Price03/2022
3836(16*10^148071+41)/3148072Robert Price03/2019
3837187^65175-2148068Lelio R Paula11/2017
38382^491851+1871453148062Enzo Doria05/2016
3839(68*10^148060-257)/9148061Robert Price07/2019
3840(151*10^148020-1)/3148022Robert Price03/2020
384139153^6032+6032^39153148017Hans Havermann10/2020
384236798^10507+10507^36798147983Hans Havermann12/2020
3843(26*10^147973-23)/3147974Robert Price12/2019
38442^491521-1865323147963Enzo Doria02/2016
3845(2^491476+7)/71147948Lelio R Paula10/2015
38462*10^147928+47147929Robert Price12/2021
38472^491391-7807147924Lelio R Paula01/2013
384839736^5279+5279^39736147920Hans Havermann11/2020
38492^491370-113297147918Enzo Doria07/2014
3850(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
385144368^2155+2155^44368147899Hans Havermann12/2020
3852(17*10^147890+79)/3147891Robert Price04/2019
385394*10^147871-3147873Robert Price05/2020
385410^147843+620967147844Patrick De Geest05/2021
385510^147843-50000000001147843Robert Price12/2020
385610^147843-182891147843Patrick De Geest05/2021
385735805^13346+13346^35805147709Hans Havermann11/2020
38582^490672+255255147707Paul Bourdelais10/2021
38592^490660-17147704Lelio R Paula12/2017
3860(229*10^147699-1)/3147701Robert Price07/2020
386140656^4289+4289^40656147678Hans Havermann11/2020
3862(85*10^147676-31)/9147677Rytis Slatkevicius12/2024
38632^490550+1179439147671Enzo Doria06/2016
386427249^33292-33292^27249147662Frank Doornink06/2024
3865(23*10^147649-59)/9147650Robert Price05/2018
38662^490303+2793653147596Enzo Doria03/2016
38672^490266+255255147585Paul Bourdelais10/2021
3868199^64181-2147543Lelio R Paula11/2017
386932849^30958+30958^32849147518Hans Havermann11/2020
38702^489871-286987147466Enzo Doria07/2015
38712^489864-351899147464Enzo Doria07/2015
3872175^65724-2147422Lelio R Paula11/2017
38732^489712+1874851147419Enzo Doria06/2016
387434473^18830+18830^34473147367Hans Havermann11/2020
387563^81896-2147359Lelio R Paula10/2017
387634580^18237+18237^34580147344Hans Havermann11/2020
3877(11*10^147313-107)/3147314Robert Price09/2018
3878(397*10^147310+17)/9147312Robert Price03/2022
38792^489305-59815147296Enzo Doria10/2015
3880(2^489280-7)/6381147285Lelio R Paula09/2015
38812*10^147264-61147265Robert Price10/2021
38822*10^147260+29147261Robert Price02/2021
388333556^24457+24457^33556147258Hans Havermann11/2020
388412^136450-11147255Riley Fisher12/2024
38852^489125+80357147242Enzo Doria06/2016
388610^147240-40000001147240Robert Price07/2022
388710^147240-371331147240Alfred Reich09/2024
388810^147240-464727147240Alfred Reich09/2024
388932835^30452+30452^32835147220Hans Havermann12/2020
3890(19*10^147213-97)/3147214Robert Price10/2021
389127123^33190-33190^27123147143Frank Doornink01/2024
3892(148*10^147139-1)/3147141Robert Price03/2020
389334338^19255+19255^34338147123Hans Havermann11/2020
38942^488648-112799147098Enzo Doria07/2014
38952^488627-350317147092Enzo Doria06/2015
389633432^25075+25075^33432147076Hans Havermann12/2020
3897(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
38982^488280-2165146987Yves Minet07/2014
38992^488278+45146987Lelio R Paula12/2017
390032568^32568+32561^32561146973Henri Lifchitz08/2024
39012^487927-39146881Lelio R Paula12/2017
3902(7*10^146860-13)/3146861Robert Price07/2018
3903(26*10^146856-77)/3146857Robert Price11/2019
390432948^28611+28611^32948146834Hans Havermann11/2020
390542596^2799+2799^42596146829Hans Havermann12/2020
39062^487726-1863341146821Enzo Doria12/2015
390743838^2229+2229^43838146775Hans Havermann11/2020
390835005^15594+15594^35005146775Hans Havermann11/2020
3909(167*10^146764+7)/3146766Robert Price04/2021
391053^85114+85114146761Kellen Shenton05/2022
3911(59*10^146738+157)/9146739Robert Price12/2021
3912((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
391332963^28234+28234^32963146711Hans Havermann12/2020
3914(22*10^146661-19)/3146662Robert Price04/2019
391533958^20825+20825^33958146651Hans Havermann12/2020
391626289^33178-33178^26289146640Frank Doornink03/2024
39172^487121-39523146639Enzo Doria09/2015
391861063^252+252^61063146637Hans Havermann12/2020
3919(7*2^486967+1)/39146591Lelio R Paula09/2015
392034099^19900+19900^34099146587Hans Havermann11/2020
39212^486893-79146570Yves Minet09/2017
392236818^9567+9567^36818146565Hans Havermann12/2020
39232^486840+1879141146554Enzo Doria08/2016
39242^486774-87146534Lelio R Paula12/2017
392538655^6176+6176^38655146530Hans Havermann11/2020
39268*10^146522-81146523Robert Price02/2021
392732820^29059+29059^32820146485Hans Havermann12/2020
392837261^8530+8530^37261146472Hans Havermann12/2020
392966953^154+154^66953146462Hans Havermann12/2020
393096^73877-95^73877146445Robert Price10/2015
39318*10^146421+81146422Robert Price08/2019
393233153^26090+26090^33153146420Hans Havermann11/2020
39332^486275+23961146384Enzo Doria10/2023
3934(52^85259+1)/53146304Paul Bourdelais09/2017
3935179^64935+2146290Lelio R Paula10/2017
393632595^30758+30758^32595146285Hans Havermann11/2020
393734972^15157+15157^34972146205Hans Havermann12/2020
3938(16*10^146200+131)/3146201Robert Price03/2022
3939(19*10^146181-49)/3146182Robert Price05/2019
39402^485531-114621146160Enzo Doria05/2015
39412^485473-933075146142Paul Bourdelais06/2021
3942(2^485461-9)/4249146135Lelio R Paula09/2015
3943(22*10^146130-193)/9146131Robert Price07/2022
39442^485389+81887146117Enzo Doria08/2016
394532554^30773+30773^32554146108Hans Havermann11/2020
394628075^32844-32844^28075146101Frank Doornink06/2024
3947(10^146063+71)/9146063Serge Batalov07/2015
39482*10^146051-63146052Robert Price01/2022
3949(2^485119+7)/2745146032Lelio R Paula09/2015
3950(22*10^146029+257)/9146030Robert Price06/2018
39517*10^145982-53145983Robert Price06/2020
39522^484743+1872923145923Enzo Doria05/2016
395333140^25287+25287^33140145913Hans Havermann01/2021
395437875^7112+7112^37875145895Hans Havermann01/2021
395530542^32529-32529^30542145890Frank Doornink06/2024
395632862^27473+27473^32862145872Hans Havermann01/2021
3957V(1046652)/2093303145817Serge Batalov07/2024
395832836^27587+27587^32836145815Hans Havermann01/2021
39592^484341+1879157145802Enzo Doria08/2016
39602*10^145784-91145785Robert Price04/2020
39612^484271-51145781Lelio R Paula11/2017
3962(188*10^145750-11)/3145752Robert Price02/2022
396370^78989-69^78989145743Robert Price01/2014
396451^85334+2145714Robert Price07/2015
39652^483886-1857101145665Enzo Doria10/2015
396629312^32607-32607^29312145657Frank Doornink06/2024
396733350^23307+23307^33350145656Hans Havermann01/2021
3968(19*10^145585+131)/3145586Robert Price06/2020
396931815^32332-32332^31815145580Frank Doornink01/2024
39702^483563-1863457145567Enzo Doria12/2015
39714*10^145563-69145564Robert Price01/2022
39722^483516-1861409145553Enzo Doria11/2015
39732^483384-115019145514Enzo Doria06/2015
3974(259*10^145501-1)/3145503Robert Price12/2020
3975(19*10^145499-61)/3145500Robert Price05/2019
39762^483302-3221145489Lelio R Paula12/2012
3977(23*10^145463+61)/3145464Robert Price01/2022
397835523^12434+12434^35523145453Hans Havermann01/2021
3979(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
39802^483046+1874029145412Enzo Doria06/2016
39812^482991-2789317145395Enzo Doria12/2015
39822^482978-2789711145391Enzo Doria12/2015
39832^482966-2789711145388Enzo Doria12/2015
39842^482817-1858843145343Enzo Doria10/2015
39852^482751-113635145323Enzo Doria08/2014
39862^482705-459763145309Enzo Doria05/2015
3987(4^241306+11)/3145281Robert Price03/2017
3988(238*10^145276-1)/3145278Robert Price04/2020
3989(19*2^482534+1)/7145258Lelio R Paula09/2015
399053^84239-52^84239145252Robert Price01/2013
3991U(1042497)145243Serge Batalov07/2024
39922^482386+212419145213Enzo Doria08/2023
399347952^1067+1067^47952145207Hans Havermann01/2021
3994(2^482333+5)/9287145193Lelio R Paula09/2015
39952^482087+72623145123Enzo Doria04/2016
39962^482016-286565145102Enzo Doria07/2015
3997(19*10^145093+101)/3145094Robert Price09/2019
39982^481956+121145084Stefano Morozzi04/2021
399927535^32676-32676^27535145078Frank Doornink06/2024
40002^481840+15145049Robert Price09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 10 2025 11:16 (Time in France)

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