PRP Records

Probable Primes Top 10000

(288949 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 ?
225110^148934-512057148934Patrick De Geest02/2021
225239000^6571+6571^39000148888Hans Havermann10/2020
22532^494586-2791991148886Enzo Doria02/2016
22548*10^148860-3148861Ray Chandler04/2011
225538262^7769+7769^38262148854Hans Havermann10/2020
22562^494333-286183148810Enzo Doria06/2015
22572^494144-264119148753Enzo Doria05/2014
225836502^11823+11823^36502148663Hans Havermann11/2020
2259(5*2^493838-1)/3721148658Lelio R Paula10/2015
226064239^206+206^64239148641Hans Havermann10/2020
2261(23*2^493761-1)/555148636Lelio R Paula10/2015
2262(23*10^148627-137)/3148628Robert Price08/2021
2263(151*10^148601-1)/3148603Robert Price03/2020
22642^493636+82081148600Enzo Doria09/2016
2265((((((((((((((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
2266177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
2267(2*10^148460-23)/3148460Robert Price04/2018
2268(28*10^148445+101)/3148446Robert Price09/2020
226936203^12556+12556^36203148391Hans Havermann10/2020
227033912^23749+23749^33912148387Hans Havermann10/2020
2271(8*10^148328+1)/9148328Serge Batalov05/2010
227234294^21117+21117^34294148309Hans Havermann10/2020
2273(71*10^148306-539)/9148307Robert Price07/2019
227438042^7875+7875^38042148222Hans Havermann10/2020
22755^211959-12874148153Enzo Doria05/2014
227634142^21831+21831^34142148145Hans Havermann10/2020
227710^148112+34059148113Patrick De Geest05/2021
227810^148112-70000001148112Robert Price03/2021
227910^148112-106593148112Patrick De Geest05/2021
228036303^12016+12016^36303148108Hans Havermann10/2020
2281(16*10^148071+41)/3148072Robert Price03/2019
2282187^65175-2148068Lelio R Paula11/2017
22832^491851+1871453148062Enzo Doria05/2016
2284(68*10^148060-257)/9148061Robert Price07/2019
2285(151*10^148020-1)/3148022Robert Price03/2020
228639153^6032+6032^39153148017Hans Havermann10/2020
228736798^10507+10507^36798147983Hans Havermann12/2020
2288(26*10^147973-23)/3147974Robert Price12/2019
22892^491521-1865323147963Enzo Doria02/2016
2290(2^491476+7)/71147948Lelio R Paula10/2015
22912*10^147928+47147929Robert Price12/2021
22922^491391-7807147924Lelio R Paula01/2013
229339736^5279+5279^39736147920Hans Havermann11/2020
22942^491370-113297147918Enzo Doria07/2014
2295(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
229644368^2155+2155^44368147899Hans Havermann12/2020
2297(17*10^147890+79)/3147891Robert Price04/2019
229894*10^147871-3147873Robert Price05/2020
229910^147843+620967147844Patrick De Geest05/2021
230010^147843-50000000001147843Robert Price12/2020
230110^147843-182891147843Patrick De Geest05/2021
230235805^13346+13346^35805147709Hans Havermann11/2020
23032^490672+255255147707Paul Bourdelais10/2021
23042^490660-17147704Lelio R Paula12/2017
2305(229*10^147699-1)/3147701Robert Price07/2020
230640656^4289+4289^40656147678Hans Havermann11/2020
23072^490550+1179439147671Enzo Doria06/2016
2308(23*10^147649-59)/9147650Robert Price05/2018
23092^490303+2793653147596Enzo Doria03/2016
23102^490266+255255147585Paul Bourdelais10/2021
2311199^64181-2147543Lelio R Paula11/2017
231232849^30958+30958^32849147518Hans Havermann11/2020
23132^489871-286987147466Enzo Doria07/2015
23142^489864-351899147464Enzo Doria07/2015
2315175^65724-2147422Lelio R Paula11/2017
23162^489712+1874851147419Enzo Doria06/2016
231734473^18830+18830^34473147367Hans Havermann11/2020
231863^81896-2147359Lelio R Paula10/2017
231934580^18237+18237^34580147344Hans Havermann11/2020
2320(11*10^147313-107)/3147314Robert Price09/2018
23212^489305-59815147296Enzo Doria10/2015
2322(2^489280-7)/6381147285Lelio R Paula09/2015
23232*10^147264-61147265Robert Price10/2021
23242*10^147260+29147261Robert Price02/2021
232533556^24457+24457^33556147258Hans Havermann11/2020
23262^489125+80357147242Enzo Doria06/2016
232732835^30452+30452^32835147220Hans Havermann12/2020
2328(19*10^147213-97)/3147214Robert Price10/2021
2329(148*10^147139-1)/3147141Robert Price03/2020
233034338^19255+19255^34338147123Hans Havermann11/2020
23312^488648-112799147098Enzo Doria07/2014
23322^488627-350317147092Enzo Doria06/2015
233333432^25075+25075^33432147076Hans Havermann12/2020
2334(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
23352^488280-2165146987Yves Minet07/2014
23362^488278+45146987Lelio R Paula12/2017
23372^487927-39146881Lelio R Paula12/2017
2338(7*10^146860-13)/3146861Robert Price07/2018
2339(26*10^146856-77)/3146857Robert Price11/2019
234032948^28611+28611^32948146834Hans Havermann11/2020
234142596^2799+2799^42596146829Hans Havermann12/2020
23422^487726-1863341146821Enzo Doria12/2015
234343838^2229+2229^43838146775Hans Havermann11/2020
234435005^15594+15594^35005146775Hans Havermann11/2020
2345(167*10^146764+7)/3146766Robert Price04/2021
2346(59*10^146738+157)/9146739Robert Price12/2021
2347((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
234832963^28234+28234^32963146711Hans Havermann12/2020
2349(22*10^146661-19)/3146662Robert Price04/2019
235033958^20825+20825^33958146651Hans Havermann12/2020
23512^487121-39523146639Enzo Doria09/2015
235261063^252+252^61063146637Hans Havermann12/2020
2353(7*2^486967+1)/39146591Lelio R Paula09/2015
235434099^19900+19900^34099146587Hans Havermann11/2020
23552^486893-79146570Yves Minet09/2017
235636818^9567+9567^36818146565Hans Havermann12/2020
23572^486840+1879141146554Enzo Doria08/2016
23582^486774-87146534Lelio R Paula12/2017
235938655^6176+6176^38655146530Hans Havermann11/2020
23608*10^146522-81146523Robert Price02/2021
236132820^29059+29059^32820146485Hans Havermann12/2020
236237261^8530+8530^37261146472Hans Havermann12/2020
236366953^154+154^66953146462Hans Havermann12/2020
236496^73877-95^73877146445Robert Price10/2015
23658*10^146421+81146422Robert Price08/2019
236633153^26090+26090^33153146420Hans Havermann11/2020
2367(52^85259+1)/53146304Paul Bourdelais09/2017
2368179^64935+2146290Lelio R Paula10/2017
236932595^30758+30758^32595146285Hans Havermann11/2020
237034972^15157+15157^34972146205Hans Havermann12/2020
2371(19*10^146181-49)/3146182Robert Price05/2019
23722^485531-114621146160Enzo Doria05/2015
23732^485473-933075146142Paul Bourdelais06/2021
2374(2^485461-9)/4249146135Lelio R Paula09/2015
23752^485389+81887146117Enzo Doria08/2016
237632554^30773+30773^32554146108Hans Havermann11/2020
2377(10^146063+71)/9146063Serge Batalov07/2015
23782*10^146051-63146052Robert Price01/2022
2379(2^485119+7)/2745146032Lelio R Paula09/2015
2380(22*10^146029+257)/9146030Robert Price06/2018
23817*10^145982-53145983Robert Price06/2020
23822^484743+1872923145923Enzo Doria05/2016
238333140^25287+25287^33140145913Hans Havermann01/2021
238437875^7112+7112^37875145895Hans Havermann01/2021
238532862^27473+27473^32862145872Hans Havermann01/2021
238632836^27587+27587^32836145815Hans Havermann01/2021
23872^484341+1879157145802Enzo Doria08/2016
23882*10^145784-91145785Robert Price04/2020
23892^484271-51145781Lelio R Paula11/2017
239070^78989-69^78989145743Robert Price01/2014
239151^85334+2145714Robert Price07/2015
23922^483886-1857101145665Enzo Doria10/2015
239333350^23307+23307^33350145656Hans Havermann01/2021
2394(19*10^145585+131)/3145586Robert Price06/2020
23952^483563-1863457145567Enzo Doria12/2015
23962^483516-1861409145553Enzo Doria11/2015
23972^483384-115019145514Enzo Doria06/2015
2398(259*10^145501-1)/3145503Robert Price12/2020
2399(19*10^145499-61)/3145500Robert Price05/2019
24002^483302-3221145489Lelio R Paula12/2012
2401(23*10^145463+61)/3145464Robert Price01/2022
240235523^12434+12434^35523145453Hans Havermann01/2021
24032^483046+1874029145412Enzo Doria06/2016
24042^482991-2789317145395Enzo Doria12/2015
24052^482978-2789711145391Enzo Doria12/2015
24062^482966-2789711145388Enzo Doria12/2015
24072^482817-1858843145343Enzo Doria10/2015
24082^482751-113635145323Enzo Doria08/2014
24092^482705-459763145309Enzo Doria05/2015
2410(4^241306+11)/3145281Robert Price03/2017
2411(238*10^145276-1)/3145278Robert Price04/2020
2412(19*2^482534+1)/7145258Lelio R Paula09/2015
241353^84239-52^84239145252Robert Price01/2013
241447952^1067+1067^47952145207Hans Havermann01/2021
2415(2^482333+5)/9287145193Lelio R Paula09/2015
24162^482087+72623145123Enzo Doria04/2016
24172^482016-286565145102Enzo Doria07/2015
2418(19*10^145093+101)/3145094Robert Price09/2019
24192^481956+121145084Stefano Morozzi04/2021
24202^481840+15145049Robert Price09/2015
24212^481801-481801145037Henri Lifchitz03/2005
24222^481775+1869083145029Enzo Doria05/2016
242329^99167+2145022Ray Chandler08/2011
24242^481663+1875653144996Enzo Doria07/2016
24258*10^144977+27144978Robert Price09/2021
242636486^9379+9379^36486144929Hans Havermann12/2020
242735111^13378+13378^35111144882Hans Havermann01/2021
24282^481149-459073144841Enzo Doria05/2015
242934619^15246+15246^34619144817Hans Havermann01/2021
24302^481045-113215144809Enzo Doria07/2014
2431(64*10^144797+287)/9144798Robert Price04/2019
24322^480859-113695144753Enzo Doria09/2014
2433(106*10^144744+17)/3144746Robert Price04/2021
24342^480766-2787191144725Enzo Doria11/2015
2435(21*27^101106-151)/26144720Curtis Bright05/2015
24362^480678+1874239144699Enzo Doria06/2016
2437(8*10^144683+1)/9144683Serge Batalov05/2010
2438L(692147)144651Henri Lifchitz10/2008
2439(76*10^144648+77)/9144649Robert Price10/2019
244032672^26721+26721^32672144635Hans Havermann01/2021
24412^480417+35144620Robert Price11/2015
24422^480296-59879144584Enzo Doria10/2015
244333157^22878+22878^33157144546Hans Havermann12/2020
244445494^1497+1497^45494144454Hans Havermann12/2020
24452^479844+3144448Donovan Johnson06/2006
244633442^20803+20803^33442144407Hans Havermann01/2021
2447(27*2^479642+1)/733144386Lelio R Paula08/2015
244844917^1638+1638^44917144378Hans Havermann12/2020
2449(21*2^479605-1)/11144376Lelio R Paula09/2015
2450(56*10^144336+583)/9144337Robert Price08/2021
24512^479348-2792219144299Enzo Doria02/2016
24523^302389-6242144277Enzo Doria05/2014
245333778^18641+18641^33778144248Hans Havermann01/2021
24542*10^144220-3144221Robert Price07/2015
24552^478904-109109144165Enzo Doria04/2014
245643698^1987+1987^43698144125Hans Havermann12/2020
245736128^9723+9723^36128144072Hans Havermann01/2021
245832817^24518+24518^32817144050Hans Havermann12/2020
245934295^15828+15828^34295144020Hans Havermann01/2021
24602^478337-115333143994Enzo Doria07/2015
2461(7*2^478330-1)/3143993Lelio R Paula08/2015
246288^74047-87^74047143984Robert Price05/2015
246333242^21441+21441^33242143980Hans Havermann01/2021
2464(19*10^143963+467)/9143964Robert Price02/2018
2465(71^77761+1)/72143954Paul Bourdelais09/2017
246633490^19859+19859^33490143939Hans Havermann01/2021
2467(853*10^143931-7)/9143933Robert Price07/2021
24682^478088+27143919Robert Price11/2015
24697*10^143857-93143858Robert Price08/2020
24703*10^143844+61143845Robert Price09/2020
247141358^3005+3005^41358143837Hans Havermann01/2021
24722^477475-22071143735Enzo Doria07/2013
24732^477417-22123143717Enzo Doria07/2013
24742^477359-3577143700Yves Minet03/2017
247539435^4402+4402^39435143688Hans Havermann01/2021
2476(14*10^143662-71)/3143663Robert Price12/2018
24776^184614+5143658Paul Bourdelais01/2021
247846371^1252+1252^46371143640Hans Havermann12/2020
247934975^12748+12748^34975143588Hans Havermann01/2021
24802^476936-396765143573Enzo Doria07/2013
24812^476888-2791229143558Enzo Doria01/2016
24822^476868-1859939143552Enzo Doria11/2015
248340807^3294+3294^40807143548Hans Havermann12/2020
2484755^49878+49878^755143547Norbert Schneider04/2019
2485(19^112247-4^112247)/15143536Robert Price03/2021
248635561^10872+10872^35561143536Hans Havermann06/2021
248737637^6492+6492^37637143487Hans Havermann05/2021
248861567^214+214^61567143477Hans Havermann05/2021
24892^476558-113627143459Enzo Doria08/2014
24902^476478-45143435Lelio R Paula11/2017
249136380^8757+8757^36380143423Hans Havermann06/2021
249232510^25707+25707^32510143371Hans Havermann05/2021
24938*10^143361+17143362Robert Price07/2021
2494(2^475854+9)/73143245Lelio R Paula08/2015
24952^475813-113239143234Enzo Doria07/2014
249632218^27849+27849^32218143203Hans Havermann04/2021
24972^475624-114059143178Enzo Doria11/2014
2498(11*2^475553-7)/15143156Renaud Lifchitz03/2011
24992^475480-2786129143134Enzo Doria10/2015
250033912^16621+16621^33912143131Hans Havermann05/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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