PRP Records

Probable Primes Top 10000

(294687 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 ?
3251numbpart(18140942830)150033Serge Batalov04/2017
325210^150029+4381150030Patrick De Geest05/2016
325310^150029-41150029Serge Batalov12/2014
32549*34^97952+529150013Eric Chen08/2023
325510^150000+1158603150001Patrick De Geest09/2018
325610^150000-245703150000Patrick De Geest09/2018
3257(38*10^149999+691)/9150000Robert Price10/2018
32582043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
3259(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
32602^498238-53149985Lelio R Paula12/2017
326145728^1905+1905^45728149984Hans Havermann10/2020
3262(211^65024+1)/(211^512+1)149945Martin Hopf12/2023
32635*10^149907+23149908Robert Price03/2019
326432^99585-829149891Eric Chen11/2023
326539347^6442+6442^39347149874Hans Havermann09/2020
32662^497850+81049149868Enzo Doria07/2016
326737228^10575+10575^37228149816Hans Havermann10/2020
3268(5*2^497673+1)/2743149812Lelio R Paula10/2015
3269(5*2^497671+1)/373703149810Lelio R Paula10/2015
3270(2*10^149803-143)/3149803Robert Price03/2018
327133845^26604+26604^33845149763Hans Havermann09/2020
32722^497434-2784191149743Enzo Doria10/2015
3273(865*10^149737-1)/9149739Robert Price04/2020
327410^149695-7000001149695Robert Price06/2021
327538237^8214+8214^38237149681Hans Havermann09/2020
3276(23*10^149655+19)/3149656Robert Price07/2019
32772^497068-113579149633Enzo Doria08/2014
32782^497037+73727149624Enzo Doria04/2016
327911*10^149618+3149620Robert Price07/2021
328034942^19067+19067^34942149562Hans Havermann09/2020
328133696^27449+27449^33696149561Hans Havermann09/2020
32822^496773+77747149544Enzo Doria05/2016
3283(7*10^149483-493)/9149483Robert Price04/2021
3284(206*10^149459+7)/3149461Robert Price07/2020
328534589^20940+20940^34589149459Hans Havermann09/2020
32862^496477-113485149455Enzo Doria08/2014
32873*2^496411-5149436Jon Grantham07/2023
3288((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
32892^496270-49451149393Enzo Doria10/2015
32902^496238-1865081149383Enzo Doria01/2016
329133831^26030+26030^33831149380Hans Havermann09/2020
329234131^23780+23780^34131149365Hans Havermann09/2020
3293(5*10^149335-53)/3149336Robert Price09/2020
32942^495968-1853699149302Enzo Doria09/2015
32952^495935-4117149292Yves Minet02/2018
32965*2^495930+3149291Jon Grantham07/2023
329735816^14709+14709^35816149267Hans Havermann09/2020
3298(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
329910^149240-40000001149240Robert Price07/2022
33002^495712-396765149225Enzo Doria07/2013
3301(21*2^495676-1)/4835149211Lelio R Paula10/2015
33022^495420+1880701149137Enzo Doria10/2016
330325646^33823-33823^25646149127Frank Doornink02/2024
33042^495337-1847293149112Enzo Doria07/2015
3305(2^495193-7)/5149068Lelio R Paula10/2015
33062^495163+111546435149059Paul Bourdelais10/2021
330733282^30097+30097^33282149055Hans Havermann09/2020
330837384^9705+9705^37384149050Hans Havermann09/2020
330934808^19143+19143^34808149049Hans Havermann09/2020
3310413^56963-412^56963149013Jean-Louis Charton08/2012
331147^89113-46^89113149006Robert Price10/2012
33122^494916+87855148985Lelio R Paula01/2016
33136*10^148982+73148983Robert Price04/2019
33143^312155-4148936Anonymous02/2023
331510^148934+1530019148935Patrick De Geest02/2021
331610^148934-1000000001148934Robert Price11/2020
331710^148934-512057148934Patrick De Geest02/2021
331839000^6571+6571^39000148888Hans Havermann10/2020
33192^494586-2791991148886Enzo Doria02/2016
33208*10^148860-3148861Ray Chandler04/2011
332138262^7769+7769^38262148854Hans Havermann10/2020
332210^148816-500001148816Robert Price03/2022
3323(53*10^148811-287)/9148812Robert Price02/2022
33242^494333-286183148810Enzo Doria06/2015
33252^494144-264119148753Enzo Doria05/2014
33266*10^148734+47148735Robert Price06/2022
332736502^11823+11823^36502148663Hans Havermann11/2020
3328(5*2^493838-1)/3721148658Lelio R Paula10/2015
332964239^206+206^64239148641Hans Havermann10/2020
3330(23*2^493761-1)/555148636Lelio R Paula10/2015
3331(23*10^148627-137)/3148628Robert Price08/2021
3332(151*10^148601-1)/3148603Robert Price03/2020
33332^493636+82081148600Enzo Doria09/2016
3334((((((((((((((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
333527134^33509-33509^27134148563Frank Doornink01/2024
3336177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
3337(2*10^148460-23)/3148460Robert Price04/2018
3338(28*10^148445+101)/3148446Robert Price09/2020
333936203^12556+12556^36203148391Hans Havermann10/2020
334033912^23749+23749^33912148387Hans Havermann10/2020
3341(8*10^148328+1)/9148328Serge Batalov05/2010
334234294^21117+21117^34294148309Hans Havermann10/2020
3343(71*10^148306-539)/9148307Robert Price07/2019
334438042^7875+7875^38042148222Hans Havermann10/2020
33455^211959-12874148153Enzo Doria05/2014
334634142^21831+21831^34142148145Hans Havermann10/2020
334710^148112+34059148113Patrick De Geest05/2021
334810^148112-70000001148112Robert Price03/2021
334910^148112-106593148112Patrick De Geest05/2021
335036303^12016+12016^36303148108Hans Havermann10/2020
3351(77*10^148089-149)/9148090Robert Price03/2022
3352(16*10^148071+41)/3148072Robert Price03/2019
3353187^65175-2148068Lelio R Paula11/2017
33542^491851+1871453148062Enzo Doria05/2016
3355(68*10^148060-257)/9148061Robert Price07/2019
3356(151*10^148020-1)/3148022Robert Price03/2020
335739153^6032+6032^39153148017Hans Havermann10/2020
335836798^10507+10507^36798147983Hans Havermann12/2020
3359(26*10^147973-23)/3147974Robert Price12/2019
33602^491521-1865323147963Enzo Doria02/2016
3361(2^491476+7)/71147948Lelio R Paula10/2015
33622*10^147928+47147929Robert Price12/2021
33632^491391-7807147924Lelio R Paula01/2013
336439736^5279+5279^39736147920Hans Havermann11/2020
33652^491370-113297147918Enzo Doria07/2014
3366(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
336744368^2155+2155^44368147899Hans Havermann12/2020
3368(17*10^147890+79)/3147891Robert Price04/2019
336994*10^147871-3147873Robert Price05/2020
337010^147843+620967147844Patrick De Geest05/2021
337110^147843-50000000001147843Robert Price12/2020
337210^147843-182891147843Patrick De Geest05/2021
337335805^13346+13346^35805147709Hans Havermann11/2020
33742^490672+255255147707Paul Bourdelais10/2021
33752^490660-17147704Lelio R Paula12/2017
3376(229*10^147699-1)/3147701Robert Price07/2020
337740656^4289+4289^40656147678Hans Havermann11/2020
33782^490550+1179439147671Enzo Doria06/2016
3379(23*10^147649-59)/9147650Robert Price05/2018
33802^490303+2793653147596Enzo Doria03/2016
33812^490266+255255147585Paul Bourdelais10/2021
3382199^64181-2147543Lelio R Paula11/2017
338332849^30958+30958^32849147518Hans Havermann11/2020
33842^489871-286987147466Enzo Doria07/2015
33852^489864-351899147464Enzo Doria07/2015
3386175^65724-2147422Lelio R Paula11/2017
33872^489712+1874851147419Enzo Doria06/2016
338834473^18830+18830^34473147367Hans Havermann11/2020
338963^81896-2147359Lelio R Paula10/2017
339034580^18237+18237^34580147344Hans Havermann11/2020
3391(11*10^147313-107)/3147314Robert Price09/2018
3392(397*10^147310+17)/9147312Robert Price03/2022
33932^489305-59815147296Enzo Doria10/2015
3394(2^489280-7)/6381147285Lelio R Paula09/2015
33952*10^147264-61147265Robert Price10/2021
33962*10^147260+29147261Robert Price02/2021
339733556^24457+24457^33556147258Hans Havermann11/2020
33982^489125+80357147242Enzo Doria06/2016
339910^147240-40000001147240Robert Price07/2022
340032835^30452+30452^32835147220Hans Havermann12/2020
3401(19*10^147213-97)/3147214Robert Price10/2021
340227123^33190-33190^27123147143Frank Doornink01/2024
3403(148*10^147139-1)/3147141Robert Price03/2020
340434338^19255+19255^34338147123Hans Havermann11/2020
34052^488648-112799147098Enzo Doria07/2014
34062^488627-350317147092Enzo Doria06/2015
340733432^25075+25075^33432147076Hans Havermann12/2020
3408(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
34092^488280-2165146987Yves Minet07/2014
34102^488278+45146987Lelio R Paula12/2017
34112^487927-39146881Lelio R Paula12/2017
3412(7*10^146860-13)/3146861Robert Price07/2018
3413(26*10^146856-77)/3146857Robert Price11/2019
341432948^28611+28611^32948146834Hans Havermann11/2020
341542596^2799+2799^42596146829Hans Havermann12/2020
34162^487726-1863341146821Enzo Doria12/2015
341743838^2229+2229^43838146775Hans Havermann11/2020
341835005^15594+15594^35005146775Hans Havermann11/2020
3419(167*10^146764+7)/3146766Robert Price04/2021
342053^85114+85114146761Kellen Shenton05/2022
3421(59*10^146738+157)/9146739Robert Price12/2021
3422((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
342332963^28234+28234^32963146711Hans Havermann12/2020
3424(22*10^146661-19)/3146662Robert Price04/2019
342533958^20825+20825^33958146651Hans Havermann12/2020
342626289^33178-33178^26289146640Frank Doornink03/2024
34272^487121-39523146639Enzo Doria09/2015
342861063^252+252^61063146637Hans Havermann12/2020
3429(7*2^486967+1)/39146591Lelio R Paula09/2015
343034099^19900+19900^34099146587Hans Havermann11/2020
34312^486893-79146570Yves Minet09/2017
343236818^9567+9567^36818146565Hans Havermann12/2020
34332^486840+1879141146554Enzo Doria08/2016
34342^486774-87146534Lelio R Paula12/2017
343538655^6176+6176^38655146530Hans Havermann11/2020
34368*10^146522-81146523Robert Price02/2021
343732820^29059+29059^32820146485Hans Havermann12/2020
343837261^8530+8530^37261146472Hans Havermann12/2020
343966953^154+154^66953146462Hans Havermann12/2020
344096^73877-95^73877146445Robert Price10/2015
34418*10^146421+81146422Robert Price08/2019
344233153^26090+26090^33153146420Hans Havermann11/2020
34432^486275+23961146384Enzo Doria10/2023
3444(52^85259+1)/53146304Paul Bourdelais09/2017
3445179^64935+2146290Lelio R Paula10/2017
344632595^30758+30758^32595146285Hans Havermann11/2020
344734972^15157+15157^34972146205Hans Havermann12/2020
3448(16*10^146200+131)/3146201Robert Price03/2022
3449(19*10^146181-49)/3146182Robert Price05/2019
34502^485531-114621146160Enzo Doria05/2015
34512^485473-933075146142Paul Bourdelais06/2021
3452(2^485461-9)/4249146135Lelio R Paula09/2015
3453(22*10^146130-193)/9146131Robert Price07/2022
34542^485389+81887146117Enzo Doria08/2016
345532554^30773+30773^32554146108Hans Havermann11/2020
3456(10^146063+71)/9146063Serge Batalov07/2015
34572*10^146051-63146052Robert Price01/2022
3458(2^485119+7)/2745146032Lelio R Paula09/2015
3459(22*10^146029+257)/9146030Robert Price06/2018
34607*10^145982-53145983Robert Price06/2020
34612^484743+1872923145923Enzo Doria05/2016
346233140^25287+25287^33140145913Hans Havermann01/2021
346337875^7112+7112^37875145895Hans Havermann01/2021
346432862^27473+27473^32862145872Hans Havermann01/2021
346532836^27587+27587^32836145815Hans Havermann01/2021
34662^484341+1879157145802Enzo Doria08/2016
34672*10^145784-91145785Robert Price04/2020
34682^484271-51145781Lelio R Paula11/2017
3469(188*10^145750-11)/3145752Robert Price02/2022
347070^78989-69^78989145743Robert Price01/2014
347151^85334+2145714Robert Price07/2015
34722^483886-1857101145665Enzo Doria10/2015
347333350^23307+23307^33350145656Hans Havermann01/2021
3474(19*10^145585+131)/3145586Robert Price06/2020
347531815^32332-32332^31815145580Frank Doornink01/2024
34762^483563-1863457145567Enzo Doria12/2015
34774*10^145563-69145564Robert Price01/2022
34782^483516-1861409145553Enzo Doria11/2015
34792^483384-115019145514Enzo Doria06/2015
3480(259*10^145501-1)/3145503Robert Price12/2020
3481(19*10^145499-61)/3145500Robert Price05/2019
34822^483302-3221145489Lelio R Paula12/2012
3483(23*10^145463+61)/3145464Robert Price01/2022
348435523^12434+12434^35523145453Hans Havermann01/2021
3485(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
34862^483046+1874029145412Enzo Doria06/2016
34872^482991-2789317145395Enzo Doria12/2015
34882^482978-2789711145391Enzo Doria12/2015
34892^482966-2789711145388Enzo Doria12/2015
34902^482817-1858843145343Enzo Doria10/2015
34912^482751-113635145323Enzo Doria08/2014
34922^482705-459763145309Enzo Doria05/2015
3493(4^241306+11)/3145281Robert Price03/2017
3494(238*10^145276-1)/3145278Robert Price04/2020
3495(19*2^482534+1)/7145258Lelio R Paula09/2015
349653^84239-52^84239145252Robert Price01/2013
34972^482386+212419145213Enzo Doria08/2023
349847952^1067+1067^47952145207Hans Havermann01/2021
3499(2^482333+5)/9287145193Lelio R Paula09/2015
35002^482087+72623145123Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

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