PRP Records

Probable Primes Top 10000

(291910 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 ?
25012^498623+1866983150101Enzo Doria03/2016
2502(25*10^150050-403)/9150051Robert Price12/2020
2503numbpart(18140942830)150033Serge Batalov04/2017
250410^150029+4381150030Patrick De Geest05/2016
250510^150029-41150029Serge Batalov12/2014
250610^150000+1158603150001Patrick De Geest09/2018
250710^150000-245703150000Patrick De Geest09/2018
2508(38*10^149999+691)/9150000Robert Price10/2018
25092043563126843649194^8192+2043563126843649185^8192150000Youcef Lemsafer01/2023
2510(2043563126843649232^8192+2043563126843649201^8192)/147457149994Youcef Lemsafer01/2023
25112^498238-53149985Lelio R Paula12/2017
251245728^1905+1905^45728149984Hans Havermann10/2020
25135*10^149907+23149908Robert Price03/2019
251439347^6442+6442^39347149874Hans Havermann09/2020
25152^497850+81049149868Enzo Doria07/2016
251637228^10575+10575^37228149816Hans Havermann10/2020
2517(5*2^497673+1)/2743149812Lelio R Paula10/2015
2518(5*2^497671+1)/373703149810Lelio R Paula10/2015
2519(2*10^149803-143)/3149803Robert Price03/2018
252033845^26604+26604^33845149763Hans Havermann09/2020
25212^497434-2784191149743Enzo Doria10/2015
2522(865*10^149737-1)/9149739Robert Price04/2020
252310^149695-7000001149695Robert Price06/2021
252438237^8214+8214^38237149681Hans Havermann09/2020
2525(23*10^149655+19)/3149656Robert Price07/2019
25262^497068-113579149633Enzo Doria08/2014
25272^497037+73727149624Enzo Doria04/2016
252811*10^149618+3149620Robert Price07/2021
252934942^19067+19067^34942149562Hans Havermann09/2020
253033696^27449+27449^33696149561Hans Havermann09/2020
25312^496773+77747149544Enzo Doria05/2016
2532(7*10^149483-493)/9149483Robert Price04/2021
2533(206*10^149459+7)/3149461Robert Price07/2020
253434589^20940+20940^34589149459Hans Havermann09/2020
25352^496477-113485149455Enzo Doria08/2014
2536((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9149410Hans Havermann09/2019
25372^496270-49451149393Enzo Doria10/2015
25382^496238-1865081149383Enzo Doria01/2016
253933831^26030+26030^33831149380Hans Havermann09/2020
254034131^23780+23780^34131149365Hans Havermann09/2020
2541(5*10^149335-53)/3149336Robert Price09/2020
25422^495968-1853699149302Enzo Doria09/2015
25432^495935-4117149292Yves Minet02/2018
254435816^14709+14709^35816149267Hans Havermann09/2020
2545(10^149264+7)/191/2683/80557149254Alfred Reich07/2021
254610^149240-40000001149240Robert Price07/2022
25472^495712-396765149225Enzo Doria07/2013
2548(21*2^495676-1)/4835149211Lelio R Paula10/2015
25492^495420+1880701149137Enzo Doria10/2016
25502^495337-1847293149112Enzo Doria07/2015
2551(2^495193-7)/5149068Lelio R Paula10/2015
25522^495163+111546435149059Paul Bourdelais10/2021
255333282^30097+30097^33282149055Hans Havermann09/2020
255437384^9705+9705^37384149050Hans Havermann09/2020
255534808^19143+19143^34808149049Hans Havermann09/2020
2556413^56963-412^56963149013Jean-Louis Charton08/2012
255747^89113-46^89113149006Robert Price10/2012
25582^494916+87855148985Lelio R Paula01/2016
25596*10^148982+73148983Robert Price04/2019
256010^148934+1530019148935Patrick De Geest02/2021
256110^148934-1000000001148934Robert Price11/2020
256210^148934-512057148934Patrick De Geest02/2021
256339000^6571+6571^39000148888Hans Havermann10/2020
25642^494586-2791991148886Enzo Doria02/2016
25658*10^148860-3148861Ray Chandler04/2011
256638262^7769+7769^38262148854Hans Havermann10/2020
256710^148816-500001148816Robert Price03/2022
2568(53*10^148811-287)/9148812Robert Price02/2022
25692^494333-286183148810Enzo Doria06/2015
25702^494144-264119148753Enzo Doria05/2014
25716*10^148734+47148735Robert Price06/2022
257236502^11823+11823^36502148663Hans Havermann11/2020
2573(5*2^493838-1)/3721148658Lelio R Paula10/2015
257464239^206+206^64239148641Hans Havermann10/2020
2575(23*2^493761-1)/555148636Lelio R Paula10/2015
2576(23*10^148627-137)/3148628Robert Price08/2021
2577(151*10^148601-1)/3148603Robert Price03/2020
25782^493636+82081148600Enzo Doria09/2016
2579((((((((((((((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
2580177487#+(519643#)/(177487#)148558Makoto Morimoto11/2017
2581(2*10^148460-23)/3148460Robert Price04/2018
2582(28*10^148445+101)/3148446Robert Price09/2020
258336203^12556+12556^36203148391Hans Havermann10/2020
258433912^23749+23749^33912148387Hans Havermann10/2020
2585(8*10^148328+1)/9148328Serge Batalov05/2010
258634294^21117+21117^34294148309Hans Havermann10/2020
2587(71*10^148306-539)/9148307Robert Price07/2019
258838042^7875+7875^38042148222Hans Havermann10/2020
25895^211959-12874148153Enzo Doria05/2014
259034142^21831+21831^34142148145Hans Havermann10/2020
259110^148112+34059148113Patrick De Geest05/2021
259210^148112-70000001148112Robert Price03/2021
259310^148112-106593148112Patrick De Geest05/2021
259436303^12016+12016^36303148108Hans Havermann10/2020
2595(77*10^148089-149)/9148090Robert Price03/2022
2596(16*10^148071+41)/3148072Robert Price03/2019
2597187^65175-2148068Lelio R Paula11/2017
25982^491851+1871453148062Enzo Doria05/2016
2599(68*10^148060-257)/9148061Robert Price07/2019
2600(151*10^148020-1)/3148022Robert Price03/2020
260139153^6032+6032^39153148017Hans Havermann10/2020
260236798^10507+10507^36798147983Hans Havermann12/2020
2603(26*10^147973-23)/3147974Robert Price12/2019
26042^491521-1865323147963Enzo Doria02/2016
2605(2^491476+7)/71147948Lelio R Paula10/2015
26062*10^147928+47147929Robert Price12/2021
26072^491391-7807147924Lelio R Paula01/2013
260839736^5279+5279^39736147920Hans Havermann11/2020
26092^491370-113297147918Enzo Doria07/2014
2610(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
261144368^2155+2155^44368147899Hans Havermann12/2020
2612(17*10^147890+79)/3147891Robert Price04/2019
261394*10^147871-3147873Robert Price05/2020
261410^147843+620967147844Patrick De Geest05/2021
261510^147843-50000000001147843Robert Price12/2020
261610^147843-182891147843Patrick De Geest05/2021
261735805^13346+13346^35805147709Hans Havermann11/2020
26182^490672+255255147707Paul Bourdelais10/2021
26192^490660-17147704Lelio R Paula12/2017
2620(229*10^147699-1)/3147701Robert Price07/2020
262140656^4289+4289^40656147678Hans Havermann11/2020
26222^490550+1179439147671Enzo Doria06/2016
2623(23*10^147649-59)/9147650Robert Price05/2018
26242^490303+2793653147596Enzo Doria03/2016
26252^490266+255255147585Paul Bourdelais10/2021
2626199^64181-2147543Lelio R Paula11/2017
262732849^30958+30958^32849147518Hans Havermann11/2020
26282^489871-286987147466Enzo Doria07/2015
26292^489864-351899147464Enzo Doria07/2015
2630175^65724-2147422Lelio R Paula11/2017
26312^489712+1874851147419Enzo Doria06/2016
263234473^18830+18830^34473147367Hans Havermann11/2020
263363^81896-2147359Lelio R Paula10/2017
263434580^18237+18237^34580147344Hans Havermann11/2020
2635(11*10^147313-107)/3147314Robert Price09/2018
2636(397*10^147310+17)/9147312Robert Price03/2022
26372^489305-59815147296Enzo Doria10/2015
2638(2^489280-7)/6381147285Lelio R Paula09/2015
26392*10^147264-61147265Robert Price10/2021
26402*10^147260+29147261Robert Price02/2021
264133556^24457+24457^33556147258Hans Havermann11/2020
26422^489125+80357147242Enzo Doria06/2016
264310^147240-40000001147240Robert Price07/2022
264432835^30452+30452^32835147220Hans Havermann12/2020
2645(19*10^147213-97)/3147214Robert Price10/2021
2646(148*10^147139-1)/3147141Robert Price03/2020
264734338^19255+19255^34338147123Hans Havermann11/2020
26482^488648-112799147098Enzo Doria07/2014
26492^488627-350317147092Enzo Doria06/2015
265033432^25075+25075^33432147076Hans Havermann12/2020
2651(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
26522^488280-2165146987Yves Minet07/2014
26532^488278+45146987Lelio R Paula12/2017
26542^487927-39146881Lelio R Paula12/2017
2655(7*10^146860-13)/3146861Robert Price07/2018
2656(26*10^146856-77)/3146857Robert Price11/2019
265732948^28611+28611^32948146834Hans Havermann11/2020
265842596^2799+2799^42596146829Hans Havermann12/2020
26592^487726-1863341146821Enzo Doria12/2015
266043838^2229+2229^43838146775Hans Havermann11/2020
266135005^15594+15594^35005146775Hans Havermann11/2020
2662(167*10^146764+7)/3146766Robert Price04/2021
266353^85114+85114146761Kellen Shenton05/2022
2664(59*10^146738+157)/9146739Robert Price12/2021
2665((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
266632963^28234+28234^32963146711Hans Havermann12/2020
2667(22*10^146661-19)/3146662Robert Price04/2019
266833958^20825+20825^33958146651Hans Havermann12/2020
26692^487121-39523146639Enzo Doria09/2015
267061063^252+252^61063146637Hans Havermann12/2020
2671(7*2^486967+1)/39146591Lelio R Paula09/2015
267234099^19900+19900^34099146587Hans Havermann11/2020
26732^486893-79146570Yves Minet09/2017
267436818^9567+9567^36818146565Hans Havermann12/2020
26752^486840+1879141146554Enzo Doria08/2016
26762^486774-87146534Lelio R Paula12/2017
267738655^6176+6176^38655146530Hans Havermann11/2020
26788*10^146522-81146523Robert Price02/2021
267932820^29059+29059^32820146485Hans Havermann12/2020
268037261^8530+8530^37261146472Hans Havermann12/2020
268166953^154+154^66953146462Hans Havermann12/2020
268296^73877-95^73877146445Robert Price10/2015
26838*10^146421+81146422Robert Price08/2019
268433153^26090+26090^33153146420Hans Havermann11/2020
2685(52^85259+1)/53146304Paul Bourdelais09/2017
2686179^64935+2146290Lelio R Paula10/2017
268732595^30758+30758^32595146285Hans Havermann11/2020
268834972^15157+15157^34972146205Hans Havermann12/2020
2689(16*10^146200+131)/3146201Robert Price03/2022
2690(19*10^146181-49)/3146182Robert Price05/2019
26912^485531-114621146160Enzo Doria05/2015
26922^485473-933075146142Paul Bourdelais06/2021
2693(2^485461-9)/4249146135Lelio R Paula09/2015
2694(22*10^146130-193)/9146131Robert Price07/2022
26952^485389+81887146117Enzo Doria08/2016
269632554^30773+30773^32554146108Hans Havermann11/2020
2697(10^146063+71)/9146063Serge Batalov07/2015
26982*10^146051-63146052Robert Price01/2022
2699(2^485119+7)/2745146032Lelio R Paula09/2015
2700(22*10^146029+257)/9146030Robert Price06/2018
27017*10^145982-53145983Robert Price06/2020
27022^484743+1872923145923Enzo Doria05/2016
270333140^25287+25287^33140145913Hans Havermann01/2021
270437875^7112+7112^37875145895Hans Havermann01/2021
270532862^27473+27473^32862145872Hans Havermann01/2021
270632836^27587+27587^32836145815Hans Havermann01/2021
27072^484341+1879157145802Enzo Doria08/2016
27082*10^145784-91145785Robert Price04/2020
27092^484271-51145781Lelio R Paula11/2017
2710(188*10^145750-11)/3145752Robert Price02/2022
271170^78989-69^78989145743Robert Price01/2014
271251^85334+2145714Robert Price07/2015
27132^483886-1857101145665Enzo Doria10/2015
271433350^23307+23307^33350145656Hans Havermann01/2021
2715(19*10^145585+131)/3145586Robert Price06/2020
27162^483563-1863457145567Enzo Doria12/2015
27174*10^145563-69145564Robert Price01/2022
27182^483516-1861409145553Enzo Doria11/2015
27192^483384-115019145514Enzo Doria06/2015
2720(259*10^145501-1)/3145503Robert Price12/2020
2721(19*10^145499-61)/3145500Robert Price05/2019
27222^483302-3221145489Lelio R Paula12/2012
2723(23*10^145463+61)/3145464Robert Price01/2022
272435523^12434+12434^35523145453Hans Havermann01/2021
27252^483046+1874029145412Enzo Doria06/2016
27262^482991-2789317145395Enzo Doria12/2015
27272^482978-2789711145391Enzo Doria12/2015
27282^482966-2789711145388Enzo Doria12/2015
27292^482817-1858843145343Enzo Doria10/2015
27302^482751-113635145323Enzo Doria08/2014
27312^482705-459763145309Enzo Doria05/2015
2732(4^241306+11)/3145281Robert Price03/2017
2733(238*10^145276-1)/3145278Robert Price04/2020
2734(19*2^482534+1)/7145258Lelio R Paula09/2015
273553^84239-52^84239145252Robert Price01/2013
273647952^1067+1067^47952145207Hans Havermann01/2021
2737(2^482333+5)/9287145193Lelio R Paula09/2015
27382^482087+72623145123Enzo Doria04/2016
27392^482016-286565145102Enzo Doria07/2015
2740(19*10^145093+101)/3145094Robert Price09/2019
27412^481956+121145084Stefano Morozzi04/2021
27422^481840+15145049Robert Price09/2015
27432^481801-481801145037Henri Lifchitz03/2005
27442^481775+1869083145029Enzo Doria05/2016
274529^99167+2145022Ray Chandler08/2011
27462^481663+1875653144996Enzo Doria07/2016
27478*10^144977+27144978Robert Price09/2021
274836486^9379+9379^36486144929Hans Havermann12/2020
274935111^13378+13378^35111144882Hans Havermann01/2021
27502^481149-459073144841Enzo Doria05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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