PRP Records

Probable Primes Top 10000

(280928 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 ?
22512*10^141407-27141408Robert Price05/2018
2252(214*10^141385-1)/3141387Robert Price01/2021
22532^469630-59711141373Enzo Doria10/2015
2254(25*10^141366-331)/9141367Robert Price08/2018
2255(2^469564-3)/611141351Lelio R Paula08/2015
2256197^61601+2141342Lelio R Paula08/2017
22572^469372-112949141296Enzo Doria07/2014
22585*10^141294-63141295Robert Price04/2021
22593^296115+4141283Tyler NeSmith01/2021
2261143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2260143^65536+106^65536141253Serge Batalov03/2018
22622^469198+782569141243Enzo Doria10/2016
22632^469076-2786939141206Enzo Doria11/2015
22642^468804+1874941141125Enzo Doria06/2016
22652^468787+81353141119Enzo Doria08/2016
22662^468595-350407141062Enzo Doria06/2015
22672^468564+87855141052Lelio R Paula01/2016
22682^468551-21987141048Enzo Doria07/2013
22692^468523-7141040Lelio R Paula08/2015
2270(25*10^141019-13)/3141020Robert Price09/2019
22712^468405+87855141004Lelio R Paula01/2016
22722^467978-113051140876Enzo Doria07/2014
22732^467780-344429140816Enzo Doria07/2015
22749*10^140802-89140803Robert Price04/2020
22752^467605-1855603140764Enzo Doria09/2015
22765*10^140744-7140745Robert Price09/2015
2277(5^201359-1)/4140744Paul Bourdelais12/2008
22782^467401-1850023140702Enzo Doria08/2015
2279(266*10^140681-17)/3140683Robert Price07/2020
2280(2^467270+78557)/23247140658Lelio R Paula07/2015
2281(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
22822^467166-1854941140631Enzo Doria09/2015
2283(203*10^140615-11)/3140617Robert Price12/2020
2284(85*10^140609+473)/9140610Robert Price01/2020
22852^466866-1840571140541Enzo Doria06/2015
22862^466829-459523140530Enzo Doria05/2015
22872^466692-113213140489Enzo Doria07/2014
2288(44*10^140410-503)/9140411Robert Price12/2018
2289153^64265-2140400Lelio R Paula11/2017
2290(112*10^140357-1)/3140359Serge Batalov12/2014
2291(29*10^140337-17)/3140338Robert Price09/2019
22922^466181-112735140335Enzo Doria07/2014
2293(5*10^140281-119)/3140282Robert Price03/2018
2294(27*2^465872+1)/691140241Lelio R Paula08/2015
22952^465803-114817140221Enzo Doria05/2015
2296floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
22972^465503-112735140131Enzo Doria07/2014
2298(16*10^140091+167)/3140092Robert Price06/2019
22996^179964+179964^6-1140040Robert Price04/2014
2300(89*10^140008-179)/9140009Robert Price12/2019
2301(29*2^465077-1)/9140003Lelio R Paula08/2015
23022^465072-344789140001Enzo Doria07/2015
23035*10^139945+81139946Robert Price03/2019
23042^464864-17139939Lelio R Paula09/2017
23058*10^139920+51139921Robert Price08/2019
2306(85*10^139913-1)/3139915Robert Price02/2020
2307(17^113621+1)/18139804Paul Bourdelais09/2011
23082*10^139800-21139801Robert Price09/2020
2309(13*10^139782+191)/3139783Robert Price11/2018
2310(19*2^464312-1)/3139773Lelio R Paula08/2015
2311(74*10^139723+133)/9139724Robert Price06/2019
23123*10^139722+13139723Robert Price07/2018
231377*10^139692+3139694Robert Price06/2020
2314(31*2^463970+1)/5139670Lelio R Paula08/2015
2315(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
23162^463633-2788423139568Enzo Doria11/2015
23172^463271-109501139459Enzo Doria04/2014
2318(5*10^139457+79)/3139458Robert Price03/2018
23192^463237-99139449Lelio R Paula09/2017
2320(49*10^139442+383)/9139443Robert Price04/2019
2321(7*10^139417-547)/9139417Robert Price01/2018
2322(10^139398+191)/3139398Robert Price02/2018
23232^463019+79463139383Enzo Doria06/2016
23243^292129-112756139381Enzo Doria07/2014
2325(15*2^462951+1)/527139361Lelio R Paula08/2015
23262^462855-1865707139334Enzo Doria02/2016
2327(86*10^139315+121)/9139316Robert Price08/2019
23282^462786-292043139313Enzo Doria08/2015
2329(26*10^139289+1)/9139290Serge Batalov05/2010
2330(17*10^139239+67)/3139240Robert Price01/2019
23312^462238-935139148Yves Minet02/2014
2332(109*10^139100-7)/3139102Robert Price03/2021
23332^461228+1870441138844Enzo Doria05/2016
23342^461204-113675138837Enzo Doria08/2014
2335(2^461139-7)/47138815Lelio R Paula08/2015
2336(17*10^138812-521)/9138813Robert Price04/2018
23373*10^138811-11138812Robert Price07/2018
2338(28*10^138768+173)/3138769Robert Price12/2019
2339(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2340(379*10^138737-1)/9138739Robert Price02/2020
2341(43*10^138648+101)/9138649Robert Price11/2018
23422^460567-113541138645Enzo Doria08/2014
23437*10^138604+3138605Robert Price08/2015
23442^460330+69138574Lelio R Paula09/2017
2345(17*10^138569-77)/3138570Robert Price08/2019
2346(16*10^138545+89)/3138546Robert Price03/2021
23476*10^138520-37138521Robert Price02/2021
23482^460078-69581138498Enzo Doria12/2015
23492^459768+1531138404Lelio R Paula06/2012
2350(266*10^138328-17)/3138330Robert Price07/2020
23512^459343-113611138277Enzo Doria08/2014
2352(28*10^138240+113)/3138241Robert Price03/2020
23532^459199+1874393138233Enzo Doria06/2016
23542^459063-345307138192Enzo Doria06/2015
23552*10^138162-43138163Robert Price04/2018
23562^458927-112747138151Enzo Doria06/2014
23572^458927-69217138151Enzo Doria11/2015
2358555555*2^458524+1513138036Darren Bedwell08/2009
23592^458465+2^32+1138012T. D. Noe06/2007
23602^458321-113053137969Enzo Doria07/2014
23612^458298+79459137962Enzo Doria06/2016
23622^458248-21815137947Enzo Doria07/2013
23632^458194+1876549137931Enzo Doria07/2016
2364(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2365(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
23662^457937+57137853Lelio R Paula09/2017
2367(8*10^137845+13)/3137846Robert Price06/2018
23682^457822+105137819Donovan Johnson06/2006
23692^457754-113711137798Enzo Doria09/2014
237011^132315-360137792Enzo Doria09/2012
23712^457347-37137676Lelio R Paula09/2017
23722^457322-2786393137668Enzo Doria10/2015
2373gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
23742^457240-59939137643Enzo Doria10/2015
2375(856*10^137633-1)/9137635Robert Price03/2020
23762^457120-21575137607Enzo Doria07/2013
2377(11*2^456978+1)/15137564Lelio R Paula07/2015
2378(7*25^98399+10613)/12137556Curtis Bright05/2015
2379419^52446+52446^419137525Norbert Schneider11/2020
23802^456796-113513137510Enzo Doria08/2014
2381(7*2^456655+1)/39137467Lelio R Paula07/2015
23822^456503-114361137422Enzo Doria01/2015
2383(11*2^456387+1)/19137386Lelio R Paula07/2015
2384(71*10^137250+1)/9137251Serge Batalov05/2010
23852^455922+76249137247Enzo Doria05/2016
238614^119741-119741^14137239Serge Batalov04/2016
2387(19*2^455760+1)/3455137196Lelio R Paula07/2015
2389124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
2388124^65536+57^65536137195Serge Batalov03/2018
23902^455689+72677137177Enzo Doria04/2016
2391(17948!)^2+Prime(17948)137118Robert Price08/2014
2392(37^87421-1)/36137093Robert Price03/2012
23932^455323-57137066Lelio R Paula09/2017
2394(73*17^111333-9)/16136991Curtis Bright05/2015
23952^455025-112723136977Enzo Doria06/2014
239666*10^136894+7136896Robert Price07/2020
23972^454675-1777136871Yves Minet10/2011
23983*10^136829+29136830Robert Price05/2018
23994*10^136813-57136814Robert Price10/2018
2400(6092*28^94536-143)/9136812Curtis Bright05/2015
24012^454348-53136773Lelio R Paula09/2017
240231^91680-2136729Lelio R Paula05/2017
24032^454199-113697136728Enzo Doria09/2014
24047*10^136716+69136717Robert Price07/2019
24056*10^136692+53136693Robert Price05/2020
2406(13*10^136687+47)/3136688Robert Price10/2018
24072^453935-2791357136649Enzo Doria01/2016
24082^453906-69131136640Enzo Doria11/2015
24092^453791+1873913136605Enzo Doria06/2016
2410(21*2^453740-1)/2735136588Lelio R Paula07/2015
2411580^49413+49413^580136550Norbert Schneider02/2019
24122^453503-2788297136519Enzo Doria11/2015
241334989^7958+7958^34989136486Hans Havermann12/2020
241431007^25158+25158^31007136452Hans Havermann11/2020
24152^453267-113827136447Enzo Doria09/2014
241632234^17085+17085^32234136435Hans Havermann12/2020
24172^453102+1877629136398Enzo Doria08/2016
241831016^24981+24981^31016136397Hans Havermann12/2020
2419(62*10^136384-791)/9136385Robert Price06/2019
242034171^9798+9798^34171136382Hans Havermann12/2020
242132756^14541+14541^32756136350Hans Havermann11/2020
242232205^17086+17086^32205136313Hans Havermann12/2020
2423(25*10^136303+161)/3136304Robert Price09/2019
242435337^7196+7196^35337136299Hans Havermann12/2020
2425(182*10^136291+1)/3136293Robert Price02/2020
242623*10^136225-7136227Robert Price02/2020
2427L(651821)136223Henri Lifchitz09/2008
24282^452460+77701136205Enzo Doria05/2016
24292^452440-114755136199Enzo Doria04/2015
243032286^16489+16489^32286136157Hans Havermann11/2020
2431(47*10^136141+493)/9136142Robert Price03/2019
243240392^2339+2339^40392136082Hans Havermann12/2020
24332*10^136057-43136058Robert Price04/2018
2434(2^451956-5)/181136051Lelio R Paula07/2015
24352^451947-22165136050Enzo Doria07/2013
24362^451787-21805136002Enzo Doria07/2013
24372^451734-112817135986Enzo Doria06/2014
2438(11*2^451714+1)/75135979Lelio R Paula07/2015
24392^451705-21879135977Enzo Doria07/2013
24402^451560-112349135934Enzo Doria06/2014
24412^451530+45135925Lelio R Paula08/2017
244231622^19875+19875^31622135922Hans Havermann11/2020
2443(25*10^135906-73)/3135907Robert Price09/2019
24442^451450-21743135900Enzo Doria07/2013
244535218^7199+7199^35218135846Hans Havermann11/2020
244635661^6446+6446^35661135844Hans Havermann11/2020
244731869^18248+18248^31869135801Hans Havermann12/2020
24482^450805+65135706Lelio R Paula08/2017
244930761^25728+25728^30761135669Hans Havermann12/2020
24502*10^135663+69135664Robert Price06/2020
245133962^9867+9867^33962135651Hans Havermann11/2020
245234474^8605+8605^34474135647Hans Havermann11/2020
245334501^8508+8508^34501135583Hans Havermann12/2020
245435487^6614+6614^35487135577Hans Havermann12/2020
2455(13725^32768+1)/131074135573Lelio R Paula03/2012
2456(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
2457(5^193939+1)/6135557Paul Bourdelais12/2008
245840387^2260+2260^40387135463Hans Havermann12/2020
24592^449944-113247135447Enzo Doria07/2014
24602^449770-113247135395Enzo Doria07/2014
24612^449637-21471135355Enzo Doria07/2013
24622^449571-75135335Lelio R Paula08/2017
2463(14*10^135301-53)/3135302Robert Price12/2018
2464(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
2465(13*10^135279+437)/9135280Robert Price04/2018
24662^449330-35135262Lelio R Paula08/2017
2467(19*2^449325+1)/9135261Lelio R Paula07/2015
2468(13*10^135184-43)/3135185Robert Price11/2018
24692^449049-115309135178Enzo Doria07/2015
2470(10^135174+191)/3135174Robert Price02/2018
24712^449030-15135172Lelio R Paula08/2017
2472(27*2^448936-1)/11135144Lelio R Paula07/2015
247332221^15586+15586^32221135095Hans Havermann12/2020
24742^448762-351401135091Enzo Doria07/2015
24752*10^135083-43135084Robert Price04/2018
247631357^20278+20278^31357135056Hans Havermann12/2020
247732242^15445+15445^32242135055Hans Havermann12/2020
2478k(198476)135054Robert Price07/2020
247932461^14470+14470^32461135053Hans Havermann12/2020
248031353^20288+20288^31353135045Hans Havermann12/2020
24815*10^135019+77135020Robert Price12/2018
2482(10^135011+719)/9135011Serge Batalov12/2014
2483(197*10^134978+7)/3134980Robert Price12/2020
24842^448386-2786261134978Enzo Doria03/2016
2485(73*10^134939+143)/9134940Robert Price07/2019
248633957^9392+9392^33957134903Hans Havermann12/2020
24872^448113-113949134896Enzo Doria11/2014
248830958^22755+22755^30958134887Hans Havermann12/2020
24892^447888-2786639134828Enzo Doria03/2016
24902^447870-396765134823Enzo Doria07/2013
24912^447766-21791134791Enzo Doria07/2013
2492(19*10^134786-49)/3134787Robert Price05/2019
2493Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2494(23*2^447647+1)/155134755Lelio R Paula07/2015
24952^447552-1019134727Yves Minet02/2014
2496(2*10^134720-41)/3134720Robert Price02/2018
24972^447437-113569134692Enzo Doria08/2014
24982^447426-65134689Lelio R Paula08/2017
24992^447357-2797573134668Enzo Doria04/2016
25002^447278+93134645Lelio R Paula08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 12 2021 20:10 (Time in France)

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