PRP Records

Probable Primes Top 10000

(271019 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 ?
250110^126919-100001126919Robert Price07/2020
2502(71^68539+1)/72126882Paul Bourdelais09/2017
2503(5*10^126871-119)/3126872Robert Price03/2018
2504331^50339-10004126846Enzo Doria07/2012
25052^421363-2790757126843Enzo Doria03/2016
2506(106*10^126839-1)/3126841Serge Batalov12/2014
2507(7*2^421243+1)/39126807Lelio R Paula05/2014
2508(14*10^126784-83)/3126785Robert Price12/2018
25092^421161-286183126783Enzo Doria06/2015
25102^420939-113935126716Enzo Doria10/2014
2511177^56363-2126703Lelio R Paula10/2017
25122^420741-113659126656Enzo Doria08/2014
25132^420694-21126642Lelio R Paula05/2017
2514(13*10^126638+437)/9126639Robert Price04/2018
2515(167*10^126637-17)/3126639Robert Price03/2020
25164*10^126625+87126626Robert Price08/2018
2518(31*2^420556+1)/7126601Lelio R Paula05/2014
25177*10^126600-99126601Robert Price06/2019
25192^420424-59189126561Enzo Doria10/2015
25202^420126+71893126471Enzo Doria04/2016
2521(43*10^126441+47)/9126442Robert Price12/2018
25222^419866+1877059126393Enzo Doria07/2016
2523F(604711)126377Henri Lifchitz02/2005
25242^419757+72707126360Enzo Doria04/2016
25252^419720-21569126349Enzo Doria07/2013
25262^419637+29126324Henri Lifchitz02/2006
25272^419612+1876741126316Enzo Doria07/2016
25282^419520+2793271126289Enzo Doria03/2016
2529(2^419447-5)/369126264Lelio R Paula05/2014
25302^419328-1859939126231Enzo Doria03/2016
25312^419282-1851507126217Enzo Doria08/2015
25322^419251+1866143126208Enzo Doria03/2016
253311^121185+2126202Robert Price05/2014
2534(23*2^419036-1)/1393126141Lelio R Paula05/2014
25352^418851+23126087Robert Price09/2015
2536(2^418849-9)/2681126083Lelio R Paula05/2014
25372^418829+167126081Lelio R Paula01/2012
2538(31*2^418782-1)/75891126063Lelio R Paula05/2014
2539(19*2^418754-1)/15126058Lelio R Paula05/2014
25402^418319-109501125927Enzo Doria04/2014
25412^418316-112373125926Enzo Doria06/2014
2542(8*10^125894-29)/3125895Robert Price07/2018
2543(26*10^125886-413)/9125887Robert Price05/2018
25442^417968+1869811125821Enzo Doria06/2016
25452^417902+63125802Lelio R Paula09/2015
2546(10^125792-91)/9125792Serge Batalov12/2014
2547(35*10^125754-593)/9125755Robert Price07/2018
2548(32*10^125751-77)/9125752Robert Price06/2018
25492^417704+77011125742Enzo Doria05/2016
2550(10^125706+149)/3125706Serge Batalov12/2014
25512^417419-115309125656Enzo Doria07/2015
25522^417300+77281125620Enzo Doria05/2016
25532^417095-1657125559Yves Minet07/2014
25542^416773-25125462Lelio R Paula09/2015
2555(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2556(11*2^416691+1)/43125436Lelio R Paula05/2014
2557(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
25582^416641-2*416641+1125422Robert Price05/2018
2559(21*2^416566-1)/17125399Lelio R Paula05/2014
25602^416530+1870429125389Enzo Doria05/2016
2561(56*10^125385+691)/9125386Robert Price05/2019
25622^416490+1875109125376Enzo Doria09/2016
25632^416416-114929125354Enzo Doria05/2015
2564(77*10^125330-293)/9125331Robert Price09/2019
2565(172*10^125292-1)/9125294Serge Batalov12/2014
25662^416134+1865899125269Enzo Doria03/2016
2567153^57337-152125264Norbert Schneider12/2018
2568(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2569(23^91943-1)/22125201Robert Price01/2012
257043125^27010-106125185Enzo Doria08/2012
2571(38*10^125166+349)/9125167Robert Price10/2018
25722^415765-112603125158Enzo Doria06/2014
25738*10^125088-13125089Robert Price08/2019
2574(25*10^125076-13)/3125077Robert Price09/2019
2575(29*10^125021-113)/3125022Robert Price10/2019
25762^415290-113591125015Enzo Doria08/2014
25772^415276-460919125011Enzo Doria06/2015
25782^415259+77243125006Enzo Doria05/2016
25792^415144-3683124971Yves Minet10/2011
25802^414874+79124890Lelio R Paula01/2015
2581(2^414765+7)/1389124854Lelio R Paula05/2014
25822^414618+79459124813Enzo Doria06/2016
2583(61*10^124809-1)/3124811Robert Price01/2020
25842^414432-1846709124757Enzo Doria07/2015
25852*10^124751-51124752Robert Price04/2018
2586(56*10^124735+367)/9124736Robert Price06/2019
2587(13*2^414274-1)/153124708Lelio R Paula05/2014
258856*10^124656-3124658Robert Price03/2020
2589(7*10^124648+197)/3124649Robert Price07/2018
25912^414032-5124637Henri Lifchitz07/2006
25902^414032+1872331124637Enzo Doria05/2016
259214120^30009-30009^14120124533Norbert Schneider02/2015
259364^68909-63^68909124463Robert Price07/2013
25942^413387+76253124442Enzo Doria04/2016
25952^413352+524287124432Paul Underwood09/2018
2596287117#+391613124424Nicolas PALAU01/2017
2597(4*10^124420+83)/3124421Robert Price02/2018
2598(27*2^413207-1)/108335124385Lelio R Paula05/2014
2599(41*10^124335-383)/9124336Robert Price11/2018
2600(304*10^124329-43)/9124331Robert Price02/2020
26012^412868-120599124286Paul Bourdelais02/2012
260210^124248-1000001124248Robert Price08/2020
260345^75145-2124231Lelio R Paula08/2015
26042^412645-112213124219Enzo Doria06/2014
26052^412248+74611124100Enzo Doria04/2016
2606(22*10^124096-13)/9124097Robert Price06/2018
26072^412192-3329124083Yves Minet12/2014
2608(25*2^412191-1)/23124082Lelio R Paula05/2014
2609(25*10^124076-67)/3124077Robert Price06/2019
2610F(593689)124074Henri Lifchitz01/2005
2611(11*2^412161+1)/19124073Lelio R Paula05/2014
2612(266*10^124022-11)/3124024Robert Price04/2020
26132^411884-113279123990Enzo Doria07/2014
2614(2^411832+1)/257123972Lelio R Paula05/2014
2615(2^411833+2)/514123972Stefano Morozzi03/2020
2616(26*10^123970-89)/9123971Robert Price06/2018
26172^411790-1853531123962Enzo Doria08/2015
2618(5^177337+1)/6123953Paul Bourdelais11/2008
26192^411711-113257123938Enzo Doria07/2014
2620(23*2^411675-1)/3123928Lelio R Paula05/2014
2621(11*10^123899-179)/3123900Robert Price09/2018
26222^411325-351103123822Enzo Doria06/2015
26232^411052+1872481123739Enzo Doria05/2016
26242^410997+39123723Lelio R Paula05/2014
2625(649^43987-1)/648123700Michael Stocker05/2020
2626(148*10^123688-1)/3123690Robert Price03/2020
26278*10^123657+87123658Robert Price10/2019
2628155^56438+154123618Norbert Schneider01/2019
26292^410596-39123602Lelio R Paula05/2014
26302^410540-115079123585Enzo Doria06/2015
2631(7*10^123563+107)/3123564Robert Price02/2018
26329*10^123549+89123550Robert Price11/2019
2633(3*2^410392-1)/9229123537Lelio R Paula05/2014
26342^410206-113081123485Enzo Doria07/2014
2635(25*2^410192+1)/10397123478Lelio R Paula04/2014
26362^409909-189123395Enzo Doria05/2014
26372^409896-109043123391Enzo Doria04/2014
26382^409890+75409123390Enzo Doria04/2016
2639133^58076-2123345Lelio R Paula10/2017
2640F(590041)123311Henri Lifchitz01/2005
26412^409566-113501123292Enzo Doria08/2014
26422^409533+77747123282Enzo Doria05/2016
26432^409436-112799123253Enzo Doria06/2014
26442^409225+1873787123189Enzo Doria06/2016
26452^409174+73009123174Enzo Doria04/2016
26462^409058-112685123139Enzo Doria06/2014
2647(13*10^123137-61)/3123138Robert Price11/2018
26484*10^123113+21123114Robert Price12/2018
26492^408778+77689123055Enzo Doria05/2016
26502^408690-75123028Lelio R Paula11/2013
2651(29*10^122996+673)/9122997Robert Price12/2018
26522^408574-2787341122994Enzo Doria03/2016
26533*10^122977+37122978Robert Price08/2018
2654Phi(157825,10)122961Maksym Voznyy06/2015
2655(68*10^122933-419)/9122934Robert Price07/2019
2656(13*2^408283+1)/1665122904Lelio R Paula05/2014
2657(266*10^122872-17)/3122874Robert Price07/2020
2658(16*10^122871+77)/3122872Robert Price03/2019
2659(11*2^408100-1)/35122850Lelio R Paula04/2014
2660(19*10^122836-43)/3122837Robert Price05/2019
2661(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2662(32*10^122733-77)/9122734Robert Price06/2018
2663(21*2^407604-1)/215122701Lelio R Paula04/2014
2664(22*10^122681+161)/3122682Robert Price05/2019
2665(21*2^407433-1)/13122650Lelio R Paula04/2014
2666(26*10^122625-131)/3122626Robert Price10/2019
2667(73*10^122592-1)/9122593Robert Price01/2015
2668(5*10^122592+91)/3122593Robert Price04/2018
2669(85*10^122585-1)/3122587Robert Price02/2020
26702^407179-112075122574Enzo Doria06/2014
2671(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2672(66^67349+1)/67122543Paul Bourdelais09/2017
26732^407008-1867919122522Enzo Doria04/2016
267411^117642-300122512Enzo Doria10/2012
2675(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
26762^406949+72197122504Enzo Doria04/2016
2677(19*10^122501+149)/3122502Robert Price05/2019
26782^406826-65122467Lelio R Paula11/2013
26792^406821-2797363122466Enzo Doria04/2016
26802^406758-17122447Lelio R Paula11/2013
2681(30^82883-1)/29122427Robert Price12/2011
2682(2^406583-1)/813167122388Jens K. Andersen02/2009
26834*10^122377+19122378Robert Price10/2018
2684Phi(246362,10)122365Makoto Kamada09/2019
26853*10^122345-97122346Robert Price07/2018
268697^61575-2122336Lelio R Paula12/2014
26872^406298+2799109122308Enzo Doria04/2016
26887*10^122294+57122295Robert Price06/2019
2689(27*2^406241-1)/10277122289Lelio R Paula04/2014
26902^406229-1849993122288Enzo Doria08/2015
26913*10^122274+7122275Robert Price07/2015
26922^406117+1876577122254Enzo Doria07/2016
26933^256199-2^256199122238Mike Oakes06/2005
26942^405992-78557122216Jorge Menendez03/2018
2695(8*10^122203+43)/3122204Robert Price06/2018
2696(58*10^122170+329)/9122171Robert Price05/2019
26972^405774+179149122151Enzo Doria06/2016
269834*10^122082-9122084Robert Price06/2020
26995*10^122082+41122083Robert Price03/2019
27012^405514-3311122072Yves Minet12/2014
27022^405514-115511122072Enzo Doria07/2015
270023*10^122070-7122072Robert Price02/2020
27032^405422-113261122045Enzo Doria07/2014
27042^405173+71237121970Enzo Doria04/2016
2705(2^405016+1)/257121920Lelio R Paula04/2014
27062^404858+71329121875Enzo Doria04/2016
27072^404813-114703121861Enzo Doria04/2015
27082^404764+77791121847Enzo Doria05/2016
2709317^48694+48694^317121787Norbert Schneider08/2015
27102^404536-115259121778Enzo Doria06/2015
27112^404501-631121767Yves Minet07/2012
271263^67620+2121672Lelio R Paula08/2015
2713(16*10^121633+167)/3121634Robert Price06/2019
2714(17*10^121621+1)/9121622Serge Batalov05/2010
2715(15*2^403912+1)/271121589Lelio R Paula05/2014
2716(10^121543-79)/3121543Robert Price01/2018
27172^403676+76831121519Enzo Doria05/2016
2718(7*10^121487+143)/3121488Robert Price03/2018
27192^403363-113635121425Enzo Doria08/2014
27202^403336-1861469121417Enzo Doria03/2016
2721p(24442)#/2-64121381Robert Price04/2017
272211^116555-720121380Enzo Doria11/2012
27232^403100-461267121346Enzo Doria07/2015
27242^403093-112213121344Enzo Doria06/2014
2725(316^48539+1)/317121330Eric Chen10/2017
2726(23*10^121320-71)/3121321Robert Price07/2020
27272^403004+1866361121317Enzo Doria03/2016
27282^402953+89121301Lelio R Paula10/2013
27292^402944-2788319121299Enzo Doria03/2016
2730(44*10^121297-719)/9121298Robert Price12/2018
2731(27*2^402865+1)/5121276Lelio R Paula04/2014
27322^402828-113183121264Enzo Doria07/2014
2733(17*10^121242+1)/9121243Serge Batalov05/2010
2734(15*2^402757+1)/101121242Lelio R Paula05/2014
27352^402715+1874223121230Enzo Doria06/2016
2736(35*10^121229-593)/9121230Robert Price07/2018
2737(91^61879+1)/92121222Paul Bourdelais09/2017
27387*10^121144+9121145Robert Price09/2015
27392^401725-113251120932Enzo Doria07/2014
2740(15*2^401677-1)/19120917Lelio R Paula05/2014
27412^401652+73711120910Enzo Doria04/2016
2742(2^401632+3)/79120902Lelio R Paula04/2014
274310^120841+88417120842Patrick De Geest04/2020
274410^120841-123456789120841Robert Price02/2020
274510^120841-176853120841Patrick De Geest04/2020
27462^401406-2791331120836Enzo Doria03/2016
2747(28^83497+1)/29120832Robert Price07/2013
2748(22*10^120828+161)/3120829Robert Price05/2019
27492^401369+1867367120825Enzo Doria03/2016
2750(10^120782+29)/3120782Serge Batalov12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

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