PRP Records

Probable Primes Top 10000

(280932 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 ?
30012^412868-120599124286Paul Bourdelais02/2012
300210^124248-1000001124248Robert Price08/2020
300345^75145-2124231Lelio R Paula08/2015
300429901^14272+14272^29901124224Hans Havermann03/2021
30052^412645-112213124219Enzo Doria06/2014
300629837^14500+14500^29837124163Hans Havermann03/2021
300728074^26455+26455^28074124158Hans Havermann03/2021
30082^412248+74611124100Enzo Doria04/2016
3009(22*10^124096-13)/9124097Robert Price06/2018
30102^412192-3329124083Yves Minet12/2014
3011(25*2^412191-1)/23124082Lelio R Paula05/2014
3013(25*10^124076-67)/3124077Robert Price06/2019
301228132^25735+25735^28132124077Hans Havermann03/2021
3014F(593689)124074Henri Lifchitz01/2005
3015(11*2^412161+1)/19124073Lelio R Paula05/2014
301635364^3215+3215^35364124028Hans Havermann03/2021
3018(266*10^124022-11)/3124024Robert Price04/2020
301729987^13674+13674^29987124024Hans Havermann03/2021
30192^411884-113279123990Enzo Doria07/2014
3020(2^411832+1)/257123972Lelio R Paula05/2014
3021(2^411833+2)/514123972Stefano Morozzi03/2020
3022(26*10^123970-89)/9123971Robert Price06/2018
30232^411790-1853531123962Enzo Doria08/2015
3024(5^177337+1)/6123953Paul Bourdelais11/2008
30252^411711-113257123938Enzo Doria07/2014
3026(23*2^411675-1)/3123928Lelio R Paula05/2014
302736289^2598+2598^36289123914Hans Havermann03/2021
3028(11*10^123899-179)/3123900Robert Price09/2018
302932276^6879+6879^32276123860Hans Havermann02/2021
30302^411325-351103123822Enzo Doria06/2015
303130738^10643+10643^30738123784Hans Havermann03/2021
303231074^9607+9607^31074123755Hans Havermann03/2021
30332^411052+1872481123739Enzo Doria05/2016
303434365^3986+3986^34365123733Hans Havermann03/2021
30352^410997+39123723Lelio R Paula05/2014
3036(649^43987-1)/648123700Michael Stocker05/2020
3037(148*10^123688-1)/3123690Robert Price03/2020
303836825^2284+2284^36825123684Hans Havermann03/2021
303929582^15171+15171^29582123683Hans Havermann03/2021
30408*10^123657+87123658Robert Price10/2019
304130505^11302+11302^30505123642Hans Havermann03/2021
304229956^13401+13401^29956123633Hans Havermann03/2021
3043155^56438+154123618Norbert Schneider01/2019
30442^410596-39123602Lelio R Paula05/2014
304528995^18302+18302^28995123592Hans Havermann03/2021
304628302^23269+23269^28302123589Hans Havermann03/2021
30472^410540-115079123585Enzo Doria06/2015
3048(7*10^123563+107)/3123564Robert Price02/2018
30499*10^123549+89123550Robert Price11/2019
3050(197*10^123545+7)/3123547Robert Price12/2020
3051(3*2^410392-1)/9229123537Lelio R Paula05/2014
305228118^24687+24687^28118123508Hans Havermann03/2021
305339994^1225+1225^39994123507Hans Havermann03/2021
30542^410206-113081123485Enzo Doria07/2014
3055(25*2^410192+1)/10397123478Lelio R Paula04/2014
305628974^18215+18215^28974123442Hans Havermann03/2021
305728901^18618+18618^28901123406Hans Havermann03/2021
30582^409909-189123395Enzo Doria05/2014
30592^409896-109043123391Enzo Doria04/2014
30602^409890+75409123390Enzo Doria04/2016
306181254^33+33^81254123386Hans Havermann03/2021
306233463^4854+4854^33463123348Hans Havermann03/2021
306334061^4182+4182^34061123348Hans Havermann03/2021
3064133^58076-2123345Lelio R Paula10/2017
3065F(590041)123311Henri Lifchitz01/2005
30662^409566-113501123292Enzo Doria08/2014
30672^409533+77747123282Enzo Doria05/2016
30682^409436-112799123253Enzo Doria06/2014
306928212^23321+23321^28212123223Hans Havermann03/2021
30702^409225+1873787123189Enzo Doria06/2016
30712^409174+73009123174Enzo Doria04/2016
30722^409058-112685123139Enzo Doria06/2014
3073(13*10^123137-61)/3123138Robert Price11/2018
30744*10^123113+21123114Robert Price12/2018
30752^408778+77689123055Enzo Doria05/2016
30762^408690-75123028Lelio R Paula11/2013
307728327^22032+22032^28327123026Hans Havermann03/2021
3078(29*10^122996+673)/9122997Robert Price12/2018
30792^408574-2787341122994Enzo Doria03/2016
30803*10^122977+37122978Robert Price08/2018
3081Phi(157825,10)122961Maksym Voznyy06/2015
3082(68*10^122933-419)/9122934Robert Price07/2019
308329712^13721+13721^29712122931Hans Havermann03/2021
3084(13*2^408283+1)/1665122904Lelio R Paula05/2014
3085(266*10^122872-17)/3122874Robert Price07/2020
3086(16*10^122871+77)/3122872Robert Price03/2019
308730395^11022+11022^30395122865Hans Havermann03/2021
308833331^4852+4852^33331122856Hans Havermann03/2021
3089(11*2^408100-1)/35122850Lelio R Paula04/2014
3090(19*10^122836-43)/3122837Robert Price05/2019
309128420^20969+20969^28420122820Hans Havermann03/2021
309229865^12934+12934^29865122797Hans Havermann03/2021
3093(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
3094(32*10^122733-77)/9122734Robert Price06/2018
3095(21*2^407604-1)/215122701Lelio R Paula04/2014
3097(22*10^122681+161)/3122682Robert Price05/2019
309629513^14350+14350^29513122682Hans Havermann03/2021
3098(21*2^407433-1)/13122650Lelio R Paula04/2014
3099(26*10^122625-131)/3122626Robert Price10/2019
310027925^24562+24562^27925122599Hans Havermann03/2021
3101(73*10^122592-1)/9122593Robert Price01/2015
3102(5*10^122592+91)/3122593Robert Price04/2018
310336751^2166+2166^36751122589Hans Havermann03/2021
3104(85*10^122585-1)/3122587Robert Price02/2020
310529368^14931+14931^29368122585Hans Havermann03/2021
31062^407179-112075122574Enzo Doria06/2014
3107(21*2^407131+1)/207517523122552Lelio R Paula04/2014
3108(66^67349+1)/67122543Paul Bourdelais09/2017
31092^407008-1867919122522Enzo Doria04/2016
311011^117642-300122512Enzo Doria10/2012
3111(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
31122^406949+72197122504Enzo Doria04/2016
3113(19*10^122501+149)/3122502Robert Price05/2019
311428632^18977+18977^28632122495Hans Havermann03/2021
311531815^7076+7076^31815122481Hans Havermann03/2021
31162^406826-65122467Lelio R Paula11/2013
31172^406821-2797363122466Enzo Doria04/2016
31182^406758-17122447Lelio R Paula11/2013
311929941^12282+12282^29941122437Hans Havermann03/2021
3120(30^82883-1)/29122427Robert Price12/2011
312127496^27577+27577^27496122422Norbert Schneider12/2020
312228732^18215+18215^28732122411Hans Havermann03/2021
3123(2^406583-1)/813167122388Jens K. Andersen02/2009
31244*10^122377+19122378Robert Price10/2018
312528227^21634+21634^28227122368Hans Havermann03/2021
3126Phi(246362,10)122365Makoto Kamada09/2019
31273*10^122345-97122346Robert Price07/2018
312897^61575-2122336Lelio R Paula12/2014
3129208^52765+52765^208122313Norbert Schneider11/2020
31302^406298+2799109122308Enzo Doria04/2016
31317*10^122294+57122295Robert Price06/2019
3132(27*2^406241-1)/10277122289Lelio R Paula04/2014
31332^406229-1849993122288Enzo Doria08/2015
31343*10^122274+7122275Robert Price07/2015
31352^406117+1876577122254Enzo Doria07/2016
313629308^14835+14835^29308122253Hans Havermann03/2021
313728119^22268+22268^28119122253Hans Havermann03/2021
313832167^6312+6312^32167122240Hans Havermann03/2021
31393^256199-2^256199122238Mike Oakes06/2005
314027678^26053+26053^27678122223Hans Havermann03/2021
31412^405992-78557122216Jorge Menendez03/2018
3142(8*10^122203+43)/3122204Robert Price06/2018
3143(58*10^122170+329)/9122171Robert Price05/2019
31442^405774+179149122151Enzo Doria06/2016
314529189^15246+15246^29189122103Hans Havermann03/2021
314734*10^122082-9122084Robert Price06/2020
314633442^4473+4473^33442122084Hans Havermann03/2021
31485*10^122082+41122083Robert Price03/2019
314931849^6808+6808^31849122078Hans Havermann03/2021
31502^405514-3311122072Yves Minet12/2014
31512^405514-115511122072Enzo Doria07/2015
315223*10^122070-7122072Robert Price02/2020
31532^405422-113261122045Enzo Doria07/2014
31542^405173+71237121970Enzo Doria04/2016
3155(2^405016+1)/257121920Lelio R Paula04/2014
315628557^18590+18590^28557121918Hans Havermann03/2021
315728641^18002+18002^28641121877Hans Havermann03/2021
31582^404858+71329121875Enzo Doria04/2016
31592^404813-114703121861Enzo Doria04/2015
31602^404764+77791121847Enzo Doria05/2016
316128830^16841+16841^28830121847Hans Havermann03/2021
3162317^48694+48694^317121787Norbert Schneider08/2015
31632^404536-115259121778Enzo Doria06/2015
31642^404501-631121767Yves Minet07/2012
31655*10^121764-69121765Robert Price02/2021
316628236^20485+20485^28236121738Hans Havermann02/2021
316763^67620+2121672Lelio R Paula08/2015
3168(16*10^121633+167)/3121634Robert Price06/2019
316929955^11494+11494^29955121632Hans Havermann02/2021
3170(17*10^121621+1)/9121622Serge Batalov05/2010
317131088^8163+8163^31088121612Hans Havermann02/2021
3172(15*2^403912+1)/271121589Lelio R Paula05/2014
3173(10^121543-79)/3121543Robert Price01/2018
31742^403676+76831121519Enzo Doria05/2016
3175(7*10^121487+143)/3121488Robert Price03/2018
317627965^22086+22086^27965121484Hans Havermann02/2021
31772^403363-113635121425Enzo Doria08/2014
31782^403336-1861469121417Enzo Doria03/2016
317927929^22186+22186^27929121382Hans Havermann02/2021
3180p(24442)#/2-64121381Robert Price04/2017
318111^116555-720121380Enzo Doria11/2012
31822^403100-461267121346Enzo Doria07/2015
31832^403093-112213121344Enzo Doria06/2014
318429404^13385+13385^29404121340Hans Havermann02/2021
318528106^20745+20745^28106121332Hans Havermann02/2021
3186(316^48539+1)/317121330Eric Chen10/2017
3187(23*10^121320-71)/3121321Robert Price07/2020
31882^403004+1866361121317Enzo Doria03/2016
31892^402953+89121301Lelio R Paula10/2013
31902^402944-2788319121299Enzo Doria03/2016
3191(44*10^121297-719)/9121298Robert Price12/2018
3192(27*2^402865+1)/5121276Lelio R Paula04/2014
31932^402828-113183121264Enzo Doria07/2014
3194(17*10^121242+1)/9121243Serge Batalov05/2010
3195(15*2^402757+1)/101121242Lelio R Paula05/2014
31972^402715+1874223121230Enzo Doria06/2016
3196(35*10^121229-593)/9121230Robert Price07/2018
3198(91^61879+1)/92121222Paul Bourdelais09/2017
319928719^16568+16568^28719121174Hans Havermann02/2021
32007*10^121144+9121145Robert Price09/2015
320127490^25467+25467^27490121121Hans Havermann02/2021
320234575^3182+3182^34575121106Hans Havermann02/2021
320329954^10935+10935^29954120979Hans Havermann02/2021
320433585^3992+3992^33585120946Hans Havermann02/2021
320540296^1003+1003^40296120941Hans Havermann02/2021
32062^401725-113251120932Enzo Doria07/2014
3207(15*2^401677-1)/19120917Lelio R Paula05/2014
32082^401652+73711120910Enzo Doria04/2016
3209(2^401632+3)/79120902Lelio R Paula04/2014
321040450^973+973^40450120870Hans Havermann01/2021
321110^120841+88417120842Patrick De Geest04/2020
321210^120841-123456789120841Robert Price02/2020
321310^120841-176853120841Patrick De Geest04/2020
32142^401406-2791331120836Enzo Doria03/2016
3215(28^83497+1)/29120832Robert Price07/2013
3216(22*10^120828+161)/3120829Robert Price05/2019
32172^401369+1867367120825Enzo Doria03/2016
3218(10^120782+29)/3120782Serge Batalov12/2014
32192^401215-1657120778Yves Minet07/2014
32202^401159+53120761Lelio R Paula10/2013
322127782^22179+22179^27782120739Hans Havermann01/2021
322232974^4585+4585^32974120730Hans Havermann02/2021
32232^401031-113047120723Enzo Doria07/2014
322430598^8813+8813^30598120713Hans Havermann02/2021
3225(71*10^120703-287)/9120704Robert Price09/2019
3226(29*2^400909-1)/303120685Lelio R Paula04/2014
322734793^2940+2940^34793120675Hans Havermann02/2021
3228(2^400846+538)/2120667Stefano Morozzi09/2020
3229(166*10^120654+11)/3120656Robert Price03/2021
323034066^3481+3481^34066120652Hans Havermann02/2021
3231(2^400709+3546)/2120626Stefano Morozzi09/2020
3232(2^400700+3126)/2120623Stefano Morozzi09/2020
3233(2^400693+2634)/2120621Stefano Morozzi09/2020
32342^400571-15120584Lelio R Paula10/2013
3235(10^120574+359)/9120574Serge Batalov12/2014
323627431^24810+24810^27431120550Hans Havermann02/2021
32372^400424-216413120540Enzo Doria04/2013
323829090^13911+13911^29090120531Hans Havermann02/2021
3239(2^400346+1722)/2120516Stefano Morozzi09/2020
324027899^20868+20868^27899120510Hans Havermann02/2021
324133740^3729+3729^33740120506Hans Havermann02/2021
3242(17*2^400200-1)/587120471Lelio R Paula05/2014
32432^400166+1874899120462Enzo Doria06/2016
3244(2^400165+1602)/2120462Stefano Morozzi09/2020
324537078^1771+1771^37078120438Hans Havermann02/2021
3246(2^400084+1638)/2120437Stefano Morozzi09/2020
3247(3*2^400045-1)/865120424Lelio R Paula04/2014
3248(2^399974+2790)/2120404Stefano Morozzi02/2021
32492^399966+73759120402Enzo Doria04/2016
3250(2^399961+2306)/2120400Stefano Morozzi02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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