PRP Records

Probable Primes Top 10000

(288515 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 ?
325110^127821-700001127821Robert Price08/2021
32522^424577-113755127811Enzo Doria09/2014
3253(7*2^424512-1)/3127792Lelio R Paula05/2014
3254(56*10^127752+691)/9127753Robert Price05/2019
325511^122629-720127705Enzo Doria11/2012
325622*10^127645+3127647Robert Price01/2020
325728715^27844+27844^28715127631Hans Havermann03/2021
3258(56*10^127612+187)/9127613Robert Price10/2021
3259(5*36^81995+821)/7127609Eric Chen01/2021
32604*10^127562-39127563Robert Price09/2020
326132595^8186+8186^32595127547Hans Havermann03/2021
32622^423696-21429127546Enzo Doria07/2013
32632^423664-1864559127536Enzo Doria03/2016
326437889^2322+2322^37889127530Hans Havermann03/2021
326537668^2429+2429^37668127523Hans Havermann03/2021
32663^267267-4127519Henri Lifchitz10/2014
3267(103*10^127491+17)/3127493Robert Price08/2020
326829376^21869+21869^29376127487Hans Havermann03/2021
326931186^12241+12241^31186127483Hans Havermann02/2021
3270(19^99689+5^99689)/24127477Robert Price09/2013
3271(21*2^423372+1)/101127447Lelio R Paula05/2014
327230594^14645+14645^30594127446Hans Havermann03/2021
32732^423328-21537127435Enzo Doria07/2013
3274(67*10^127413-7)/3127415Robert Price01/2020
3275(2*10^127407+73)/3127407Robert Price09/2020
3276(2^423165-7)/25127384Lelio R Paula05/2015
3277(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
327829512^20647+20647^29512127341Hans Havermann03/2021
3279(112*10^127324+17)/3127326Robert Price03/2020
328029565^20252+20252^29565127321Hans Havermann03/2021
3281(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
3282(16*10^127259+197)/3127260Robert Price04/2019
3283(26*10^127240+61)/3127241Robert Price10/2019
3284(234483*27^88884-145)/26127230Curtis Bright05/2015
32852^422515-114997127190Enzo Doria06/2015
32865*10^127179-3127180Robert Price07/2015
328731678^10343+10343^31678127176Hans Havermann03/2021
3288(44*10^127169-233)/9127170Robert Price01/2019
328934947^4352+4352^34947127162Hans Havermann03/2021
32906*10^127158+19127159Robert Price11/2021
329130469^14902+14902^30469127155Hans Havermann03/2021
32925*10^127153+77127154Robert Price12/2018
329329941^17620+17620^29941127130Hans Havermann02/2021
329431607^10516+10516^31607127119Hans Havermann03/2021
3295(19*10^127118-97)/3127119Robert Price10/2021
3296(29*10^127111+691)/9127112Robert Price08/2021
3297736^44335+44335^736127104Norbert Schneider07/2019
329833040^7023+7023^33040127090Hans Havermann03/2021
329929748^18661+18661^29748127052Hans Havermann03/2021
3300-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
3301(78^67141-1)/77127036Paul Bourdelais09/2017
3302(14*10^127014-137)/3127015Robert Price04/2021
330331436^10965+10965^31436127002Hans Havermann03/2021
330428905^24758+24758^28905127001Hans Havermann03/2021
33052^421860-113285126993Enzo Doria07/2014
3306(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
3307(2^421827-7)/11126982Lelio R Paula05/2015
330811^121910-840126957Enzo Doria12/2012
3309(56*10^126935+187)/9126936Robert Price10/2021
331028915^24538+24538^28915126933Hans Havermann03/2021
3311(29*10^126928-77)/3126929Robert Price02/2020
3312(259*10^126919-1)/3126921Robert Price12/2020
331310^126919+204567126920Patrick De Geest05/2021
331410^126919-100001126919Robert Price07/2020
331528340^28503+28503^28340126907Norbert Schneider02/2021
3316(71^68539+1)/72126882Paul Bourdelais09/2017
3317(5*10^126871-119)/3126872Robert Price03/2018
3318331^50339-10004126846Enzo Doria07/2012
33192^421363-2790757126843Enzo Doria03/2016
3320(106*10^126839-1)/3126841Serge Batalov12/2014
332137938^2203+2203^37938126828Hans Havermann03/2021
3322(7*2^421243+1)/39126807Lelio R Paula05/2014
3323(14*10^126784-83)/3126785Robert Price12/2018
33242^421161-286183126783Enzo Doria06/2015
3325(106*10^126726+17)/3126728Robert Price04/2021
332630718^13347+13347^30718126724Hans Havermann03/2021
33272^420939-113935126716Enzo Doria10/2014
3328177^56363-2126703Lelio R Paula10/2017
33292^420741-113659126656Enzo Doria08/2014
33302^420694-21126642Lelio R Paula05/2017
3331(13*10^126638+437)/9126639Robert Price04/2018
3332(167*10^126637-17)/3126639Robert Price03/2020
33334*10^126625+87126626Robert Price08/2018
3334(31*2^420556+1)/7126601Lelio R Paula05/2014
33357*10^126600-99126601Robert Price06/2019
33362^420424-59189126561Enzo Doria10/2015
333728717^25534+25534^28717126560Hans Havermann03/2021
333828922^23655+23655^28922126503Hans Havermann03/2021
33392^420126+71893126471Enzo Doria04/2016
3340(43*10^126441+47)/9126442Robert Price12/2018
33412^419866+1877059126393Enzo Doria07/2016
334229315^20484+20484^29315126390Hans Havermann03/2021
334329433^19676+19676^29433126384Hans Havermann03/2021
3344F(604711)126377Henri Lifchitz02/2005
33452^419757+72707126360Enzo Doria04/2016
33462^419720-21569126349Enzo Doria07/2013
33472^419637+29126324Henri Lifchitz02/2006
334831004^11865+11865^31004126319Hans Havermann03/2021
33492^419612+1876741126316Enzo Doria07/2016
33502^419520+2793271126289Enzo Doria03/2016
3351(2^419447-5)/369126264Lelio R Paula05/2014
33522^419328-1859939126231Enzo Doria03/2016
33532^419282-1851507126217Enzo Doria08/2015
3354(133*10^126212+17)/3126214Robert Price11/2021
33552^419251+1866143126208Enzo Doria03/2016
335611^121185+2126202Robert Price05/2014
335728203^28352+28352^28203126175Norbert Schneider01/2021
3358(23*2^419036-1)/1393126141Lelio R Paula05/2014
33592^418851+23126087Robert Price09/2015
3360(2^418849-9)/2681126083Lelio R Paula05/2014
33612^418829+167126081Lelio R Paula01/2012
336231037^11530+11530^31037126067Hans Havermann03/2021
3363(31*2^418782-1)/75891126063Lelio R Paula05/2014
3364(19*2^418754-1)/15126058Lelio R Paula05/2014
3365(35*10^126048-323)/9126049Robert Price10/2021
336633016^6551+6551^33016126000Hans Havermann03/2021
33672^418548-111546435125996Paul Bourdelais10/2021
336834736^4227+4227^34736125954Hans Havermann03/2021
33692^418319-109501125927Enzo Doria04/2014
33702^418316-112373125926Enzo Doria06/2014
337140398^1309+1309^40398125919Hans Havermann03/2021
3372(8*10^125894-29)/3125895Robert Price07/2018
3373(26*10^125886-413)/9125887Robert Price05/2018
33742^417968+1869811125821Enzo Doria06/2016
33752^417902+63125802Lelio R Paula09/2015
3376(10^125792-91)/9125792Serge Batalov12/2014
337730438^13573+13573^30438125791Hans Havermann03/2021
337832867^6714+6714^32867125782Hans Havermann03/2021
337931155^10892+10892^31155125777Hans Havermann03/2021
3380(35*10^125754-593)/9125755Robert Price07/2018
338130455^13464+13464^30455125754Hans Havermann03/2021
3382(32*10^125751-77)/9125752Robert Price06/2018
33832^417704+77011125742Enzo Doria05/2016
338429755^16816+16816^29755125737Hans Havermann03/2021
3385(22*10^125734+203)/9125735Robert Price10/2021
338629918^15915+15915^29918125710Hans Havermann03/2021
3387(10^125706+149)/3125706Serge Batalov12/2014
338828531^25368+25368^28531125659Hans Havermann03/2021
33892^417419-115309125656Enzo Doria07/2015
33902^417300+77281125620Enzo Doria05/2016
339130638^12537+12537^30638125561Hans Havermann03/2021
33922^417095-1657125559Yves Minet07/2014
339330162^14525+14525^30162125538Hans Havermann03/2021
3394(56*10^125535+583)/9125536Robert Price08/2021
3395(88*10^125492-637)/9125493Robert Price11/2020
339628958^21525+21525^28958125474Hans Havermann02/2021
33982^416773-25125462Lelio R Paula09/2015
3397(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
339933889^5032+5032^33889125449Hans Havermann03/2021
3400(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
3401(11*2^416691+1)/43125436Lelio R Paula05/2014
3402(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
34032^416641-2*416641+1125422Robert Price05/2018
340433392^5697+5697^33392125409Hans Havermann03/2021
3405(21*2^416566-1)/17125399Lelio R Paula05/2014
34062^416530+1870429125389Enzo Doria05/2016
3407(56*10^125385+691)/9125386Robert Price05/2019
340827953^28198+28198^27953125381Norbert Schneider01/2021
340931074^10837+10837^31074125381Hans Havermann03/2021
341033745^5194+5194^33745125380Hans Havermann03/2021
34112^416490+1875109125376Enzo Doria09/2016
341228360^26331+26331^28360125365Hans Havermann03/2021
34132^416416-114929125354Enzo Doria05/2015
3414(77*10^125330-293)/9125331Robert Price09/2019
3415(172*10^125292-1)/9125294Serge Batalov12/2014
34162^416134+1865899125269Enzo Doria03/2016
3417153^57337-152125264Norbert Schneider12/2018
3418(9*2^415992+1)/13560845125220Lelio R Paula05/2014
341930054^14657+14657^30054125207Hans Havermann03/2021
3420(23^91943-1)/22125201Robert Price01/2012
34212^415884-933075125194Paul Bourdelais06/2021
342243125^27010-106125185Enzo Doria08/2012
3423(38*10^125166+349)/9125167Robert Price10/2018
34242^415765-112603125158Enzo Doria06/2014
34258*10^125088-13125089Robert Price08/2019
3426(25*10^125076-13)/3125077Robert Price09/2019
3427(11*10^125054+73)/3125055Robert Price08/2021
3428(29*10^125021-113)/3125022Robert Price10/2019
34292^415290-113591125015Enzo Doria08/2014
34302^415276-460919125011Enzo Doria06/2015
34312^415259+77243125006Enzo Doria05/2016
3432(67*10^124990+77)/9124991Robert Price10/2021
34332^415144-3683124971Yves Minet10/2011
34342^415092+111546435124956Paul Bourdelais10/2021
343531936^8173+8173^31936124946Hans Havermann03/2021
34365^178715-4124916Tyler NeSmith07/2021
343729767^15700+15700^29767124900Hans Havermann03/2021
34382^414874+79124890Lelio R Paula01/2015
3439(2^414765+7)/1389124854Lelio R Paula05/2014
34402^414618+79459124813Enzo Doria06/2016
3441(61*10^124809-1)/3124811Robert Price01/2020
3442(29*10^124765-71)/3124766Robert Price07/2021
34432^414432-1846709124757Enzo Doria07/2015
34442*10^124751-51124752Robert Price04/2018
3445(56*10^124735+367)/9124736Robert Price06/2019
3446(13*2^414274-1)/153124708Lelio R Paula05/2014
344756*10^124656-3124658Robert Price03/2020
3448(7*10^124648+197)/3124649Robert Price07/2018
34502^414032-5124637Henri Lifchitz07/2006
34492^414032+1872331124637Enzo Doria05/2016
345137373^2158+2158^37373124604Hans Havermann03/2021
345229811^15112+15112^29811124590Hans Havermann03/2021
345314120^30009-30009^14120124533Norbert Schneider02/2015
345429757^15296+15296^29757124521Hans Havermann03/2021
345535056^3561+3561^35056124504Hans Havermann03/2021
345640588^1167+1167^40588124487Hans Havermann02/2021
3457(85*10^124485-49)/9124486Robert Price12/2020
345864^68909-63^68909124463Robert Price07/2013
345935016^3581+3581^35016124448Hans Havermann03/2021
34602^413387+76253124442Enzo Doria04/2016
346128749^21298+21298^28749124436Hans Havermann03/2021
34622^413352+524287124432Paul Underwood09/2018
3463287117#+391613124424Nicolas PALAU01/2017
3464(4*10^124420+83)/3124421Robert Price02/2018
346534578^3965+3965^34578124421Hans Havermann03/2021
3466(68*10^124392-329)/9124393Robert Price03/2021
3467(27*2^413207-1)/108335124385Lelio R Paula05/2014
346810^124383+58407124384Patrick De Geest08/2021
347010^124383-8000001124383Robert Price04/2021
346910^124383-5801124383Patrick De Geest08/2021
3471(41*10^124335-383)/9124336Robert Price11/2018
3472(304*10^124329-43)/9124331Robert Price02/2020
347334716^3811+3811^34716124320Hans Havermann03/2021
34742^412868-120599124286Paul Bourdelais02/2012
347510^124248+899089124249Patrick De Geest05/2021
347710^124248-1000001124248Robert Price08/2020
347610^124248-501903124248Patrick De Geest05/2021
347845^75145-2124231Lelio R Paula08/2015
347929901^14272+14272^29901124224Hans Havermann03/2021
34802^412645-112213124219Enzo Doria06/2014
348129837^14500+14500^29837124163Hans Havermann03/2021
348228074^26455+26455^28074124158Hans Havermann03/2021
34832^412248+74611124100Enzo Doria04/2016
3484(22*10^124096-13)/9124097Robert Price06/2018
3485(455*10^124093+31)/9124095Robert Price06/2021
34862^412192-3329124083Yves Minet12/2014
3487(25*2^412191-1)/23124082Lelio R Paula05/2014
3489(25*10^124076-67)/3124077Robert Price06/2019
348828132^25735+25735^28132124077Hans Havermann03/2021
3490F(593689)124074Henri Lifchitz01/2005
3491(11*2^412161+1)/19124073Lelio R Paula05/2014
349235364^3215+3215^35364124028Hans Havermann03/2021
3494(266*10^124022-11)/3124024Robert Price04/2020
349329987^13674+13674^29987124024Hans Havermann03/2021
34952^411932-111546435124004Paul Bourdelais10/2021
34962^411884-113279123990Enzo Doria07/2014
3497(2^411832+1)/257123972Lelio R Paula05/2014
3498(2^411833+2)/514123972Stefano Morozzi03/2020
3499(26*10^123970-89)/9123971Robert Price06/2018
35002^411790-1853531123962Enzo Doria08/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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