PRP Records

Probable Primes Top 10000

(301723 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
55012^422515-114997127190Enzo Doria06/2015
55025*10^127179-3127180Robert Price07/2015
550331678^10343+10343^31678127176Hans Havermann03/2021
5504(44*10^127169-233)/9127170Robert Price01/2019
550534947^4352+4352^34947127162Hans Havermann03/2021
55066*10^127158+19127159Robert Price11/2021
550730469^14902+14902^30469127155Hans Havermann03/2021
55085*10^127153+77127154Robert Price12/2018
550929941^17620+17620^29941127130Hans Havermann02/2021
551031607^10516+10516^31607127119Hans Havermann03/2021
5511(19*10^127118-97)/3127119Robert Price10/2021
5512(29*10^127111+691)/9127112Robert Price08/2021
5513736^44335+44335^736127104Norbert Schneider07/2019
551433040^7023+7023^33040127090Hans Havermann03/2021
5515(4*10^127081+167)/9127081Robert Price03/2022
551629748^18661+18661^29748127052Hans Havermann03/2021
551727905^28578-28578^27905127049Frank Doornink03/2024
5518-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
5519(78^67141-1)/77127036Paul Bourdelais09/2017
5520(14*10^127014-137)/3127015Robert Price04/2021
552131436^10965+10965^31436127002Hans Havermann03/2021
552228905^24758+24758^28905127001Hans Havermann03/2021
55232^421860-113285126993Enzo Doria07/2014
5524(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
5525(2^421827-7)/11126982Lelio R Paula05/2015
552626268^28729-28729^26268126966Frank Doornink03/2024
552711^121910-840126957Enzo Doria12/2012
5528(56*10^126935+187)/9126936Robert Price10/2021
552928915^24538+24538^28915126933Hans Havermann03/2021
5530(29*10^126928-77)/3126929Robert Price02/2020
5531(259*10^126919-1)/3126921Robert Price12/2020
553210^126919+204567126920Patrick De Geest05/2021
5533(2^421617+100280245065)126920Paul Bourdelais05/2022
553410^126919-100001126919Robert Price07/2020
553528340^28503+28503^28340126907Norbert Schneider02/2021
55362^421534-3001935126895Paul Bourdelais07/2023
5537(71^68539+1)/72126882Paul Bourdelais09/2017
5538(5*10^126871-119)/3126872Robert Price03/2018
5539331^50339-10004126846Enzo Doria07/2012
55402^421363-2790757126843Enzo Doria03/2016
5541(106*10^126839-1)/3126841Serge Batalov12/2014
554237938^2203+2203^37938126828Hans Havermann03/2021
5543(13*10^126819+77)/9126820Robert Price07/2022
5544(7*2^421243+1)/39126807Lelio R Paula05/2014
5546(14*10^126784-83)/3126785Robert Price12/2018
55452^421169-3001935126785Paul Bourdelais07/2023
55472^421161-286183126783Enzo Doria06/2015
554826733^28628-28628^26733126738Frank Doornink03/2024
5549(106*10^126726+17)/3126728Robert Price04/2021
555030718^13347+13347^30718126724Hans Havermann03/2021
55512^420939-113935126716Enzo Doria10/2014
555211*23^93048+356126708Eric Chen08/2023
5553177^56363-2126703Lelio R Paula10/2017
55542^420741-113659126656Enzo Doria08/2014
55552^420694-21126642Lelio R Paula05/2017
5556(13*10^126638+437)/9126639Robert Price04/2018
5557(167*10^126637-17)/3126639Robert Price03/2020
55584*10^126625+87126626Robert Price08/2018
5559(31*2^420556+1)/7126601Lelio R Paula05/2014
55607*10^126600-99126601Robert Price06/2019
5561U(655247)/250330563881/206066063082749126596Serge Batalov07/2024
55622^420424-59189126561Enzo Doria10/2015
556328717^25534+25534^28717126560Hans Havermann03/2021
5564(86*10^126542+103)/9126543Robert Price12/2021
5565(19*10^126517-7)/3126518Robert Price12/2023
556628922^23655+23655^28922126503Hans Havermann03/2021
55672^420126+71893126471Enzo Doria04/2016
556825982^28643-28643^25982126450Frank Doornink03/2024
5569(43*10^126441+47)/9126442Robert Price12/2018
55708*10^126408+71126409Robert Price05/2022
55712^419866+1877059126393Enzo Doria07/2016
557229315^20484+20484^29315126390Hans Havermann03/2021
557329433^19676+19676^29433126384Hans Havermann03/2021
5574F(604711)126377Henri Lifchitz02/2005
55752^419757+72707126360Enzo Doria04/2016
55762^419720-21569126349Enzo Doria07/2013
55772^419637+29126324Henri Lifchitz02/2006
557831004^11865+11865^31004126319Hans Havermann03/2021
55792^419612+1876741126316Enzo Doria07/2016
55802^419520+2793271126289Enzo Doria03/2016
5581(2^419447-5)/369126264Lelio R Paula05/2014
55822^419328-1859939126231Enzo Doria03/2016
55832^419282-1851507126217Enzo Doria08/2015
5584(133*10^126212+17)/3126214Robert Price11/2021
55852^419251+1866143126208Enzo Doria03/2016
558611^121185+2126202Robert Price05/2014
558728203^28352+28352^28203126175Norbert Schneider01/2021
5588(23*2^419036-1)/1393126141Lelio R Paula05/2014
55892^418851+23126087Robert Price09/2015
5590(2^418849-9)/2681126083Lelio R Paula05/2014
55912^418829+167126081Lelio R Paula01/2012
559231037^11530+11530^31037126067Hans Havermann03/2021
55934*10^126064-69126065Robert Price01/2022
5594(31*2^418782-1)/75891126063Lelio R Paula05/2014
5595(19*2^418754-1)/15126058Lelio R Paula05/2014
5596(35*10^126048-323)/9126049Robert Price10/2021
559733016^6551+6551^33016126000Hans Havermann03/2021
55982^418548-111546435125996Paul Bourdelais10/2021
559925134^28625-28625^25134125958Frank Doornink12/2023
560034736^4227+4227^34736125954Hans Havermann03/2021
5601(23*35^81566-144013)/34125944Eric Chen05/2025
560226197^28502-28502^26197125930Frank Doornink03/2024
56032^418319-109501125927Enzo Doria04/2014
56042^418316-112373125926Enzo Doria06/2014
560540398^1309+1309^40398125919Hans Havermann03/2021
5606(8*10^125894-29)/3125895Robert Price07/2018
5607(26*10^125886-413)/9125887Robert Price05/2018
560810^(2*62938+1)-7*10^62938-1125877Robert Price07/2023
560955*10^125847+9125849Robert Price03/2022
56104*10^125832+57125833Robert Price05/2022
56112^417968+1869811125821Enzo Doria06/2016
56122^417902+63125802Lelio R Paula09/2015
5613(10^125792-91)/9125792Serge Batalov12/2014
561430438^13573+13573^30438125791Hans Havermann03/2021
561532867^6714+6714^32867125782Hans Havermann03/2021
561631155^10892+10892^31155125777Hans Havermann03/2021
5617(35*10^125754-593)/9125755Robert Price07/2018
561830455^13464+13464^30455125754Hans Havermann03/2021
5619(32*10^125751-77)/9125752Robert Price06/2018
56202^417704+77011125742Enzo Doria05/2016
562129755^16816+16816^29755125737Hans Havermann03/2021
5622(22*10^125734+203)/9125735Robert Price10/2021
562329918^15915+15915^29918125710Hans Havermann03/2021
5624(10^125706+149)/3125706Serge Batalov12/2014
562528531^25368+25368^28531125659Hans Havermann03/2021
56262^417419-115309125656Enzo Doria07/2015
5627(46*10^125642+593)/9125643Robert Price04/2022
56282^417315+213953125625Enzo Doria10/2023
56292^417300+77281125620Enzo Doria05/2016
563030638^12537+12537^30638125561Hans Havermann03/2021
56312^417095-1657125559Yves Minet07/2014
563230162^14525+14525^30162125538Hans Havermann03/2021
5633(56*10^125535+583)/9125536Robert Price08/2021
5634(23*10^125517-179)/3125518Robert Price06/2022
56359*10^125516+29125517Robert Price03/2022
5636404*35^81280+23125505Eric Chen05/2025
5637(88*10^125492-637)/9125493Robert Price11/2020
563828958^21525+21525^28958125474Hans Havermann02/2021
56412^416773-25125462Lelio R Paula09/2015
5639(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
564026078^28409-28409^26078125462Frank Doornink03/2024
564233889^5032+5032^33889125449Hans Havermann03/2021
5643(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
5644(2861^36481+1)/(2861^191+1)125438Martin Hopf12/2023
5645(11*2^416691+1)/43125436Lelio R Paula05/2014
5646(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
56472^416641-2*416641+1125422Robert Price05/2018
564833392^5697+5697^33392125409Hans Havermann03/2021
5649(21*2^416566-1)/17125399Lelio R Paula05/2014
56502^416530+1870429125389Enzo Doria05/2016
5651(56*10^125385+691)/9125386Robert Price05/2019
565227953^28198+28198^27953125381Norbert Schneider01/2021
565331074^10837+10837^31074125381Hans Havermann03/2021
565433745^5194+5194^33745125380Hans Havermann03/2021
56552^416490+1875109125376Enzo Doria09/2016
565628360^26331+26331^28360125365Hans Havermann03/2021
56572^416416-114929125354Enzo Doria05/2015
565825805^28412-28412^25805125346Frank Doornink03/2024
5659(77*10^125330-293)/9125331Robert Price09/2019
5660(172*10^125292-1)/9125294Serge Batalov12/2014
56612^416134+1865899125269Enzo Doria03/2016
5662153^57337-152125264Norbert Schneider12/2018
5663(599*10^125224+13)/9125226Robert Price02/2022
5664(9*2^415992+1)/13560845125220Lelio R Paula05/2014
566530054^14657+14657^30054125207Hans Havermann03/2021
5666(23^91943-1)/22125201Robert Price01/2012
56672^415884-933075125194Paul Bourdelais06/2021
566843125^27010-106125185Enzo Doria08/2012
5669(38*10^125166+349)/9125167Robert Price10/2018
567010^125166-5001125166Robert Price12/2021
56712^415765-112603125158Enzo Doria06/2014
56728*10^125088-13125089Robert Price08/2019
5673(25*10^125076-13)/3125077Robert Price09/2019
5674(11*10^125054+73)/3125055Robert Price08/2021
5675(101^62383-1)/17542099700125026Paul Vanderveen06/2025
5676(29*10^125021-113)/3125022Robert Price10/2019
56772^415290-113591125015Enzo Doria08/2014
56782^415276-460919125011Enzo Doria06/2015
56792^415259+77243125006Enzo Doria05/2016
5680(67*10^124990+77)/9124991Robert Price10/2021
56812^415144-3683124971Yves Minet10/2011
56822^415092+111546435124956Paul Bourdelais10/2021
568331936^8173+8173^31936124946Hans Havermann03/2021
568427458^28145-28145^27458124927Frank Doornink03/2024
56855^178715-4124917Tyler NeSmith07/2021
568629767^15700+15700^29767124900Hans Havermann03/2021
5687(310^50131-1)/309124892Tom Wu07/2024
56882^414874+79124890Lelio R Paula01/2015
568925292^28361-28361^25292124874Frank Doornink01/2024
5690(2^414765+7)/1389124854Lelio R Paula05/2014
56912^414618+79459124813Enzo Doria06/2016
5692(61*10^124809-1)/3124811Robert Price01/2020
5693(235*29^85334+129)/28124794Eric Chen06/2025
5694(29*10^124765-71)/3124766Robert Price07/2021
56952^414432-1846709124757Enzo Doria07/2015
56962*10^124751-51124752Robert Price04/2018
5697(56*10^124735+367)/9124736Robert Price06/2019
569827362^28111-28111^27362124733Frank Doornink03/2024
5699(13*2^414274-1)/153124708Lelio R Paula05/2014
5700(23*10^124690+37)/3124691Robert Price02/2022
5701p(25046)#-p(25046+1)124675Henri Lifchitz11/2024
570256*10^124656-3124658Robert Price03/2020
5703(7*10^124648+197)/3124649Robert Price07/2018
57052^414032-5124637Henri Lifchitz07/2006
57042^414032+1872331124637Enzo Doria05/2016
570637373^2158+2158^37373124604Hans Havermann03/2021
570729811^15112+15112^29811124590Hans Havermann03/2021
5708(22^92791-3^92791)/19124564Robert Price02/2025
5709F(596093)/36870605281541124563Serge Batalov07/2024
57102^413781-2023124561Riley Fisher09/2023
571114120^30009-30009^14120124533Norbert Schneider02/2015
571229757^15296+15296^29757124521Hans Havermann03/2021
571335056^3561+3561^35056124504Hans Havermann03/2021
571440588^1167+1167^40588124487Hans Havermann02/2021
5715(85*10^124485-49)/9124486Robert Price12/2020
571664^68909-63^68909124463Robert Price07/2013
571735016^3581+3581^35016124448Hans Havermann03/2021
57182^413387+76253124442Enzo Doria04/2016
571928749^21298+21298^28749124436Hans Havermann03/2021
57202^413352+524287124432Paul Underwood09/2018
5721287117#+391613124424Nicolas PALAU01/2017
5722(4*10^124420+83)/3124421Robert Price02/2018
572334578^3965+3965^34578124421Hans Havermann03/2021
5724(68*10^124392-329)/9124393Robert Price03/2021
5725(27*2^413207-1)/108335124385Lelio R Paula05/2014
572610^124383+58407124384Patrick De Geest08/2021
572810^124383-8000001124383Robert Price04/2021
572710^124383-5801124383Patrick De Geest08/2021
572926091^28154-28154^26091124342Frank Doornink03/2024
5730(41*10^124335-383)/9124336Robert Price11/2018
5731(304*10^124329-43)/9124331Robert Price02/2020
573234716^3811+3811^34716124320Hans Havermann03/2021
573326892^28063-28063^26892124309Frank Doornink03/2024
57342^412868-120599124286Paul Bourdelais02/2012
573510^124248+899089124249Patrick De Geest05/2021
573710^124248-1000001124248Robert Price08/2020
573610^124248-501903124248Patrick De Geest05/2021
573845^75145-2124231Lelio R Paula08/2015
573929901^14272+14272^29901124224Hans Havermann03/2021
57402^412645-112213124219Enzo Doria06/2014
574129837^14500+14500^29837124163Hans Havermann03/2021
574228074^26455+26455^28074124158Hans Havermann03/2021
5743954^41669-41669^954124155Norman Luhn10/2024
5744432^47093-47093^432124113Norman Luhn10/2024
57452^412285+213317124111Enzo Doria09/2023
5746(12^115001-1)/2530033124101Paul Vanderveen06/2025
57472^412248+74611124100Enzo Doria04/2016
5748(22*10^124096-13)/9124097Robert Price06/2018
5749(455*10^124093+31)/9124095Robert Price06/2021
57502^412192-3329124083Yves Minet12/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!