PRP Records

Probable Primes Top 10000

(294613 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 ?
45014*10^127562-39127563Robert Price09/2020
450232595^8186+8186^32595127547Hans Havermann03/2021
45032^423696-21429127546Enzo Doria07/2013
45042^423664-1864559127536Enzo Doria03/2016
450537889^2322+2322^37889127530Hans Havermann03/2021
450637668^2429+2429^37668127523Hans Havermann03/2021
45073^267267-4127519Henri Lifchitz10/2014
4508fibonacci(610144)-2127513Jon Grantham08/2023
4509(103*10^127491+17)/3127493Robert Price08/2020
451029376^21869+21869^29376127487Hans Havermann03/2021
451131186^12241+12241^31186127483Hans Havermann02/2021
4512(19^99689+5^99689)/24127477Robert Price09/2013
451327069^28754-28754^27069127452Frank Doornink01/2024
4514(21*2^423372+1)/101127447Lelio R Paula05/2014
451530594^14645+14645^30594127446Hans Havermann03/2021
45162^423328-21537127435Enzo Doria07/2013
4517(67*10^127413-7)/3127415Robert Price01/2020
4518(5*34^83193+700233)/11127408Eric Chen08/2023
4519(2*10^127407+73)/3127407Robert Price09/2020
4520(2^423165-7)/25127384Lelio R Paula05/2015
4521(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
4522(4*10^127349+17)/3127350Tyler Busby01/2023
452329512^20647+20647^29512127341Hans Havermann03/2021
45242^422987-3001935127332Paul Bourdelais07/2023
4525(112*10^127324+17)/3127326Robert Price03/2020
452629565^20252+20252^29565127321Hans Havermann03/2021
4527fibonacci(609165)-3127308Jon Grantham08/2023
4529(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
4528(5^182099-3^182099)/2127282Kellen Shenton05/2022
4530(16*10^127259+197)/3127260Robert Price04/2019
4531(26*10^127240+61)/3127241Robert Price10/2019
4532(234483*27^88884-145)/26127230Curtis Bright05/2015
45332^422515-114997127190Enzo Doria06/2015
45345*10^127179-3127180Robert Price07/2015
453531678^10343+10343^31678127176Hans Havermann03/2021
4536(44*10^127169-233)/9127170Robert Price01/2019
453734947^4352+4352^34947127162Hans Havermann03/2021
45386*10^127158+19127159Robert Price11/2021
453930469^14902+14902^30469127155Hans Havermann03/2021
45405*10^127153+77127154Robert Price12/2018
454129941^17620+17620^29941127130Hans Havermann02/2021
454231607^10516+10516^31607127119Hans Havermann03/2021
4543(19*10^127118-97)/3127119Robert Price10/2021
4544(29*10^127111+691)/9127112Robert Price08/2021
4545736^44335+44335^736127104Norbert Schneider07/2019
454633040^7023+7023^33040127090Hans Havermann03/2021
4547(4*10^127081+167)/9127081Robert Price03/2022
454829748^18661+18661^29748127052Hans Havermann03/2021
4549-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
4550(78^67141-1)/77127036Paul Bourdelais09/2017
4551(14*10^127014-137)/3127015Robert Price04/2021
455231436^10965+10965^31436127002Hans Havermann03/2021
455328905^24758+24758^28905127001Hans Havermann03/2021
45542^421860-113285126993Enzo Doria07/2014
4555(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
4556(2^421827-7)/11126982Lelio R Paula05/2015
455711^121910-840126957Enzo Doria12/2012
4558(56*10^126935+187)/9126936Robert Price10/2021
455928915^24538+24538^28915126933Hans Havermann03/2021
4560(29*10^126928-77)/3126929Robert Price02/2020
4561(259*10^126919-1)/3126921Robert Price12/2020
456210^126919+204567126920Patrick De Geest05/2021
4563(2^421617+100280245065)126920Paul Bourdelais05/2022
456410^126919-100001126919Robert Price07/2020
456528340^28503+28503^28340126907Norbert Schneider02/2021
45662^421534-3001935126895Paul Bourdelais07/2023
4567(71^68539+1)/72126882Paul Bourdelais09/2017
4568(5*10^126871-119)/3126872Robert Price03/2018
4569331^50339-10004126846Enzo Doria07/2012
45702^421363-2790757126843Enzo Doria03/2016
4571(106*10^126839-1)/3126841Serge Batalov12/2014
457237938^2203+2203^37938126828Hans Havermann03/2021
4573(13*10^126819+77)/9126820Robert Price07/2022
4574(7*2^421243+1)/39126807Lelio R Paula05/2014
4576(14*10^126784-83)/3126785Robert Price12/2018
45752^421169-3001935126785Paul Bourdelais07/2023
45772^421161-286183126783Enzo Doria06/2015
4578(106*10^126726+17)/3126728Robert Price04/2021
457930718^13347+13347^30718126724Hans Havermann03/2021
45802^420939-113935126716Enzo Doria10/2014
458111*23^93048+356126708Eric Chen08/2023
4582177^56363-2126703Lelio R Paula10/2017
45832^420741-113659126656Enzo Doria08/2014
45842^420694-21126642Lelio R Paula05/2017
4585(13*10^126638+437)/9126639Robert Price04/2018
4586(167*10^126637-17)/3126639Robert Price03/2020
45874*10^126625+87126626Robert Price08/2018
4588(31*2^420556+1)/7126601Lelio R Paula05/2014
45897*10^126600-99126601Robert Price06/2019
45902^420424-59189126561Enzo Doria10/2015
459128717^25534+25534^28717126560Hans Havermann03/2021
4592(86*10^126542+103)/9126543Robert Price12/2021
4593(19*10^126517-7)/3126518Robert Price12/2023
459428922^23655+23655^28922126503Hans Havermann03/2021
45952^420126+71893126471Enzo Doria04/2016
4596(43*10^126441+47)/9126442Robert Price12/2018
45978*10^126408+71126409Robert Price05/2022
45982^419866+1877059126393Enzo Doria07/2016
459929315^20484+20484^29315126390Hans Havermann03/2021
460029433^19676+19676^29433126384Hans Havermann03/2021
4601F(604711)126377Henri Lifchitz02/2005
46022^419757+72707126360Enzo Doria04/2016
46032^419720-21569126349Enzo Doria07/2013
46042^419637+29126324Henri Lifchitz02/2006
460531004^11865+11865^31004126319Hans Havermann03/2021
46062^419612+1876741126316Enzo Doria07/2016
46072^419520+2793271126289Enzo Doria03/2016
4608(2^419447-5)/369126264Lelio R Paula05/2014
46092^419328-1859939126231Enzo Doria03/2016
46102^419282-1851507126217Enzo Doria08/2015
4611(133*10^126212+17)/3126214Robert Price11/2021
46122^419251+1866143126208Enzo Doria03/2016
461311^121185+2126202Robert Price05/2014
461428203^28352+28352^28203126175Norbert Schneider01/2021
4615(23*2^419036-1)/1393126141Lelio R Paula05/2014
46162^418851+23126087Robert Price09/2015
4617(2^418849-9)/2681126083Lelio R Paula05/2014
46182^418829+167126081Lelio R Paula01/2012
461931037^11530+11530^31037126067Hans Havermann03/2021
46204*10^126064-69126065Robert Price01/2022
4621(31*2^418782-1)/75891126063Lelio R Paula05/2014
4622(19*2^418754-1)/15126058Lelio R Paula05/2014
4623(35*10^126048-323)/9126049Robert Price10/2021
462433016^6551+6551^33016126000Hans Havermann03/2021
46252^418548-111546435125996Paul Bourdelais10/2021
462625134^28625-28625^25134125958Frank Doornink12/2023
462734736^4227+4227^34736125954Hans Havermann03/2021
46282^418319-109501125927Enzo Doria04/2014
46292^418316-112373125926Enzo Doria06/2014
463040398^1309+1309^40398125919Hans Havermann03/2021
4631(8*10^125894-29)/3125895Robert Price07/2018
4632(26*10^125886-413)/9125887Robert Price05/2018
463310^(2*62938+1)-7*10^62938-1125877Robert Price07/2023
463455*10^125847+9125849Robert Price03/2022
46354*10^125832+57125833Robert Price05/2022
46362^417968+1869811125821Enzo Doria06/2016
46372^417902+63125802Lelio R Paula09/2015
4638(10^125792-91)/9125792Serge Batalov12/2014
463930438^13573+13573^30438125791Hans Havermann03/2021
464032867^6714+6714^32867125782Hans Havermann03/2021
464131155^10892+10892^31155125777Hans Havermann03/2021
4642(35*10^125754-593)/9125755Robert Price07/2018
464330455^13464+13464^30455125754Hans Havermann03/2021
4644(32*10^125751-77)/9125752Robert Price06/2018
46452^417704+77011125742Enzo Doria05/2016
464629755^16816+16816^29755125737Hans Havermann03/2021
4647(22*10^125734+203)/9125735Robert Price10/2021
464829918^15915+15915^29918125710Hans Havermann03/2021
4649(10^125706+149)/3125706Serge Batalov12/2014
465028531^25368+25368^28531125659Hans Havermann03/2021
46512^417419-115309125656Enzo Doria07/2015
4652(46*10^125642+593)/9125643Robert Price04/2022
46532^417315+213953125625Enzo Doria10/2023
46542^417300+77281125620Enzo Doria05/2016
465530638^12537+12537^30638125561Hans Havermann03/2021
46562^417095-1657125559Yves Minet07/2014
465730162^14525+14525^30162125538Hans Havermann03/2021
4658(56*10^125535+583)/9125536Robert Price08/2021
4659(23*10^125517-179)/3125518Robert Price06/2022
46609*10^125516+29125517Robert Price03/2022
4661(88*10^125492-637)/9125493Robert Price11/2020
466228958^21525+21525^28958125474Hans Havermann02/2021
46642^416773-25125462Lelio R Paula09/2015
4663(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
466533889^5032+5032^33889125449Hans Havermann03/2021
4666(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
4667(2861^36481+1)/(2861^191+1)125438Martin Hopf12/2023
4668(11*2^416691+1)/43125436Lelio R Paula05/2014
4669(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
46702^416641-2*416641+1125422Robert Price05/2018
467133392^5697+5697^33392125409Hans Havermann03/2021
4672(21*2^416566-1)/17125399Lelio R Paula05/2014
46732^416530+1870429125389Enzo Doria05/2016
4674(56*10^125385+691)/9125386Robert Price05/2019
467527953^28198+28198^27953125381Norbert Schneider01/2021
467631074^10837+10837^31074125381Hans Havermann03/2021
467733745^5194+5194^33745125380Hans Havermann03/2021
46782^416490+1875109125376Enzo Doria09/2016
467928360^26331+26331^28360125365Hans Havermann03/2021
46802^416416-114929125354Enzo Doria05/2015
4681(77*10^125330-293)/9125331Robert Price09/2019
4682(172*10^125292-1)/9125294Serge Batalov12/2014
46832^416134+1865899125269Enzo Doria03/2016
4684153^57337-152125264Norbert Schneider12/2018
4685(599*10^125224+13)/9125226Robert Price02/2022
4686(9*2^415992+1)/13560845125220Lelio R Paula05/2014
468730054^14657+14657^30054125207Hans Havermann03/2021
4688(23^91943-1)/22125201Robert Price01/2012
46892^415884-933075125194Paul Bourdelais06/2021
469043125^27010-106125185Enzo Doria08/2012
4691(38*10^125166+349)/9125167Robert Price10/2018
469210^125166-5001125166Robert Price12/2021
46932^415765-112603125158Enzo Doria06/2014
46948*10^125088-13125089Robert Price08/2019
4695(25*10^125076-13)/3125077Robert Price09/2019
4696(11*10^125054+73)/3125055Robert Price08/2021
4697(29*10^125021-113)/3125022Robert Price10/2019
46982^415290-113591125015Enzo Doria08/2014
46992^415276-460919125011Enzo Doria06/2015
47002^415259+77243125006Enzo Doria05/2016
4701(67*10^124990+77)/9124991Robert Price10/2021
47022^415144-3683124971Yves Minet10/2011
47032^415092+111546435124956Paul Bourdelais10/2021
470431936^8173+8173^31936124946Hans Havermann03/2021
47055^178715-4124916Tyler NeSmith07/2021
470629767^15700+15700^29767124900Hans Havermann03/2021
47072^414874+79124890Lelio R Paula01/2015
470825292^28361-28361^25292124874Frank Doornink01/2024
4709(2^414765+7)/1389124854Lelio R Paula05/2014
47102^414618+79459124813Enzo Doria06/2016
4711(61*10^124809-1)/3124811Robert Price01/2020
4712(29*10^124765-71)/3124766Robert Price07/2021
47132^414432-1846709124757Enzo Doria07/2015
47142*10^124751-51124752Robert Price04/2018
4715(56*10^124735+367)/9124736Robert Price06/2019
4716(13*2^414274-1)/153124708Lelio R Paula05/2014
4717(23*10^124690+37)/3124691Robert Price02/2022
471856*10^124656-3124658Robert Price03/2020
4719(7*10^124648+197)/3124649Robert Price07/2018
47212^414032-5124637Henri Lifchitz07/2006
47202^414032+1872331124637Enzo Doria05/2016
472237373^2158+2158^37373124604Hans Havermann03/2021
472329811^15112+15112^29811124590Hans Havermann03/2021
47242^413781-2023124561Riley Fisher09/2023
472514120^30009-30009^14120124533Norbert Schneider02/2015
472629757^15296+15296^29757124521Hans Havermann03/2021
472735056^3561+3561^35056124504Hans Havermann03/2021
472840588^1167+1167^40588124487Hans Havermann02/2021
4729(85*10^124485-49)/9124486Robert Price12/2020
473064^68909-63^68909124463Robert Price07/2013
473135016^3581+3581^35016124448Hans Havermann03/2021
47322^413387+76253124442Enzo Doria04/2016
473328749^21298+21298^28749124436Hans Havermann03/2021
47342^413352+524287124432Paul Underwood09/2018
4735287117#+391613124424Nicolas PALAU01/2017
4736(4*10^124420+83)/3124421Robert Price02/2018
473734578^3965+3965^34578124421Hans Havermann03/2021
4738(68*10^124392-329)/9124393Robert Price03/2021
4739(27*2^413207-1)/108335124385Lelio R Paula05/2014
474010^124383+58407124384Patrick De Geest08/2021
474210^124383-8000001124383Robert Price04/2021
474110^124383-5801124383Patrick De Geest08/2021
4743(41*10^124335-383)/9124336Robert Price11/2018
4744(304*10^124329-43)/9124331Robert Price02/2020
474534716^3811+3811^34716124320Hans Havermann03/2021
47462^412868-120599124286Paul Bourdelais02/2012
474710^124248+899089124249Patrick De Geest05/2021
474910^124248-1000001124248Robert Price08/2020
474810^124248-501903124248Patrick De Geest05/2021
475045^75145-2124231Lelio R Paula08/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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