PRP Records

Probable Primes Top 10000

(280928 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 ?
275111^123594-240128710Enzo Doria09/2012
27522^427504-21503128692Enzo Doria07/2013
27532^427420+91128667Lelio R Paula05/2017
2754(68*10^128645-257)/9128646Robert Price07/2019
27552^427269-113635128621Enzo Doria08/2014
27562^427130+1877569128579Enzo Doria08/2016
27572^427016-115349128545Enzo Doria07/2015
2758(4*10^128510+137)/3128511Robert Price03/2018
27592^426889-112879128507Enzo Doria06/2014
27602^426804+1869931128481Enzo Doria05/2016
27612^426750+77635128465Enzo Doria05/2016
276236988^2969+2969^36988128445Hans Havermann03/2021
276336664^3185+3185^36664128439Hans Havermann03/2021
27642^426425-91128367Lelio R Paula05/2017
2765(15*2^426398-1)/11128359Lelio R Paula05/2014
27672^426352+74971128345Enzo Doria04/2016
2766(199*10^128343-7)/3128345Robert Price05/2020
27684*10^128343-21128344Robert Price09/2018
27692^426300-1863689128330Enzo Doria03/2016
27702^426293+1881017128327Enzo Doria11/2016
2771(88*10^128324-637)/9128325Robert Price11/2020
277239103^1908+1908^39103128281Hans Havermann04/2021
27732^426043+35128252Robert Price11/2015
2774(4*10^128244-19)/3128245Robert Price03/2018
2775(305*10^128198+1)/9128200Robert Price02/2020
27762^425808-459959128181Enzo Doria06/2015
277730632^15291+15291^30632128178Hans Havermann04/2021
277835981^3648+3648^35981128167Hans Havermann04/2021
27792^425627-113605128127Enzo Doria08/2014
2780(22*10^128094+53)/3128095Robert Price07/2019
2781(86*10^128086-221)/9128087Robert Price09/2019
278218565^30002-30002^18565128070Norbert Schneider01/2015
2783(2^425287-9)/2737128021Lelio R Paula05/2015
2784(3*2^425233-1)/25128007Lelio R Paula05/2014
27852^425205+4911128000Marek Hubal02/2017
278629241^23836+23836^29241127995Hans Havermann04/2021
27872^425118-113663127974Enzo Doria08/2014
2788(86*10^127967-329)/9127968Robert Price01/2020
27892^425061+1869761127957Enzo Doria05/2016
2790746^44541+44541^746127955Norbert Schneider07/2019
279130236^17043+17043^30236127946Hans Havermann03/2021
27922^424918-21141127914Enzo Doria07/2013
27932^424864-29489127897Enzo Doria08/2015
279430438^15893+15893^30438127877Hans Havermann02/2021
2795(97*10^127858-1)/3127860Serge Batalov12/2014
279628929^26258+26258^28929127845Hans Havermann03/2021
279730563^15220+15220^30563127828Hans Havermann03/2021
27982^424632-2786639127827Enzo Doria03/2016
27992^424577-113755127811Enzo Doria09/2014
2800(7*2^424512-1)/3127792Lelio R Paula05/2014
2801(56*10^127752+691)/9127753Robert Price05/2019
280211^122629-720127705Enzo Doria11/2012
280322*10^127645+3127647Robert Price01/2020
280428715^27844+27844^28715127631Hans Havermann03/2021
2805(5*36^81995+821)/7127609Eric Chen01/2021
28064*10^127562-39127563Robert Price09/2020
280732595^8186+8186^32595127547Hans Havermann03/2021
28082^423696-21429127546Enzo Doria07/2013
28092^423664-1864559127536Enzo Doria03/2016
281037889^2322+2322^37889127530Hans Havermann03/2021
281137668^2429+2429^37668127523Hans Havermann03/2021
28123^267267-4127519Henri Lifchitz10/2014
2813(103*10^127491+17)/3127493Robert Price08/2020
281429376^21869+21869^29376127487Hans Havermann03/2021
281531186^12241+12241^31186127483Hans Havermann02/2021
2816(19^99689+5^99689)/24127477Robert Price09/2013
2817(21*2^423372+1)/101127447Lelio R Paula05/2014
281830594^14645+14645^30594127446Hans Havermann03/2021
28192^423328-21537127435Enzo Doria07/2013
2820(67*10^127413-7)/3127415Robert Price01/2020
2821(2*10^127407+73)/3127407Robert Price09/2020
2822(2^423165-7)/25127384Lelio R Paula05/2015
282329512^20647+20647^29512127341Hans Havermann03/2021
2824(112*10^127324+17)/3127326Robert Price03/2020
282529565^20252+20252^29565127321Hans Havermann03/2021
2826(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2827(16*10^127259+197)/3127260Robert Price04/2019
2828(26*10^127240+61)/3127241Robert Price10/2019
2829(234483*27^88884-145)/26127230Curtis Bright05/2015
28302^422515-114997127190Enzo Doria06/2015
28315*10^127179-3127180Robert Price07/2015
283231678^10343+10343^31678127176Hans Havermann03/2021
2833(44*10^127169-233)/9127170Robert Price01/2019
283434947^4352+4352^34947127162Hans Havermann03/2021
283530469^14902+14902^30469127155Hans Havermann03/2021
28365*10^127153+77127154Robert Price12/2018
283729941^17620+17620^29941127130Hans Havermann02/2021
283831607^10516+10516^31607127119Hans Havermann03/2021
2839736^44335+44335^736127104Norbert Schneider07/2019
284033040^7023+7023^33040127090Hans Havermann03/2021
284129748^18661+18661^29748127052Hans Havermann03/2021
2842-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2843(78^67141-1)/77127036Paul Bourdelais09/2017
284431436^10965+10965^31436127002Hans Havermann03/2021
284528905^24758+24758^28905127001Hans Havermann03/2021
28462^421860-113285126993Enzo Doria07/2014
2847(2^421827-7)/11126982Lelio R Paula05/2015
284811^121910-840126957Enzo Doria12/2012
284928915^24538+24538^28915126933Hans Havermann03/2021
2850(29*10^126928-77)/3126929Robert Price02/2020
2851(259*10^126919-1)/3126921Robert Price12/2020
285210^126919-100001126919Robert Price07/2020
285328340^28503+28503^28340126907Norbert Schneider02/2021
2854(71^68539+1)/72126882Paul Bourdelais09/2017
2855(5*10^126871-119)/3126872Robert Price03/2018
2856331^50339-10004126846Enzo Doria07/2012
28572^421363-2790757126843Enzo Doria03/2016
2858(106*10^126839-1)/3126841Serge Batalov12/2014
285937938^2203+2203^37938126828Hans Havermann03/2021
2860(7*2^421243+1)/39126807Lelio R Paula05/2014
2861(14*10^126784-83)/3126785Robert Price12/2018
28622^421161-286183126783Enzo Doria06/2015
286330718^13347+13347^30718126724Hans Havermann03/2021
28642^420939-113935126716Enzo Doria10/2014
2865177^56363-2126703Lelio R Paula10/2017
28662^420741-113659126656Enzo Doria08/2014
28672^420694-21126642Lelio R Paula05/2017
2868(13*10^126638+437)/9126639Robert Price04/2018
2869(167*10^126637-17)/3126639Robert Price03/2020
28704*10^126625+87126626Robert Price08/2018
2872(31*2^420556+1)/7126601Lelio R Paula05/2014
28717*10^126600-99126601Robert Price06/2019
28732^420424-59189126561Enzo Doria10/2015
287428717^25534+25534^28717126560Hans Havermann03/2021
287528922^23655+23655^28922126503Hans Havermann03/2021
28762^420126+71893126471Enzo Doria04/2016
2877(43*10^126441+47)/9126442Robert Price12/2018
28782^419866+1877059126393Enzo Doria07/2016
287929315^20484+20484^29315126390Hans Havermann03/2021
288029433^19676+19676^29433126384Hans Havermann03/2021
2881F(604711)126377Henri Lifchitz02/2005
28822^419757+72707126360Enzo Doria04/2016
28832^419720-21569126349Enzo Doria07/2013
28842^419637+29126324Henri Lifchitz02/2006
288531004^11865+11865^31004126319Hans Havermann03/2021
28862^419612+1876741126316Enzo Doria07/2016
28872^419520+2793271126289Enzo Doria03/2016
2888(2^419447-5)/369126264Lelio R Paula05/2014
28892^419328-1859939126231Enzo Doria03/2016
28902^419282-1851507126217Enzo Doria08/2015
28912^419251+1866143126208Enzo Doria03/2016
289211^121185+2126202Robert Price05/2014
289328203^28352+28352^28203126175Norbert Schneider01/2021
2894(23*2^419036-1)/1393126141Lelio R Paula05/2014
28952^418851+23126087Robert Price09/2015
2896(2^418849-9)/2681126083Lelio R Paula05/2014
28972^418829+167126081Lelio R Paula01/2012
289831037^11530+11530^31037126067Hans Havermann03/2021
2899(31*2^418782-1)/75891126063Lelio R Paula05/2014
2900(19*2^418754-1)/15126058Lelio R Paula05/2014
290133016^6551+6551^33016126000Hans Havermann03/2021
290234736^4227+4227^34736125954Hans Havermann03/2021
29032^418319-109501125927Enzo Doria04/2014
29042^418316-112373125926Enzo Doria06/2014
290540398^1309+1309^40398125919Hans Havermann03/2021
2906(8*10^125894-29)/3125895Robert Price07/2018
2907(26*10^125886-413)/9125887Robert Price05/2018
29082^417968+1869811125821Enzo Doria06/2016
29092^417902+63125802Lelio R Paula09/2015
2910(10^125792-91)/9125792Serge Batalov12/2014
291130438^13573+13573^30438125791Hans Havermann03/2021
291232867^6714+6714^32867125782Hans Havermann03/2021
291331155^10892+10892^31155125777Hans Havermann03/2021
2914(35*10^125754-593)/9125755Robert Price07/2018
291530455^13464+13464^30455125754Hans Havermann03/2021
2916(32*10^125751-77)/9125752Robert Price06/2018
29172^417704+77011125742Enzo Doria05/2016
291829755^16816+16816^29755125737Hans Havermann03/2021
291929918^15915+15915^29918125710Hans Havermann03/2021
2920(10^125706+149)/3125706Serge Batalov12/2014
292128531^25368+25368^28531125659Hans Havermann03/2021
29222^417419-115309125656Enzo Doria07/2015
29232^417300+77281125620Enzo Doria05/2016
292430638^12537+12537^30638125561Hans Havermann03/2021
29252^417095-1657125559Yves Minet07/2014
292630162^14525+14525^30162125538Hans Havermann03/2021
2927(88*10^125492-637)/9125493Robert Price11/2020
292828958^21525+21525^28958125474Hans Havermann02/2021
29292^416773-25125462Lelio R Paula09/2015
293033889^5032+5032^33889125449Hans Havermann03/2021
2931(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2932(11*2^416691+1)/43125436Lelio R Paula05/2014
2933(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
29342^416641-2*416641+1125422Robert Price05/2018
293533392^5697+5697^33392125409Hans Havermann03/2021
2936(21*2^416566-1)/17125399Lelio R Paula05/2014
29372^416530+1870429125389Enzo Doria05/2016
2938(56*10^125385+691)/9125386Robert Price05/2019
293927953^28198+28198^27953125381Norbert Schneider01/2021
294031074^10837+10837^31074125381Hans Havermann03/2021
294133745^5194+5194^33745125380Hans Havermann03/2021
29422^416490+1875109125376Enzo Doria09/2016
294328360^26331+26331^28360125365Hans Havermann03/2021
29442^416416-114929125354Enzo Doria05/2015
2945(77*10^125330-293)/9125331Robert Price09/2019
2946(172*10^125292-1)/9125294Serge Batalov12/2014
29472^416134+1865899125269Enzo Doria03/2016
2948153^57337-152125264Norbert Schneider12/2018
2949(9*2^415992+1)/13560845125220Lelio R Paula05/2014
295030054^14657+14657^30054125207Hans Havermann03/2021
2951(23^91943-1)/22125201Robert Price01/2012
295243125^27010-106125185Enzo Doria08/2012
2953(38*10^125166+349)/9125167Robert Price10/2018
29542^415765-112603125158Enzo Doria06/2014
29558*10^125088-13125089Robert Price08/2019
2956(25*10^125076-13)/3125077Robert Price09/2019
2957(29*10^125021-113)/3125022Robert Price10/2019
29582^415290-113591125015Enzo Doria08/2014
29592^415276-460919125011Enzo Doria06/2015
29602^415259+77243125006Enzo Doria05/2016
29612^415144-3683124971Yves Minet10/2011
296231936^8173+8173^31936124946Hans Havermann03/2021
296329767^15700+15700^29767124900Hans Havermann03/2021
29642^414874+79124890Lelio R Paula01/2015
2965(2^414765+7)/1389124854Lelio R Paula05/2014
29662^414618+79459124813Enzo Doria06/2016
2967(61*10^124809-1)/3124811Robert Price01/2020
29682^414432-1846709124757Enzo Doria07/2015
29692*10^124751-51124752Robert Price04/2018
2970(56*10^124735+367)/9124736Robert Price06/2019
2971(13*2^414274-1)/153124708Lelio R Paula05/2014
297256*10^124656-3124658Robert Price03/2020
2973(7*10^124648+197)/3124649Robert Price07/2018
29752^414032-5124637Henri Lifchitz07/2006
29742^414032+1872331124637Enzo Doria05/2016
297637373^2158+2158^37373124604Hans Havermann03/2021
297729811^15112+15112^29811124590Hans Havermann03/2021
297814120^30009-30009^14120124533Norbert Schneider02/2015
297929757^15296+15296^29757124521Hans Havermann03/2021
298035056^3561+3561^35056124504Hans Havermann03/2021
298140588^1167+1167^40588124487Hans Havermann02/2021
2982(85*10^124485-49)/9124486Robert Price12/2020
298364^68909-63^68909124463Robert Price07/2013
298435016^3581+3581^35016124448Hans Havermann03/2021
29852^413387+76253124442Enzo Doria04/2016
298628749^21298+21298^28749124436Hans Havermann03/2021
29872^413352+524287124432Paul Underwood09/2018
2988287117#+391613124424Nicolas PALAU01/2017
2990(4*10^124420+83)/3124421Robert Price02/2018
298934578^3965+3965^34578124421Hans Havermann03/2021
2991(68*10^124392-329)/9124393Robert Price03/2021
2992(27*2^413207-1)/108335124385Lelio R Paula05/2014
299310^124383-8000001124383Robert Price04/2021
2994(41*10^124335-383)/9124336Robert Price11/2018
2995(304*10^124329-43)/9124331Robert Price02/2020
299634716^3811+3811^34716124320Hans Havermann03/2021
29972^412868-120599124286Paul Bourdelais02/2012
299810^124248-1000001124248Robert Price08/2020
299945^75145-2124231Lelio R Paula08/2015
300029901^14272+14272^29901124224Hans Havermann03/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 12 2021 20:10 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!