PRP Records

Probable Primes Top 10000

(288949 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 ?
325191^65772-2128851Lelio R Paula05/2017
32522^428022+43128848Lelio R Paula05/2017
32532^427999-459397128841Enzo Doria05/2015
32542^427993+76847128839Enzo Doria05/2016
325531059^14060+14060^31059128833Hans Havermann03/2021
325610^128805+152871128806Patrick De Geest05/2021
325710^128805-10001128805Robert Price02/2021
32582^427824-1851507128788Enzo Doria08/2015
32592^427807-21469128783Enzo Doria07/2013
326029082^26783+26783^29082128772Hans Havermann04/2021
326140055^1638+1638^40055128750Hans Havermann04/2021
326211^123594-240128710Enzo Doria09/2012
32632^427504-21503128692Enzo Doria07/2013
326437727^2574+2574^37727128673Hans Havermann04/2021
326529686^21591+21591^29686128668Hans Havermann04/2021
326610^128668-70000000001128668Robert Price08/2021
32672^427420+91128667Lelio R Paula05/2017
3268(68*10^128645-257)/9128646Robert Price07/2019
32692^427269-113635128621Enzo Doria08/2014
32702^427130+1877569128579Enzo Doria08/2016
32712^427016-115349128545Enzo Doria07/2015
3272(4*10^128510+137)/3128511Robert Price03/2018
32732^426889-112879128507Enzo Doria06/2014
32742^426804+1869931128481Enzo Doria05/2016
32752^426750+77635128465Enzo Doria05/2016
327636988^2969+2969^36988128445Hans Havermann03/2021
327736664^3185+3185^36664128439Hans Havermann03/2021
327832618^8649+8649^32618128416Hans Havermann04/2021
327928883^27874+27874^28883128391Hans Havermann04/2021
32802^426425-91128367Lelio R Paula05/2017
3281(15*2^426398-1)/11128359Lelio R Paula05/2014
32822^426352+74971128345Enzo Doria04/2016
3283(199*10^128343-7)/3128345Robert Price05/2020
32844*10^128343-21128344Robert Price09/2018
3285(65*10^128338+493)/9128339Robert Price08/2021
328635632^3997+3997^35632128337Hans Havermann04/2021
32872^426300-1863689128330Enzo Doria03/2016
32882^426293+1881017128327Enzo Doria11/2016
3289(88*10^128324-637)/9128325Robert Price11/2020
329039103^1908+1908^39103128281Hans Havermann04/2021
32912^426043+35128252Robert Price11/2015
3292(4*10^128244-19)/3128245Robert Price03/2018
329335489^4102+4102^35489128222Hans Havermann04/2021
329434721^4926+4926^34721128208Hans Havermann04/2021
3295(305*10^128198+1)/9128200Robert Price02/2020
32962^425808-459959128181Enzo Doria06/2015
329730632^15291+15291^30632128178Hans Havermann04/2021
329835981^3648+3648^35981128167Hans Havermann04/2021
32992^425627-113605128127Enzo Doria08/2014
3300(4*10^128109+119)/3128110Robert Price12/2021
3301(22*10^128094+53)/3128095Robert Price07/2019
3302(86*10^128086-221)/9128087Robert Price09/2019
330318565^30002-30002^18565128070Norbert Schneider01/2015
3304(2^425287-9)/2737128021Lelio R Paula05/2015
3305(3*2^425233-1)/25128007Lelio R Paula05/2014
33062^425205+4911128000Marek Hubal02/2017
330729241^23836+23836^29241127995Hans Havermann04/2021
33082^425118-113663127974Enzo Doria08/2014
3309(86*10^127967-329)/9127968Robert Price01/2020
33102^425061+1869761127957Enzo Doria05/2016
3311746^44541+44541^746127955Norbert Schneider07/2019
331230236^17043+17043^30236127946Hans Havermann03/2021
33132^424918-21141127914Enzo Doria07/2013
3314(62*10^127903+91)/9127904Robert Price07/2021
33152^424864-29489127897Enzo Doria08/2015
331630438^15893+15893^30438127877Hans Havermann02/2021
3317(97*10^127858-1)/3127860Serge Batalov12/2014
331828929^26258+26258^28929127845Hans Havermann03/2021
331930563^15220+15220^30563127828Hans Havermann03/2021
33202^424632-2786639127827Enzo Doria03/2016
332110^127821-700001127821Robert Price08/2021
33222^424577-113755127811Enzo Doria09/2014
3323(7*2^424512-1)/3127792Lelio R Paula05/2014
3324(56*10^127752+691)/9127753Robert Price05/2019
332511^122629-720127705Enzo Doria11/2012
332622*10^127645+3127647Robert Price01/2020
332728715^27844+27844^28715127631Hans Havermann03/2021
3328(56*10^127612+187)/9127613Robert Price10/2021
3329(5*36^81995+821)/7127609Eric Chen01/2021
33304*10^127562-39127563Robert Price09/2020
333132595^8186+8186^32595127547Hans Havermann03/2021
33322^423696-21429127546Enzo Doria07/2013
33332^423664-1864559127536Enzo Doria03/2016
333437889^2322+2322^37889127530Hans Havermann03/2021
333537668^2429+2429^37668127523Hans Havermann03/2021
33363^267267-4127519Henri Lifchitz10/2014
3337(103*10^127491+17)/3127493Robert Price08/2020
333829376^21869+21869^29376127487Hans Havermann03/2021
333931186^12241+12241^31186127483Hans Havermann02/2021
3340(19^99689+5^99689)/24127477Robert Price09/2013
3341(21*2^423372+1)/101127447Lelio R Paula05/2014
334230594^14645+14645^30594127446Hans Havermann03/2021
33432^423328-21537127435Enzo Doria07/2013
3344(67*10^127413-7)/3127415Robert Price01/2020
3345(2*10^127407+73)/3127407Robert Price09/2020
3346(2^423165-7)/25127384Lelio R Paula05/2015
3347(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
334829512^20647+20647^29512127341Hans Havermann03/2021
3349(112*10^127324+17)/3127326Robert Price03/2020
335029565^20252+20252^29565127321Hans Havermann03/2021
3351(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
3352(16*10^127259+197)/3127260Robert Price04/2019
3353(26*10^127240+61)/3127241Robert Price10/2019
3354(234483*27^88884-145)/26127230Curtis Bright05/2015
33552^422515-114997127190Enzo Doria06/2015
33565*10^127179-3127180Robert Price07/2015
335731678^10343+10343^31678127176Hans Havermann03/2021
3358(44*10^127169-233)/9127170Robert Price01/2019
335934947^4352+4352^34947127162Hans Havermann03/2021
33606*10^127158+19127159Robert Price11/2021
336130469^14902+14902^30469127155Hans Havermann03/2021
33625*10^127153+77127154Robert Price12/2018
336329941^17620+17620^29941127130Hans Havermann02/2021
336431607^10516+10516^31607127119Hans Havermann03/2021
3365(19*10^127118-97)/3127119Robert Price10/2021
3366(29*10^127111+691)/9127112Robert Price08/2021
3367736^44335+44335^736127104Norbert Schneider07/2019
336833040^7023+7023^33040127090Hans Havermann03/2021
336929748^18661+18661^29748127052Hans Havermann03/2021
3370-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
3371(78^67141-1)/77127036Paul Bourdelais09/2017
3372(14*10^127014-137)/3127015Robert Price04/2021
337331436^10965+10965^31436127002Hans Havermann03/2021
337428905^24758+24758^28905127001Hans Havermann03/2021
33752^421860-113285126993Enzo Doria07/2014
3376(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
3377(2^421827-7)/11126982Lelio R Paula05/2015
337811^121910-840126957Enzo Doria12/2012
3379(56*10^126935+187)/9126936Robert Price10/2021
338028915^24538+24538^28915126933Hans Havermann03/2021
3381(29*10^126928-77)/3126929Robert Price02/2020
3382(259*10^126919-1)/3126921Robert Price12/2020
338310^126919+204567126920Patrick De Geest05/2021
338410^126919-100001126919Robert Price07/2020
338528340^28503+28503^28340126907Norbert Schneider02/2021
3386(71^68539+1)/72126882Paul Bourdelais09/2017
3387(5*10^126871-119)/3126872Robert Price03/2018
3388331^50339-10004126846Enzo Doria07/2012
33892^421363-2790757126843Enzo Doria03/2016
3390(106*10^126839-1)/3126841Serge Batalov12/2014
339137938^2203+2203^37938126828Hans Havermann03/2021
3392(7*2^421243+1)/39126807Lelio R Paula05/2014
3393(14*10^126784-83)/3126785Robert Price12/2018
33942^421161-286183126783Enzo Doria06/2015
3395(106*10^126726+17)/3126728Robert Price04/2021
339630718^13347+13347^30718126724Hans Havermann03/2021
33972^420939-113935126716Enzo Doria10/2014
3398177^56363-2126703Lelio R Paula10/2017
33992^420741-113659126656Enzo Doria08/2014
34002^420694-21126642Lelio R Paula05/2017
3401(13*10^126638+437)/9126639Robert Price04/2018
3402(167*10^126637-17)/3126639Robert Price03/2020
34034*10^126625+87126626Robert Price08/2018
3404(31*2^420556+1)/7126601Lelio R Paula05/2014
34057*10^126600-99126601Robert Price06/2019
34062^420424-59189126561Enzo Doria10/2015
340728717^25534+25534^28717126560Hans Havermann03/2021
3408(86*10^126542+103)/9126543Robert Price12/2021
340928922^23655+23655^28922126503Hans Havermann03/2021
34102^420126+71893126471Enzo Doria04/2016
3411(43*10^126441+47)/9126442Robert Price12/2018
34122^419866+1877059126393Enzo Doria07/2016
341329315^20484+20484^29315126390Hans Havermann03/2021
341429433^19676+19676^29433126384Hans Havermann03/2021
3415F(604711)126377Henri Lifchitz02/2005
34162^419757+72707126360Enzo Doria04/2016
34172^419720-21569126349Enzo Doria07/2013
34182^419637+29126324Henri Lifchitz02/2006
341931004^11865+11865^31004126319Hans Havermann03/2021
34202^419612+1876741126316Enzo Doria07/2016
34212^419520+2793271126289Enzo Doria03/2016
3422(2^419447-5)/369126264Lelio R Paula05/2014
34232^419328-1859939126231Enzo Doria03/2016
34242^419282-1851507126217Enzo Doria08/2015
3425(133*10^126212+17)/3126214Robert Price11/2021
34262^419251+1866143126208Enzo Doria03/2016
342711^121185+2126202Robert Price05/2014
342828203^28352+28352^28203126175Norbert Schneider01/2021
3429(23*2^419036-1)/1393126141Lelio R Paula05/2014
34302^418851+23126087Robert Price09/2015
3431(2^418849-9)/2681126083Lelio R Paula05/2014
34322^418829+167126081Lelio R Paula01/2012
343331037^11530+11530^31037126067Hans Havermann03/2021
3434(31*2^418782-1)/75891126063Lelio R Paula05/2014
3435(19*2^418754-1)/15126058Lelio R Paula05/2014
3436(35*10^126048-323)/9126049Robert Price10/2021
343733016^6551+6551^33016126000Hans Havermann03/2021
34382^418548-111546435125996Paul Bourdelais10/2021
343934736^4227+4227^34736125954Hans Havermann03/2021
34402^418319-109501125927Enzo Doria04/2014
34412^418316-112373125926Enzo Doria06/2014
344240398^1309+1309^40398125919Hans Havermann03/2021
3443(8*10^125894-29)/3125895Robert Price07/2018
3444(26*10^125886-413)/9125887Robert Price05/2018
34452^417968+1869811125821Enzo Doria06/2016
34462^417902+63125802Lelio R Paula09/2015
3447(10^125792-91)/9125792Serge Batalov12/2014
344830438^13573+13573^30438125791Hans Havermann03/2021
344932867^6714+6714^32867125782Hans Havermann03/2021
345031155^10892+10892^31155125777Hans Havermann03/2021
3451(35*10^125754-593)/9125755Robert Price07/2018
345230455^13464+13464^30455125754Hans Havermann03/2021
3453(32*10^125751-77)/9125752Robert Price06/2018
34542^417704+77011125742Enzo Doria05/2016
345529755^16816+16816^29755125737Hans Havermann03/2021
3456(22*10^125734+203)/9125735Robert Price10/2021
345729918^15915+15915^29918125710Hans Havermann03/2021
3458(10^125706+149)/3125706Serge Batalov12/2014
345928531^25368+25368^28531125659Hans Havermann03/2021
34602^417419-115309125656Enzo Doria07/2015
34612^417300+77281125620Enzo Doria05/2016
346230638^12537+12537^30638125561Hans Havermann03/2021
34632^417095-1657125559Yves Minet07/2014
346430162^14525+14525^30162125538Hans Havermann03/2021
3465(56*10^125535+583)/9125536Robert Price08/2021
3466(88*10^125492-637)/9125493Robert Price11/2020
346728958^21525+21525^28958125474Hans Havermann02/2021
34692^416773-25125462Lelio R Paula09/2015
3468(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
347033889^5032+5032^33889125449Hans Havermann03/2021
3471(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
3472(11*2^416691+1)/43125436Lelio R Paula05/2014
3473(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
34742^416641-2*416641+1125422Robert Price05/2018
347533392^5697+5697^33392125409Hans Havermann03/2021
3476(21*2^416566-1)/17125399Lelio R Paula05/2014
34772^416530+1870429125389Enzo Doria05/2016
3478(56*10^125385+691)/9125386Robert Price05/2019
347927953^28198+28198^27953125381Norbert Schneider01/2021
348031074^10837+10837^31074125381Hans Havermann03/2021
348133745^5194+5194^33745125380Hans Havermann03/2021
34822^416490+1875109125376Enzo Doria09/2016
348328360^26331+26331^28360125365Hans Havermann03/2021
34842^416416-114929125354Enzo Doria05/2015
3485(77*10^125330-293)/9125331Robert Price09/2019
3486(172*10^125292-1)/9125294Serge Batalov12/2014
34872^416134+1865899125269Enzo Doria03/2016
3488153^57337-152125264Norbert Schneider12/2018
3489(9*2^415992+1)/13560845125220Lelio R Paula05/2014
349030054^14657+14657^30054125207Hans Havermann03/2021
3491(23^91943-1)/22125201Robert Price01/2012
34922^415884-933075125194Paul Bourdelais06/2021
349343125^27010-106125185Enzo Doria08/2012
3494(38*10^125166+349)/9125167Robert Price10/2018
349510^125166-5001125166Robert Price12/2021
34962^415765-112603125158Enzo Doria06/2014
34978*10^125088-13125089Robert Price08/2019
3498(25*10^125076-13)/3125077Robert Price09/2019
3499(11*10^125054+73)/3125055Robert Price08/2021
3500(29*10^125021-113)/3125022Robert Price10/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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