PRP Records

Probable Primes Top 10000

(291910 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 ?
275134619^15246+15246^34619144817Hans Havermann01/2021
27522^481045-113215144809Enzo Doria07/2014
2753(64*10^144797+287)/9144798Robert Price04/2019
27542^480859-113695144753Enzo Doria09/2014
2755(106*10^144744+17)/3144746Robert Price04/2021
27567*10^144742-27144743Robert Price11/2022
27572^480766-2787191144725Enzo Doria11/2015
2758(21*27^101106-151)/26144720Curtis Bright05/2015
27592^480678+1874239144699Enzo Doria06/2016
2760(8*10^144683+1)/9144683Serge Batalov05/2010
2761L(692147)144651Henri Lifchitz10/2008
2762(76*10^144648+77)/9144649Robert Price10/2019
276332672^26721+26721^32672144635Hans Havermann01/2021
27642^480417+35144620Robert Price11/2015
27652^480296-59879144584Enzo Doria10/2015
276633157^22878+22878^33157144546Hans Havermann12/2020
276745494^1497+1497^45494144454Hans Havermann12/2020
27682^479844+3144448Donovan Johnson06/2006
276933442^20803+20803^33442144407Hans Havermann01/2021
277031892^32061-32061^31892144393Norbert Schneider01/2023
2771(27*2^479642+1)/733144386Lelio R Paula08/2015
2772(56*10^144380+169)/9144381Robert Price03/2022
277344917^1638+1638^44917144378Hans Havermann12/2020
2774(21*2^479605-1)/11144376Lelio R Paula09/2015
2775(56*10^144336+583)/9144337Robert Price08/2021
27762^479348-2792219144299Enzo Doria02/2016
27773^302389-6242144277Enzo Doria05/2014
277833778^18641+18641^33778144248Hans Havermann01/2021
27792*10^144220-3144221Robert Price07/2015
27802^478904-109109144165Enzo Doria04/2014
278143698^1987+1987^43698144125Hans Havermann12/2020
278236128^9723+9723^36128144072Hans Havermann01/2021
278332817^24518+24518^32817144050Hans Havermann12/2020
2784(772*10^144036-7)/9144038Robert Price06/2022
278534295^15828+15828^34295144020Hans Havermann01/2021
27862^478337-115333143994Enzo Doria07/2015
2787(7*2^478330-1)/3143993Lelio R Paula08/2015
278888^74047-87^74047143984Robert Price05/2015
278933242^21441+21441^33242143980Hans Havermann01/2021
2790(19*10^143963+467)/9143964Robert Price02/2018
2791(71^77761+1)/72143954Paul Bourdelais09/2017
279233490^19859+19859^33490143939Hans Havermann01/2021
2793(853*10^143931-7)/9143933Robert Price07/2021
27942^478088+27143919Robert Price11/2015
2795(8*10^143898-137)/3143899Robert Price03/2022
27967*10^143857-93143858Robert Price08/2020
27973*10^143844+61143845Robert Price09/2020
279841358^3005+3005^41358143837Hans Havermann01/2021
27992^477475-22071143735Enzo Doria07/2013
28002^477417-22123143717Enzo Doria07/2013
28012^477359-3577143700Yves Minet03/2017
280239435^4402+4402^39435143688Hans Havermann01/2021
2803(14*10^143662-71)/3143663Robert Price12/2018
28046^184614+5143658Paul Bourdelais01/2021
280546371^1252+1252^46371143640Hans Havermann12/2020
280634975^12748+12748^34975143588Hans Havermann01/2021
28072^476936-396765143573Enzo Doria07/2013
28082^476888-2791229143558Enzo Doria01/2016
28092^476868-1859939143552Enzo Doria11/2015
281040807^3294+3294^40807143548Hans Havermann12/2020
2811755^49878+49878^755143547Norbert Schneider04/2019
2812(19^112247-4^112247)/15143536Robert Price03/2021
281335561^10872+10872^35561143536Hans Havermann06/2021
281437637^6492+6492^37637143487Hans Havermann05/2021
281561567^214+214^61567143477Hans Havermann05/2021
28162^476558-113627143459Enzo Doria08/2014
28172^476478-45143435Lelio R Paula11/2017
281836380^8757+8757^36380143423Hans Havermann06/2021
281932510^25707+25707^32510143371Hans Havermann05/2021
28208*10^143361+17143362Robert Price07/2021
2821(2^475854+9)/73143245Lelio R Paula08/2015
28222^475813-113239143234Enzo Doria07/2014
2823(19*10^143212+137)/3143213Robert Price03/2022
282432218^27849+27849^32218143203Hans Havermann04/2021
28252^475624-114059143178Enzo Doria11/2014
2826(11*2^475553-7)/15143156Renaud Lifchitz03/2011
28272^475480-2786129143134Enzo Doria10/2015
282833912^16621+16621^33912143131Hans Havermann05/2021
2829(19*10^143129-43)/3143130Robert Price05/2019
283031830^31373+31373^31830143126Hans Havermann05/2021
28316*10^143105-53143106Robert Price05/2021
2832(14*10^143097+73)/3143098Robert Price12/2018
28332^475299-111937143080Enzo Doria05/2014
283435488^10753+10753^35488143071Hans Havermann04/2021
28352^475160-2797859143038Enzo Doria04/2016
2836(2^475069+3)/395143008Lelio R Paula08/2015
28372^475027-461437142998Enzo Doria07/2015
2838(2^474958+78557)/3142977Lelio R Paula07/2015
2839(8*10^142932+43)/3142933Robert Price06/2018
284035055^11942+11942^35055142922Hans Havermann05/2021
284137650^6239+6239^37650142887Hans Havermann05/2021
2842(54^82471-1)/53142871Paul Bourdelais09/2017
2843(11*2^474432-1)/95142818Lelio R Paula09/2015
28442^474417-59923142814Enzo Doria10/2015
28454*10^142810-21142811Robert Price09/2018
284632287^26494+26494^32287142811Hans Havermann06/2021
284737162^6965+6965^37162142811Hans Havermann06/2021
2848(34*10^142805-601)/9142806Robert Price07/2022
284937456^6493+6493^37456142799Hans Havermann05/2021
285035141^11572+11572^35141142793Hans Havermann05/2021
285132231^26908+26908^32231142780Hans Havermann05/2021
2852(3*2^474166+1)/7142738Lelio R Paula08/2015
28532^474053+2897142705Lelio R Paula08/2012
2854(10^142699+359)/9142699Serge Batalov12/2014
2855898^48311-897^48311142676Jean-Louis Charton12/2012
28562^473740-1856639142610Enzo Doria09/2015
2857(25*10^142573-403)/9142574Robert Price12/2020
28582^473617-114223142573Enzo Doria12/2014
285936115^8856+8856^36115142555Hans Havermann05/2021
28602^473257+1873217142465Enzo Doria06/2016
2861(19*2^473242+1)/11142461Lelio R Paula09/2015
286232750^22371+22371^32750142453Hans Havermann06/2021
2863(61*10^142446-1)/3142448Robert Price01/2020
2864(14*10^142440+61)/3142441Robert Price12/2018
2865(10^142425+359)/9142425Serge Batalov12/2014
28662^473101+773027142418Enzo Doria05/2016
2867(13*2^472838-1)/3142340Lelio R Paula09/2015
2868(17*2^472789-1)/187347142320Lelio R Paula09/2015
286936915^7162+7162^36915142309Hans Havermann05/2021
28702^472634-109511142278Enzo Doria04/2014
287131870^28997+28997^31870142216Hans Havermann06/2021
2872(48^84589+1)/49142213Robert Price01/2014
28737*10^142189+87142190Robert Price07/2019
28742^472258+7142164Lelio R Paula08/2015
287540135^3484+3484^40135142162Hans Havermann05/2021
2876(23*10^142105+91)/3142106Robert Price08/2019
2877tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2878(11*2^471913-1)/21142060Lelio R Paula09/2015
2879(16*10^142058+197)/3142059Robert Price04/2019
28809*10^142037+91142038Robert Price10/2020
2881(4*10^142034+17)/3142035Tyler Busby01/2023
28822^471792+1880881142024Enzo Doria11/2016
2883(509*10^142018+31)/9142020Robert Price08/2022
2884(31*2^471580-1)/135141960Lelio R Paula08/2015
2885(4*10^141926-79)/3141927Robert Price02/2018
28862^471464-111546435141925Paul Bourdelais10/2021
2887(904*19^110984-1)/3141924Curtis Bright05/2015
2888(14*10^141853+37)/3141854Robert Price12/2018
2889(41*10^141836-59)/9141837Robert Price10/2018
28904*5^202913-9141831Lelio R Paula04/2015
28912*7^167812-3141818Lelio R Paula12/2014
28922^471043+35141799Robert Price11/2015
2893(11*2^470956-1)/7945141770Lelio R Paula08/2015
289443636^1773+1773^43636141761Hans Havermann05/2021
2895(2*10^141751-17)/3141751Serge Batalov11/2022
2896(53*10^141722-611)/9141723Robert Price02/2022
2897(11*10^141718-131)/3141719Robert Price09/2018
2898(61*10^141716+47)/9141717Robert Price07/2022
28992^470692+76771141693Enzo Doria05/2016
290050160^667+667^50160141659Hans Havermann05/2021
290131522^31181+31181^31522141657Hans Havermann05/2021
290233076^19135+19135^33076141626Hans Havermann04/2021
2903(91*10^141610+71)/9141612Robert Price01/2022
2904(21*2^470391+1)/533141601Lelio R Paula09/2015
2905(5*10^141594-23)/9141594Serge Batalov11/2022
290631932^27155+27155^31932141582Hans Havermann05/2021
290736449^7660+7660^36449141577Hans Havermann05/2021
29082^470305-459373141576Enzo Doria05/2015
290932195^24936+24936^32195141556Hans Havermann05/2021
29102^470183+72623141540Enzo Doria04/2016
29112^470173-16465141537Enzo Doria04/2013
291237297^6234+6234^37297141534Hans Havermann05/2021
2913(509*10^141479+13)/9141481Robert Price05/2022
291444*10^141476+9141478Robert Price10/2020
29152^469974-1841141477Enzo Doria05/2014
2916(23*2^469939+1)/25141466Lelio R Paula08/2015
29172*10^141448+63141449Robert Price05/2018
29182^469824+43141432Lelio R Paula09/2017
29192*10^141407-27141408Robert Price05/2018
2920(214*10^141385-1)/3141387Robert Price01/2021
29212^469630-59711141373Enzo Doria10/2015
292235277^10172+10172^35277141370Hans Havermann04/2021
292333397^17100+17100^33397141370Hans Havermann04/2021
2924(25*10^141366-331)/9141367Robert Price08/2018
292536986^6639+6639^36986141365Hans Havermann06/2021
292634572^12271+12271^34572141361Hans Havermann06/2021
292737179^6338+6338^37179141353Hans Havermann05/2021
2928(2^469564-3)/611141351Lelio R Paula08/2015
2929197^61601+2141342Lelio R Paula08/2017
293033420^16951+16951^33420141340Hans Havermann05/2021
293131623^29458+29458^31623141330Hans Havermann05/2021
293248112^865+865^48112141306Hans Havermann05/2021
29332^469372-112949141296Enzo Doria07/2014
29345*10^141294-63141295Robert Price04/2021
29353^296115+4141283Tyler NeSmith01/2021
2936(64*10^141256+161)/9141257Robert Price08/2022
2937143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2938143^65536+106^65536141253Serge Batalov03/2018
2939(11*10^141243-23)/3141244Robert Price09/2021
29412^469198+782569141243Enzo Doria10/2016
294038129^5062+5062^38129141243Hans Havermann05/2021
29422^469076-2786939141206Enzo Doria11/2015
294338630^4521+4521^38630141202Hans Havermann05/2021
294431755^27836+27836^31755141139Hans Havermann05/2021
294535554^9325+9325^35554141137Hans Havermann05/2021
29462^468804+1874941141125Enzo Doria06/2016
29472^468787+81353141119Enzo Doria08/2016
29482^468595-350407141062Enzo Doria06/2015
29492^468564+87855141052Lelio R Paula01/2016
29502^468551-21987141048Enzo Doria07/2013
29512^468523-7141040Lelio R Paula08/2015
2952(25*10^141019-13)/3141020Robert Price09/2019
29532^468405+87855141004Lelio R Paula01/2016
295439338^3831+3831^39338140961Hans Havermann05/2021
295531458^30239+30239^31458140950Hans Havermann05/2021
29568*10^140932+29140933Robert Price11/2021
295733166^17691+17691^33166140881Hans Havermann06/2021
29582^467978-113051140876Enzo Doria07/2014
29592^467780-344429140816Enzo Doria07/2015
29609*10^140802-89140803Robert Price04/2020
29612^467605-1855603140764Enzo Doria09/2015
29625*10^140744-7140745Robert Price09/2015
2963(5^201359-1)/4140744Paul Bourdelais12/2008
29642^467401-1850023140702Enzo Doria08/2015
2965(266*10^140681-17)/3140683Robert Price07/2020
2966(2^467270+78557)/23247140658Lelio R Paula07/2015
296732138^23781+23781^32138140644Hans Havermann05/2021
296831654^27735+27735^31654140640Hans Havermann05/2021
2969(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
29702^467166-1854941140631Enzo Doria09/2015
2971(203*10^140615-11)/3140617Robert Price12/2020
2972(85*10^140609+473)/9140610Robert Price01/2020
297339231^3836+3836^39231140600Hans Havermann06/2021
29742^466866-1840571140541Enzo Doria06/2015
29752^466829-459523140530Enzo Doria05/2015
29762^466692-113213140489Enzo Doria07/2014
297723*10^140464-3140466Robert Price10/2021
2978(2*10^140461-17)/3140461Serge Batalov11/2022
297931335^30364+30364^31335140455Hans Havermann05/2021
298032795^19126+19126^32795140416Hans Havermann05/2021
2981(44*10^140410-503)/9140411Robert Price12/2018
2982153^64265-2140400Lelio R Paula11/2017
2983(112*10^140357-1)/3140359Serge Batalov12/2014
2984(29*10^140337-17)/3140338Robert Price09/2019
29852^466181-112735140335Enzo Doria07/2014
2986(16*10^140290-37)/3140291Robert Price05/2021
2987(5*10^140281-119)/3140282Robert Price03/2018
298834568^11415+11415^34568140259Hans Havermann05/2021
2989(27*2^465872+1)/691140241Lelio R Paula08/2015
299033632^14781+14781^33632140236Hans Havermann05/2021
299131803^25670+25670^31803140233Hans Havermann05/2021
29922^465803-114817140221Enzo Doria05/2015
2993floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
29942^465503-112735140131Enzo Doria07/2014
2995(16*10^140091+167)/3140092Robert Price06/2019
2996(8*10^140087-137)/3140088Robert Price03/2022
29976^179964+179964^6-1140040Robert Price04/2014
2998(89*10^140008-179)/9140009Robert Price12/2019
2999(29*2^465077-1)/9140003Lelio R Paula08/2015
30002^465072-344789140001Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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