PRP Records

Probable Primes Top 10000

(292102 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 ?
275170^78989-69^78989145743Robert Price01/2014
275251^85334+2145714Robert Price07/2015
27532^483886-1857101145665Enzo Doria10/2015
275433350^23307+23307^33350145656Hans Havermann01/2021
2755(19*10^145585+131)/3145586Robert Price06/2020
27562^483563-1863457145567Enzo Doria12/2015
27574*10^145563-69145564Robert Price01/2022
27582^483516-1861409145553Enzo Doria11/2015
27592^483384-115019145514Enzo Doria06/2015
2760(259*10^145501-1)/3145503Robert Price12/2020
2761(19*10^145499-61)/3145500Robert Price05/2019
27622^483302-3221145489Lelio R Paula12/2012
2763(23*10^145463+61)/3145464Robert Price01/2022
276435523^12434+12434^35523145453Hans Havermann01/2021
27652^483046+1874029145412Enzo Doria06/2016
27662^482991-2789317145395Enzo Doria12/2015
27672^482978-2789711145391Enzo Doria12/2015
27682^482966-2789711145388Enzo Doria12/2015
27692^482817-1858843145343Enzo Doria10/2015
27702^482751-113635145323Enzo Doria08/2014
27712^482705-459763145309Enzo Doria05/2015
2772(4^241306+11)/3145281Robert Price03/2017
2773(238*10^145276-1)/3145278Robert Price04/2020
2774(19*2^482534+1)/7145258Lelio R Paula09/2015
277553^84239-52^84239145252Robert Price01/2013
277647952^1067+1067^47952145207Hans Havermann01/2021
2777(2^482333+5)/9287145193Lelio R Paula09/2015
27782^482087+72623145123Enzo Doria04/2016
27792^482016-286565145102Enzo Doria07/2015
2780(19*10^145093+101)/3145094Robert Price09/2019
27812^481956+121145084Stefano Morozzi04/2021
27822^481840+15145049Robert Price09/2015
27832^481801-481801145037Henri Lifchitz03/2005
27842^481775+1869083145029Enzo Doria05/2016
278529^99167+2145022Ray Chandler08/2011
27862^481663+1875653144996Enzo Doria07/2016
27878*10^144977+27144978Robert Price09/2021
278836486^9379+9379^36486144929Hans Havermann12/2020
278935111^13378+13378^35111144882Hans Havermann01/2021
27902^481149-459073144841Enzo Doria05/2015
279134619^15246+15246^34619144817Hans Havermann01/2021
27922^481045-113215144809Enzo Doria07/2014
2793(64*10^144797+287)/9144798Robert Price04/2019
27942^480859-113695144753Enzo Doria09/2014
2795(106*10^144744+17)/3144746Robert Price04/2021
27967*10^144742-27144743Robert Price11/2022
27972^480766-2787191144725Enzo Doria11/2015
2798(21*27^101106-151)/26144720Curtis Bright05/2015
27992^480678+1874239144699Enzo Doria06/2016
2800(8*10^144683+1)/9144683Serge Batalov05/2010
2801L(692147)144651Henri Lifchitz10/2008
2802(76*10^144648+77)/9144649Robert Price10/2019
280332672^26721+26721^32672144635Hans Havermann01/2021
28042^480417+35144620Robert Price11/2015
28052^480296-59879144584Enzo Doria10/2015
280633157^22878+22878^33157144546Hans Havermann12/2020
280745494^1497+1497^45494144454Hans Havermann12/2020
28082^479844+3144448Donovan Johnson06/2006
280933442^20803+20803^33442144407Hans Havermann01/2021
281031892^32061-32061^31892144393Norbert Schneider01/2023
2811(27*2^479642+1)/733144386Lelio R Paula08/2015
2812(56*10^144380+169)/9144381Robert Price03/2022
281344917^1638+1638^44917144378Hans Havermann12/2020
2814(21*2^479605-1)/11144376Lelio R Paula09/2015
2815(56*10^144336+583)/9144337Robert Price08/2021
28162^479348-2792219144299Enzo Doria02/2016
28173^302389-6242144277Enzo Doria05/2014
281833778^18641+18641^33778144248Hans Havermann01/2021
28192*10^144220-3144221Robert Price07/2015
28202^478904-109109144165Enzo Doria04/2014
282143698^1987+1987^43698144125Hans Havermann12/2020
282236128^9723+9723^36128144072Hans Havermann01/2021
282332817^24518+24518^32817144050Hans Havermann12/2020
2824(772*10^144036-7)/9144038Robert Price06/2022
282534295^15828+15828^34295144020Hans Havermann01/2021
28262^478337-115333143994Enzo Doria07/2015
2827(7*2^478330-1)/3143993Lelio R Paula08/2015
282888^74047-87^74047143984Robert Price05/2015
282933242^21441+21441^33242143980Hans Havermann01/2021
2830(19*10^143963+467)/9143964Robert Price02/2018
2831(71^77761+1)/72143954Paul Bourdelais09/2017
283233490^19859+19859^33490143939Hans Havermann01/2021
2833(853*10^143931-7)/9143933Robert Price07/2021
28342^478088+27143919Robert Price11/2015
2835(8*10^143898-137)/3143899Robert Price03/2022
28367*10^143857-93143858Robert Price08/2020
28373*10^143844+61143845Robert Price09/2020
283841358^3005+3005^41358143837Hans Havermann01/2021
28392^477475-22071143735Enzo Doria07/2013
28402^477417-22123143717Enzo Doria07/2013
28412^477359-3577143700Yves Minet03/2017
284239435^4402+4402^39435143688Hans Havermann01/2021
2843(14*10^143662-71)/3143663Robert Price12/2018
28446^184614+5143658Paul Bourdelais01/2021
284546371^1252+1252^46371143640Hans Havermann12/2020
284634975^12748+12748^34975143588Hans Havermann01/2021
28472^476936-396765143573Enzo Doria07/2013
28482^476888-2791229143558Enzo Doria01/2016
28492^476868-1859939143552Enzo Doria11/2015
285040807^3294+3294^40807143548Hans Havermann12/2020
2851755^49878+49878^755143547Norbert Schneider04/2019
2852(19^112247-4^112247)/15143536Robert Price03/2021
285335561^10872+10872^35561143536Hans Havermann06/2021
285437637^6492+6492^37637143487Hans Havermann05/2021
285561567^214+214^61567143477Hans Havermann05/2021
28562^476558-113627143459Enzo Doria08/2014
28572^476478-45143435Lelio R Paula11/2017
285836380^8757+8757^36380143423Hans Havermann06/2021
285932510^25707+25707^32510143371Hans Havermann05/2021
28608*10^143361+17143362Robert Price07/2021
2861(2^475854+9)/73143245Lelio R Paula08/2015
28622^475813-113239143234Enzo Doria07/2014
2863(19*10^143212+137)/3143213Robert Price03/2022
286432218^27849+27849^32218143203Hans Havermann04/2021
28652^475624-114059143178Enzo Doria11/2014
2866(11*2^475553-7)/15143156Renaud Lifchitz03/2011
28672^475480-2786129143134Enzo Doria10/2015
286833912^16621+16621^33912143131Hans Havermann05/2021
2869(19*10^143129-43)/3143130Robert Price05/2019
287031830^31373+31373^31830143126Hans Havermann05/2021
28716*10^143105-53143106Robert Price05/2021
2872(14*10^143097+73)/3143098Robert Price12/2018
28732^475299-111937143080Enzo Doria05/2014
287435488^10753+10753^35488143071Hans Havermann04/2021
28752^475160-2797859143038Enzo Doria04/2016
2876(2^475069+3)/395143008Lelio R Paula08/2015
28772^475027-461437142998Enzo Doria07/2015
2878(2^474958+78557)/3142977Lelio R Paula07/2015
2879(8*10^142932+43)/3142933Robert Price06/2018
288035055^11942+11942^35055142922Hans Havermann05/2021
288137650^6239+6239^37650142887Hans Havermann05/2021
2882(54^82471-1)/53142871Paul Bourdelais09/2017
2883(11*2^474432-1)/95142818Lelio R Paula09/2015
28842^474417-59923142814Enzo Doria10/2015
28854*10^142810-21142811Robert Price09/2018
288632287^26494+26494^32287142811Hans Havermann06/2021
288737162^6965+6965^37162142811Hans Havermann06/2021
2888(34*10^142805-601)/9142806Robert Price07/2022
288937456^6493+6493^37456142799Hans Havermann05/2021
289035141^11572+11572^35141142793Hans Havermann05/2021
289132231^26908+26908^32231142780Hans Havermann05/2021
2892(3*2^474166+1)/7142738Lelio R Paula08/2015
28932^474053+2897142705Lelio R Paula08/2012
2894(10^142699+359)/9142699Serge Batalov12/2014
2895898^48311-897^48311142676Jean-Louis Charton12/2012
28962^473740-1856639142610Enzo Doria09/2015
2897(25*10^142573-403)/9142574Robert Price12/2020
28982^473617-114223142573Enzo Doria12/2014
289936115^8856+8856^36115142555Hans Havermann05/2021
29002^473257+1873217142465Enzo Doria06/2016
2901(19*2^473242+1)/11142461Lelio R Paula09/2015
290232750^22371+22371^32750142453Hans Havermann06/2021
2903(61*10^142446-1)/3142448Robert Price01/2020
2904(14*10^142440+61)/3142441Robert Price12/2018
2905(10^142425+359)/9142425Serge Batalov12/2014
29062^473101+773027142418Enzo Doria05/2016
2907(13*2^472838-1)/3142340Lelio R Paula09/2015
2908(17*2^472789-1)/187347142320Lelio R Paula09/2015
290936915^7162+7162^36915142309Hans Havermann05/2021
29102^472634-109511142278Enzo Doria04/2014
291131870^28997+28997^31870142216Hans Havermann06/2021
2912(48^84589+1)/49142213Robert Price01/2014
29137*10^142189+87142190Robert Price07/2019
29142^472258+7142164Lelio R Paula08/2015
291540135^3484+3484^40135142162Hans Havermann05/2021
2916(23*10^142105+91)/3142106Robert Price08/2019
2917tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2918(11*2^471913-1)/21142060Lelio R Paula09/2015
2919(16*10^142058+197)/3142059Robert Price04/2019
29209*10^142037+91142038Robert Price10/2020
2921(4*10^142034+17)/3142035Tyler Busby01/2023
29222^471792+1880881142024Enzo Doria11/2016
2923(509*10^142018+31)/9142020Robert Price08/2022
2924(31*2^471580-1)/135141960Lelio R Paula08/2015
2925(4*10^141926-79)/3141927Robert Price02/2018
29262^471464-111546435141925Paul Bourdelais10/2021
2927(904*19^110984-1)/3141924Curtis Bright05/2015
2928(14*10^141853+37)/3141854Robert Price12/2018
2929(41*10^141836-59)/9141837Robert Price10/2018
29304*5^202913-9141831Lelio R Paula04/2015
29312*7^167812-3141818Lelio R Paula12/2014
29322^471043+35141799Robert Price11/2015
2933(11*2^470956-1)/7945141770Lelio R Paula08/2015
293443636^1773+1773^43636141761Hans Havermann05/2021
2935(2*10^141751-17)/3141751Serge Batalov11/2022
2936(53*10^141722-611)/9141723Robert Price02/2022
2937(11*10^141718-131)/3141719Robert Price09/2018
2938(61*10^141716+47)/9141717Robert Price07/2022
29392^470692+76771141693Enzo Doria05/2016
294050160^667+667^50160141659Hans Havermann05/2021
294131522^31181+31181^31522141657Hans Havermann05/2021
294233076^19135+19135^33076141626Hans Havermann04/2021
2943(91*10^141610+71)/9141612Robert Price01/2022
2944(21*2^470391+1)/533141601Lelio R Paula09/2015
2945(5*10^141594-23)/9141594Serge Batalov11/2022
294631932^27155+27155^31932141582Hans Havermann05/2021
294736449^7660+7660^36449141577Hans Havermann05/2021
29482^470305-459373141576Enzo Doria05/2015
294932195^24936+24936^32195141556Hans Havermann05/2021
29502^470183+72623141540Enzo Doria04/2016
29512^470173-16465141537Enzo Doria04/2013
295237297^6234+6234^37297141534Hans Havermann05/2021
2953(509*10^141479+13)/9141481Robert Price05/2022
295444*10^141476+9141478Robert Price10/2020
29552^469974-1841141477Enzo Doria05/2014
2956(23*2^469939+1)/25141466Lelio R Paula08/2015
29572*10^141448+63141449Robert Price05/2018
29582^469824+43141432Lelio R Paula09/2017
29592*10^141407-27141408Robert Price05/2018
2960(214*10^141385-1)/3141387Robert Price01/2021
29612^469630-59711141373Enzo Doria10/2015
296235277^10172+10172^35277141370Hans Havermann04/2021
296333397^17100+17100^33397141370Hans Havermann04/2021
2964(25*10^141366-331)/9141367Robert Price08/2018
296536986^6639+6639^36986141365Hans Havermann06/2021
296634572^12271+12271^34572141361Hans Havermann06/2021
296737179^6338+6338^37179141353Hans Havermann05/2021
2968(2^469564-3)/611141351Lelio R Paula08/2015
2969197^61601+2141342Lelio R Paula08/2017
297033420^16951+16951^33420141340Hans Havermann05/2021
297131623^29458+29458^31623141330Hans Havermann05/2021
297248112^865+865^48112141306Hans Havermann05/2021
29732^469372-112949141296Enzo Doria07/2014
29745*10^141294-63141295Robert Price04/2021
29753^296115+4141283Tyler NeSmith01/2021
2976(64*10^141256+161)/9141257Robert Price08/2022
2977143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2978143^65536+106^65536141253Serge Batalov03/2018
2979(11*10^141243-23)/3141244Robert Price09/2021
29812^469198+782569141243Enzo Doria10/2016
298038129^5062+5062^38129141243Hans Havermann05/2021
29822^469076-2786939141206Enzo Doria11/2015
298338630^4521+4521^38630141202Hans Havermann05/2021
298431755^27836+27836^31755141139Hans Havermann05/2021
298535554^9325+9325^35554141137Hans Havermann05/2021
29862^468804+1874941141125Enzo Doria06/2016
29872^468787+81353141119Enzo Doria08/2016
29882^468595-350407141062Enzo Doria06/2015
29892^468564+87855141052Lelio R Paula01/2016
29902^468551-21987141048Enzo Doria07/2013
29912^468523-7141040Lelio R Paula08/2015
2992(25*10^141019-13)/3141020Robert Price09/2019
29932^468405+87855141004Lelio R Paula01/2016
299439338^3831+3831^39338140961Hans Havermann05/2021
299531458^30239+30239^31458140950Hans Havermann05/2021
29968*10^140932+29140933Robert Price11/2021
299733166^17691+17691^33166140881Hans Havermann06/2021
29982^467978-113051140876Enzo Doria07/2014
29992^467780-344429140816Enzo Doria07/2015
30009*10^140802-89140803Robert Price04/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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