PRP Records

Probable Primes Top 10000

(290751 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 ?
250151^85334+2145714Robert Price07/2015
25022^483886-1857101145665Enzo Doria10/2015
250333350^23307+23307^33350145656Hans Havermann01/2021
2504(19*10^145585+131)/3145586Robert Price06/2020
25052^483563-1863457145567Enzo Doria12/2015
25064*10^145563-69145564Robert Price01/2022
25072^483516-1861409145553Enzo Doria11/2015
25082^483384-115019145514Enzo Doria06/2015
2509(259*10^145501-1)/3145503Robert Price12/2020
2510(19*10^145499-61)/3145500Robert Price05/2019
25112^483302-3221145489Lelio R Paula12/2012
2512(23*10^145463+61)/3145464Robert Price01/2022
251335523^12434+12434^35523145453Hans Havermann01/2021
25142^483046+1874029145412Enzo Doria06/2016
25152^482991-2789317145395Enzo Doria12/2015
25162^482978-2789711145391Enzo Doria12/2015
25172^482966-2789711145388Enzo Doria12/2015
25182^482817-1858843145343Enzo Doria10/2015
25192^482751-113635145323Enzo Doria08/2014
25202^482705-459763145309Enzo Doria05/2015
2521(4^241306+11)/3145281Robert Price03/2017
2522(238*10^145276-1)/3145278Robert Price04/2020
2523(19*2^482534+1)/7145258Lelio R Paula09/2015
252453^84239-52^84239145252Robert Price01/2013
252547952^1067+1067^47952145207Hans Havermann01/2021
2526(2^482333+5)/9287145193Lelio R Paula09/2015
25272^482087+72623145123Enzo Doria04/2016
25282^482016-286565145102Enzo Doria07/2015
2529(19*10^145093+101)/3145094Robert Price09/2019
25302^481956+121145084Stefano Morozzi04/2021
25312^481840+15145049Robert Price09/2015
25322^481801-481801145037Henri Lifchitz03/2005
25332^481775+1869083145029Enzo Doria05/2016
253429^99167+2145022Ray Chandler08/2011
25352^481663+1875653144996Enzo Doria07/2016
25368*10^144977+27144978Robert Price09/2021
253736486^9379+9379^36486144929Hans Havermann12/2020
253835111^13378+13378^35111144882Hans Havermann01/2021
25392^481149-459073144841Enzo Doria05/2015
254034619^15246+15246^34619144817Hans Havermann01/2021
25412^481045-113215144809Enzo Doria07/2014
2542(64*10^144797+287)/9144798Robert Price04/2019
25432^480859-113695144753Enzo Doria09/2014
2544(106*10^144744+17)/3144746Robert Price04/2021
25452^480766-2787191144725Enzo Doria11/2015
2546(21*27^101106-151)/26144720Curtis Bright05/2015
25472^480678+1874239144699Enzo Doria06/2016
2548(8*10^144683+1)/9144683Serge Batalov05/2010
2549L(692147)144651Henri Lifchitz10/2008
2550(76*10^144648+77)/9144649Robert Price10/2019
255132672^26721+26721^32672144635Hans Havermann01/2021
25522^480417+35144620Robert Price11/2015
25532^480296-59879144584Enzo Doria10/2015
255433157^22878+22878^33157144546Hans Havermann12/2020
255545494^1497+1497^45494144454Hans Havermann12/2020
25562^479844+3144448Donovan Johnson06/2006
255733442^20803+20803^33442144407Hans Havermann01/2021
2558(27*2^479642+1)/733144386Lelio R Paula08/2015
2559(56*10^144380+169)/9144381Robert Price03/2022
256044917^1638+1638^44917144378Hans Havermann12/2020
2561(21*2^479605-1)/11144376Lelio R Paula09/2015
2562(56*10^144336+583)/9144337Robert Price08/2021
25632^479348-2792219144299Enzo Doria02/2016
25643^302389-6242144277Enzo Doria05/2014
256533778^18641+18641^33778144248Hans Havermann01/2021
25662*10^144220-3144221Robert Price07/2015
25672^478904-109109144165Enzo Doria04/2014
256843698^1987+1987^43698144125Hans Havermann12/2020
256936128^9723+9723^36128144072Hans Havermann01/2021
257032817^24518+24518^32817144050Hans Havermann12/2020
2571(772*10^144036-7)/9144038Robert Price06/2022
257234295^15828+15828^34295144020Hans Havermann01/2021
25732^478337-115333143994Enzo Doria07/2015
2574(7*2^478330-1)/3143993Lelio R Paula08/2015
257588^74047-87^74047143984Robert Price05/2015
257633242^21441+21441^33242143980Hans Havermann01/2021
2577(19*10^143963+467)/9143964Robert Price02/2018
2578(71^77761+1)/72143954Paul Bourdelais09/2017
257933490^19859+19859^33490143939Hans Havermann01/2021
2580(853*10^143931-7)/9143933Robert Price07/2021
25812^478088+27143919Robert Price11/2015
2582(8*10^143898-137)/3143899Robert Price03/2022
25837*10^143857-93143858Robert Price08/2020
25843*10^143844+61143845Robert Price09/2020
258541358^3005+3005^41358143837Hans Havermann01/2021
25862^477475-22071143735Enzo Doria07/2013
25872^477417-22123143717Enzo Doria07/2013
25882^477359-3577143700Yves Minet03/2017
258939435^4402+4402^39435143688Hans Havermann01/2021
2590(14*10^143662-71)/3143663Robert Price12/2018
25916^184614+5143658Paul Bourdelais01/2021
259246371^1252+1252^46371143640Hans Havermann12/2020
259334975^12748+12748^34975143588Hans Havermann01/2021
25942^476936-396765143573Enzo Doria07/2013
25952^476888-2791229143558Enzo Doria01/2016
25962^476868-1859939143552Enzo Doria11/2015
259740807^3294+3294^40807143548Hans Havermann12/2020
2598755^49878+49878^755143547Norbert Schneider04/2019
2599(19^112247-4^112247)/15143536Robert Price03/2021
260035561^10872+10872^35561143536Hans Havermann06/2021
260137637^6492+6492^37637143487Hans Havermann05/2021
260261567^214+214^61567143477Hans Havermann05/2021
26032^476558-113627143459Enzo Doria08/2014
26042^476478-45143435Lelio R Paula11/2017
260536380^8757+8757^36380143423Hans Havermann06/2021
260632510^25707+25707^32510143371Hans Havermann05/2021
26078*10^143361+17143362Robert Price07/2021
2608(2^475854+9)/73143245Lelio R Paula08/2015
26092^475813-113239143234Enzo Doria07/2014
2610(19*10^143212+137)/3143213Robert Price03/2022
261132218^27849+27849^32218143203Hans Havermann04/2021
26122^475624-114059143178Enzo Doria11/2014
2613(11*2^475553-7)/15143156Renaud Lifchitz03/2011
26142^475480-2786129143134Enzo Doria10/2015
261533912^16621+16621^33912143131Hans Havermann05/2021
2616(19*10^143129-43)/3143130Robert Price05/2019
261731830^31373+31373^31830143126Hans Havermann05/2021
26186*10^143105-53143106Robert Price05/2021
2619(14*10^143097+73)/3143098Robert Price12/2018
26202^475299-111937143080Enzo Doria05/2014
262135488^10753+10753^35488143071Hans Havermann04/2021
26222^475160-2797859143038Enzo Doria04/2016
2623(2^475069+3)/395143008Lelio R Paula08/2015
26242^475027-461437142998Enzo Doria07/2015
2625(2^474958+78557)/3142977Lelio R Paula07/2015
2626(8*10^142932+43)/3142933Robert Price06/2018
262735055^11942+11942^35055142922Hans Havermann05/2021
262837650^6239+6239^37650142887Hans Havermann05/2021
2629(54^82471-1)/53142871Paul Bourdelais09/2017
2630(11*2^474432-1)/95142818Lelio R Paula09/2015
26312^474417-59923142814Enzo Doria10/2015
26324*10^142810-21142811Robert Price09/2018
263332287^26494+26494^32287142811Hans Havermann06/2021
263437162^6965+6965^37162142811Hans Havermann06/2021
263537456^6493+6493^37456142799Hans Havermann05/2021
263635141^11572+11572^35141142793Hans Havermann05/2021
263732231^26908+26908^32231142780Hans Havermann05/2021
2638(3*2^474166+1)/7142738Lelio R Paula08/2015
26392^474053+2897142705Lelio R Paula08/2012
2640(10^142699+359)/9142699Serge Batalov12/2014
2641898^48311-897^48311142676Jean-Louis Charton12/2012
26422^473740-1856639142610Enzo Doria09/2015
2643(25*10^142573-403)/9142574Robert Price12/2020
26442^473617-114223142573Enzo Doria12/2014
264536115^8856+8856^36115142555Hans Havermann05/2021
26462^473257+1873217142465Enzo Doria06/2016
2647(19*2^473242+1)/11142461Lelio R Paula09/2015
264832750^22371+22371^32750142453Hans Havermann06/2021
2649(61*10^142446-1)/3142448Robert Price01/2020
2650(14*10^142440+61)/3142441Robert Price12/2018
2651(10^142425+359)/9142425Serge Batalov12/2014
26522^473101+773027142418Enzo Doria05/2016
2653(13*2^472838-1)/3142340Lelio R Paula09/2015
2654(17*2^472789-1)/187347142320Lelio R Paula09/2015
265536915^7162+7162^36915142309Hans Havermann05/2021
26562^472634-109511142278Enzo Doria04/2014
265731870^28997+28997^31870142216Hans Havermann06/2021
2658(48^84589+1)/49142213Robert Price01/2014
26597*10^142189+87142190Robert Price07/2019
26602^472258+7142164Lelio R Paula08/2015
266140135^3484+3484^40135142162Hans Havermann05/2021
2662(23*10^142105+91)/3142106Robert Price08/2019
2663tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2664(11*2^471913-1)/21142060Lelio R Paula09/2015
2665(16*10^142058+197)/3142059Robert Price04/2019
26669*10^142037+91142038Robert Price10/2020
26672^471792+1880881142024Enzo Doria11/2016
2668(31*2^471580-1)/135141960Lelio R Paula08/2015
2669(4*10^141926-79)/3141927Robert Price02/2018
26702^471464-111546435141925Paul Bourdelais10/2021
2671(904*19^110984-1)/3141924Curtis Bright05/2015
2672(14*10^141853+37)/3141854Robert Price12/2018
2673(41*10^141836-59)/9141837Robert Price10/2018
26744*5^202913-9141831Lelio R Paula04/2015
26752*7^167812-3141818Lelio R Paula12/2014
26762^471043+35141799Robert Price11/2015
2677(11*2^470956-1)/7945141770Lelio R Paula08/2015
267843636^1773+1773^43636141761Hans Havermann05/2021
2679(53*10^141722-611)/9141723Robert Price02/2022
2680(11*10^141718-131)/3141719Robert Price09/2018
26812^470692+76771141693Enzo Doria05/2016
268250160^667+667^50160141659Hans Havermann05/2021
268331522^31181+31181^31522141657Hans Havermann05/2021
268433076^19135+19135^33076141626Hans Havermann04/2021
2685(91*10^141610+71)/9141612Robert Price01/2022
2686(21*2^470391+1)/533141601Lelio R Paula09/2015
268731932^27155+27155^31932141582Hans Havermann05/2021
268836449^7660+7660^36449141577Hans Havermann05/2021
26892^470305-459373141576Enzo Doria05/2015
269032195^24936+24936^32195141556Hans Havermann05/2021
26912^470183+72623141540Enzo Doria04/2016
26922^470173-16465141537Enzo Doria04/2013
269337297^6234+6234^37297141534Hans Havermann05/2021
2694(509*10^141479+13)/9141481Robert Price05/2022
269544*10^141476+9141478Robert Price10/2020
26962^469974-1841141477Enzo Doria05/2014
2697(23*2^469939+1)/25141466Lelio R Paula08/2015
26982*10^141448+63141449Robert Price05/2018
26992^469824+43141432Lelio R Paula09/2017
27002*10^141407-27141408Robert Price05/2018
2701(214*10^141385-1)/3141387Robert Price01/2021
27022^469630-59711141373Enzo Doria10/2015
270335277^10172+10172^35277141370Hans Havermann04/2021
270433397^17100+17100^33397141370Hans Havermann04/2021
2705(25*10^141366-331)/9141367Robert Price08/2018
270636986^6639+6639^36986141365Hans Havermann06/2021
270734572^12271+12271^34572141361Hans Havermann06/2021
270837179^6338+6338^37179141353Hans Havermann05/2021
2709(2^469564-3)/611141351Lelio R Paula08/2015
2710197^61601+2141342Lelio R Paula08/2017
271133420^16951+16951^33420141340Hans Havermann05/2021
271231623^29458+29458^31623141330Hans Havermann05/2021
271348112^865+865^48112141306Hans Havermann05/2021
27142^469372-112949141296Enzo Doria07/2014
27155*10^141294-63141295Robert Price04/2021
27163^296115+4141283Tyler NeSmith01/2021
2718143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2717143^65536+106^65536141253Serge Batalov03/2018
2719(11*10^141243-23)/3141244Robert Price09/2021
27212^469198+782569141243Enzo Doria10/2016
272038129^5062+5062^38129141243Hans Havermann05/2021
27222^469076-2786939141206Enzo Doria11/2015
272338630^4521+4521^38630141202Hans Havermann05/2021
272431755^27836+27836^31755141139Hans Havermann05/2021
272535554^9325+9325^35554141137Hans Havermann05/2021
27262^468804+1874941141125Enzo Doria06/2016
27272^468787+81353141119Enzo Doria08/2016
27282^468595-350407141062Enzo Doria06/2015
27292^468564+87855141052Lelio R Paula01/2016
27302^468551-21987141048Enzo Doria07/2013
27312^468523-7141040Lelio R Paula08/2015
2732(25*10^141019-13)/3141020Robert Price09/2019
27332^468405+87855141004Lelio R Paula01/2016
273439338^3831+3831^39338140961Hans Havermann05/2021
273531458^30239+30239^31458140950Hans Havermann05/2021
27368*10^140932+29140933Robert Price11/2021
273733166^17691+17691^33166140881Hans Havermann06/2021
27382^467978-113051140876Enzo Doria07/2014
27392^467780-344429140816Enzo Doria07/2015
27409*10^140802-89140803Robert Price04/2020
27412^467605-1855603140764Enzo Doria09/2015
27425*10^140744-7140745Robert Price09/2015
2743(5^201359-1)/4140744Paul Bourdelais12/2008
27442^467401-1850023140702Enzo Doria08/2015
2745(266*10^140681-17)/3140683Robert Price07/2020
2746(2^467270+78557)/23247140658Lelio R Paula07/2015
274732138^23781+23781^32138140644Hans Havermann05/2021
274831654^27735+27735^31654140640Hans Havermann05/2021
2749(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
27502^467166-1854941140631Enzo Doria09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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