PRP Records

Probable Primes Top 10000

(288515 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 ?
225140656^4289+4289^40656147678Hans Havermann11/2020
22522^490550+1179439147671Enzo Doria06/2016
2253(23*10^147649-59)/9147650Robert Price05/2018
22542^490303+2793653147596Enzo Doria03/2016
22552^490266+255255147585Paul Bourdelais10/2021
2256199^64181-2147543Lelio R Paula11/2017
225732849^30958+30958^32849147518Hans Havermann11/2020
22582^489871-286987147466Enzo Doria07/2015
22592^489864-351899147464Enzo Doria07/2015
2260175^65724-2147422Lelio R Paula11/2017
22612^489712+1874851147419Enzo Doria06/2016
226234473^18830+18830^34473147367Hans Havermann11/2020
226363^81896-2147359Lelio R Paula10/2017
226434580^18237+18237^34580147344Hans Havermann11/2020
2265(11*10^147313-107)/3147314Robert Price09/2018
22662^489305-59815147296Enzo Doria10/2015
2267(2^489280-7)/6381147285Lelio R Paula09/2015
22682*10^147264-61147265Robert Price10/2021
22692*10^147260+29147261Robert Price02/2021
227033556^24457+24457^33556147258Hans Havermann11/2020
22712^489125+80357147242Enzo Doria06/2016
227232835^30452+30452^32835147220Hans Havermann12/2020
2273(19*10^147213-97)/3147214Robert Price10/2021
2274(148*10^147139-1)/3147141Robert Price03/2020
227534338^19255+19255^34338147123Hans Havermann11/2020
22762^488648-112799147098Enzo Doria07/2014
22772^488627-350317147092Enzo Doria06/2015
227833432^25075+25075^33432147076Hans Havermann12/2020
2279(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
22802^488280-2165146987Yves Minet07/2014
22812^488278+45146987Lelio R Paula12/2017
22822^487927-39146881Lelio R Paula12/2017
2283(7*10^146860-13)/3146861Robert Price07/2018
2284(26*10^146856-77)/3146857Robert Price11/2019
228532948^28611+28611^32948146834Hans Havermann11/2020
228642596^2799+2799^42596146829Hans Havermann12/2020
22872^487726-1863341146821Enzo Doria12/2015
228843838^2229+2229^43838146775Hans Havermann11/2020
228935005^15594+15594^35005146775Hans Havermann11/2020
2290(167*10^146764+7)/3146766Robert Price04/2021
2291((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
229232963^28234+28234^32963146711Hans Havermann12/2020
2293(22*10^146661-19)/3146662Robert Price04/2019
229433958^20825+20825^33958146651Hans Havermann12/2020
22952^487121-39523146639Enzo Doria09/2015
229661063^252+252^61063146637Hans Havermann12/2020
2297(7*2^486967+1)/39146591Lelio R Paula09/2015
229834099^19900+19900^34099146587Hans Havermann11/2020
22992^486893-79146570Yves Minet09/2017
230036818^9567+9567^36818146565Hans Havermann12/2020
23012^486840+1879141146554Enzo Doria08/2016
23022^486774-87146534Lelio R Paula12/2017
230338655^6176+6176^38655146530Hans Havermann11/2020
23048*10^146522-81146523Robert Price02/2021
230532820^29059+29059^32820146485Hans Havermann12/2020
230637261^8530+8530^37261146472Hans Havermann12/2020
230766953^154+154^66953146462Hans Havermann12/2020
230896^73877-95^73877146445Robert Price10/2015
23098*10^146421+81146422Robert Price08/2019
231033153^26090+26090^33153146420Hans Havermann11/2020
2311(52^85259+1)/53146304Paul Bourdelais09/2017
2312179^64935+2146290Lelio R Paula10/2017
231332595^30758+30758^32595146285Hans Havermann11/2020
231434972^15157+15157^34972146205Hans Havermann12/2020
2315(19*10^146181-49)/3146182Robert Price05/2019
23162^485531-114621146160Enzo Doria05/2015
23172^485473-933075146142Paul Bourdelais06/2021
2318(2^485461-9)/4249146135Lelio R Paula09/2015
23192^485389+81887146117Enzo Doria08/2016
232032554^30773+30773^32554146108Hans Havermann11/2020
2321(10^146063+71)/9146063Serge Batalov07/2015
2322(2^485119+7)/2745146032Lelio R Paula09/2015
2323(22*10^146029+257)/9146030Robert Price06/2018
23247*10^145982-53145983Robert Price06/2020
23252^484743+1872923145923Enzo Doria05/2016
232633140^25287+25287^33140145913Hans Havermann01/2021
232737875^7112+7112^37875145895Hans Havermann01/2021
232832862^27473+27473^32862145872Hans Havermann01/2021
232932836^27587+27587^32836145815Hans Havermann01/2021
23302^484341+1879157145802Enzo Doria08/2016
23312*10^145784-91145785Robert Price04/2020
23322^484271-51145781Lelio R Paula11/2017
233370^78989-69^78989145743Robert Price01/2014
233451^85334+2145714Robert Price07/2015
23352^483886-1857101145665Enzo Doria10/2015
233633350^23307+23307^33350145656Hans Havermann01/2021
2337(19*10^145585+131)/3145586Robert Price06/2020
23382^483563-1863457145567Enzo Doria12/2015
23392^483516-1861409145553Enzo Doria11/2015
23402^483384-115019145514Enzo Doria06/2015
2341(259*10^145501-1)/3145503Robert Price12/2020
2342(19*10^145499-61)/3145500Robert Price05/2019
23432^483302-3221145489Lelio R Paula12/2012
234435523^12434+12434^35523145453Hans Havermann01/2021
23452^483046+1874029145412Enzo Doria06/2016
23462^482991-2789317145395Enzo Doria12/2015
23472^482978-2789711145391Enzo Doria12/2015
23482^482966-2789711145388Enzo Doria12/2015
23492^482817-1858843145343Enzo Doria10/2015
23502^482751-113635145323Enzo Doria08/2014
23512^482705-459763145309Enzo Doria05/2015
2352(4^241306+11)/3145281Robert Price03/2017
2353(238*10^145276-1)/3145278Robert Price04/2020
2354(19*2^482534+1)/7145258Lelio R Paula09/2015
235553^84239-52^84239145252Robert Price01/2013
235647952^1067+1067^47952145207Hans Havermann01/2021
2357(2^482333+5)/9287145193Lelio R Paula09/2015
23582^482087+72623145123Enzo Doria04/2016
23592^482016-286565145102Enzo Doria07/2015
2360(19*10^145093+101)/3145094Robert Price09/2019
23612^481956+121145084Stefano Morozzi04/2021
23622^481840+15145049Robert Price09/2015
23632^481801-481801145037Henri Lifchitz03/2005
23642^481775+1869083145029Enzo Doria05/2016
236529^99167+2145022Ray Chandler08/2011
23662^481663+1875653144996Enzo Doria07/2016
23678*10^144977+27144978Robert Price09/2021
236836486^9379+9379^36486144929Hans Havermann12/2020
236935111^13378+13378^35111144882Hans Havermann01/2021
23702^481149-459073144841Enzo Doria05/2015
237134619^15246+15246^34619144817Hans Havermann01/2021
23722^481045-113215144809Enzo Doria07/2014
2373(64*10^144797+287)/9144798Robert Price04/2019
23742^480859-113695144753Enzo Doria09/2014
2375(106*10^144744+17)/3144746Robert Price04/2021
23762^480766-2787191144725Enzo Doria11/2015
2377(21*27^101106-151)/26144720Curtis Bright05/2015
23782^480678+1874239144699Enzo Doria06/2016
2379(8*10^144683+1)/9144683Serge Batalov05/2010
2380L(692147)144651Henri Lifchitz10/2008
2381(76*10^144648+77)/9144649Robert Price10/2019
238232672^26721+26721^32672144635Hans Havermann01/2021
23832^480417+35144620Robert Price11/2015
23842^480296-59879144584Enzo Doria10/2015
238533157^22878+22878^33157144546Hans Havermann12/2020
238645494^1497+1497^45494144454Hans Havermann12/2020
23872^479844+3144448Donovan Johnson06/2006
238833442^20803+20803^33442144407Hans Havermann01/2021
2389(27*2^479642+1)/733144386Lelio R Paula08/2015
239044917^1638+1638^44917144378Hans Havermann12/2020
2391(21*2^479605-1)/11144376Lelio R Paula09/2015
2392(56*10^144336+583)/9144337Robert Price08/2021
23932^479348-2792219144299Enzo Doria02/2016
23943^302389-6242144277Enzo Doria05/2014
239533778^18641+18641^33778144248Hans Havermann01/2021
23962*10^144220-3144221Robert Price07/2015
23972^478904-109109144165Enzo Doria04/2014
239843698^1987+1987^43698144125Hans Havermann12/2020
239936128^9723+9723^36128144072Hans Havermann01/2021
240032817^24518+24518^32817144050Hans Havermann12/2020
240134295^15828+15828^34295144020Hans Havermann01/2021
24022^478337-115333143994Enzo Doria07/2015
2403(7*2^478330-1)/3143993Lelio R Paula08/2015
240488^74047-87^74047143984Robert Price05/2015
240533242^21441+21441^33242143980Hans Havermann01/2021
2406(19*10^143963+467)/9143964Robert Price02/2018
2407(71^77761+1)/72143954Paul Bourdelais09/2017
240833490^19859+19859^33490143939Hans Havermann01/2021
2409(853*10^143931-7)/9143933Robert Price07/2021
24102^478088+27143919Robert Price11/2015
24117*10^143857-93143858Robert Price08/2020
24123*10^143844+61143845Robert Price09/2020
241341358^3005+3005^41358143837Hans Havermann01/2021
24142^477475-22071143735Enzo Doria07/2013
24152^477417-22123143717Enzo Doria07/2013
24162^477359-3577143700Yves Minet03/2017
241739435^4402+4402^39435143688Hans Havermann01/2021
2418(14*10^143662-71)/3143663Robert Price12/2018
24196^184614+5143658Paul Bourdelais01/2021
242046371^1252+1252^46371143640Hans Havermann12/2020
242134975^12748+12748^34975143588Hans Havermann01/2021
24222^476936-396765143573Enzo Doria07/2013
24232^476888-2791229143558Enzo Doria01/2016
24242^476868-1859939143552Enzo Doria11/2015
242540807^3294+3294^40807143548Hans Havermann12/2020
2426755^49878+49878^755143547Norbert Schneider04/2019
2427(19^112247-4^112247)/15143536Robert Price03/2021
242835561^10872+10872^35561143536Hans Havermann06/2021
242937637^6492+6492^37637143487Hans Havermann05/2021
243061567^214+214^61567143477Hans Havermann05/2021
24312^476558-113627143459Enzo Doria08/2014
24322^476478-45143435Lelio R Paula11/2017
243336380^8757+8757^36380143423Hans Havermann06/2021
243432510^25707+25707^32510143371Hans Havermann05/2021
24358*10^143361+17143362Robert Price07/2021
2436(2^475854+9)/73143245Lelio R Paula08/2015
24372^475813-113239143234Enzo Doria07/2014
243832218^27849+27849^32218143203Hans Havermann04/2021
24392^475624-114059143178Enzo Doria11/2014
2440(11*2^475553-7)/15143156Renaud Lifchitz03/2011
24412^475480-2786129143134Enzo Doria10/2015
244233912^16621+16621^33912143131Hans Havermann05/2021
2443(19*10^143129-43)/3143130Robert Price05/2019
244431830^31373+31373^31830143126Hans Havermann05/2021
24456*10^143105-53143106Robert Price05/2021
2446(14*10^143097+73)/3143098Robert Price12/2018
24472^475299-111937143080Enzo Doria05/2014
244835488^10753+10753^35488143071Hans Havermann04/2021
24492^475160-2797859143038Enzo Doria04/2016
2450(2^475069+3)/395143008Lelio R Paula08/2015
24512^475027-461437142998Enzo Doria07/2015
2452(2^474958+78557)/3142977Lelio R Paula07/2015
2453(8*10^142932+43)/3142933Robert Price06/2018
245435055^11942+11942^35055142922Hans Havermann05/2021
245537650^6239+6239^37650142887Hans Havermann05/2021
2456(54^82471-1)/53142871Paul Bourdelais09/2017
2457(11*2^474432-1)/95142818Lelio R Paula09/2015
24582^474417-59923142814Enzo Doria10/2015
24594*10^142810-21142811Robert Price09/2018
246032287^26494+26494^32287142811Hans Havermann06/2021
246137162^6965+6965^37162142811Hans Havermann06/2021
246237456^6493+6493^37456142799Hans Havermann05/2021
246335141^11572+11572^35141142793Hans Havermann05/2021
246432231^26908+26908^32231142780Hans Havermann05/2021
2465(3*2^474166+1)/7142738Lelio R Paula08/2015
24662^474053+2897142705Lelio R Paula08/2012
2467(10^142699+359)/9142699Serge Batalov12/2014
2468898^48311-897^48311142676Jean-Louis Charton12/2012
24692^473740-1856639142610Enzo Doria09/2015
2470(25*10^142573-403)/9142574Robert Price12/2020
24712^473617-114223142573Enzo Doria12/2014
247236115^8856+8856^36115142555Hans Havermann05/2021
24732^473257+1873217142465Enzo Doria06/2016
2474(19*2^473242+1)/11142461Lelio R Paula09/2015
247532750^22371+22371^32750142453Hans Havermann06/2021
2476(61*10^142446-1)/3142448Robert Price01/2020
2477(14*10^142440+61)/3142441Robert Price12/2018
2478(10^142425+359)/9142425Serge Batalov12/2014
24792^473101+773027142418Enzo Doria05/2016
2480(13*2^472838-1)/3142340Lelio R Paula09/2015
2481(17*2^472789-1)/187347142320Lelio R Paula09/2015
248236915^7162+7162^36915142309Hans Havermann05/2021
24832^472634-109511142278Enzo Doria04/2014
248431870^28997+28997^31870142216Hans Havermann06/2021
2485(48^84589+1)/49142213Robert Price01/2014
24867*10^142189+87142190Robert Price07/2019
24872^472258+7142164Lelio R Paula08/2015
248840135^3484+3484^40135142162Hans Havermann05/2021
2489(23*10^142105+91)/3142106Robert Price08/2019
2490tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2491(11*2^471913-1)/21142060Lelio R Paula09/2015
2492(16*10^142058+197)/3142059Robert Price04/2019
24939*10^142037+91142038Robert Price10/2020
24942^471792+1880881142024Enzo Doria11/2016
2495(31*2^471580-1)/135141960Lelio R Paula08/2015
2496(4*10^141926-79)/3141927Robert Price02/2018
24972^471464-111546435141925Paul Bourdelais10/2021
2498(904*19^110984-1)/3141924Curtis Bright05/2015
2499(14*10^141853+37)/3141854Robert Price12/2018
2500(41*10^141836-59)/9141837Robert Price10/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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