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 ?
2501(19*10^143129-43)/3143130Robert Price05/2019
250231830^31373+31373^31830143126Hans Havermann05/2021
25036*10^143105-53143106Robert Price05/2021
2504(14*10^143097+73)/3143098Robert Price12/2018
25052^475299-111937143080Enzo Doria05/2014
250635488^10753+10753^35488143071Hans Havermann04/2021
25072^475160-2797859143038Enzo Doria04/2016
2508(2^475069+3)/395143008Lelio R Paula08/2015
25092^475027-461437142998Enzo Doria07/2015
2510(2^474958+78557)/3142977Lelio R Paula07/2015
2511(8*10^142932+43)/3142933Robert Price06/2018
251235055^11942+11942^35055142922Hans Havermann05/2021
251337650^6239+6239^37650142887Hans Havermann05/2021
2514(54^82471-1)/53142871Paul Bourdelais09/2017
2515(11*2^474432-1)/95142818Lelio R Paula09/2015
25162^474417-59923142814Enzo Doria10/2015
25174*10^142810-21142811Robert Price09/2018
251832287^26494+26494^32287142811Hans Havermann06/2021
251937162^6965+6965^37162142811Hans Havermann06/2021
252037456^6493+6493^37456142799Hans Havermann05/2021
252135141^11572+11572^35141142793Hans Havermann05/2021
252232231^26908+26908^32231142780Hans Havermann05/2021
2523(3*2^474166+1)/7142738Lelio R Paula08/2015
25242^474053+2897142705Lelio R Paula08/2012
2525(10^142699+359)/9142699Serge Batalov12/2014
2526898^48311-897^48311142676Jean-Louis Charton12/2012
25272^473740-1856639142610Enzo Doria09/2015
2528(25*10^142573-403)/9142574Robert Price12/2020
25292^473617-114223142573Enzo Doria12/2014
253036115^8856+8856^36115142555Hans Havermann05/2021
25312^473257+1873217142465Enzo Doria06/2016
2532(19*2^473242+1)/11142461Lelio R Paula09/2015
253332750^22371+22371^32750142453Hans Havermann06/2021
2534(61*10^142446-1)/3142448Robert Price01/2020
2535(14*10^142440+61)/3142441Robert Price12/2018
2536(10^142425+359)/9142425Serge Batalov12/2014
25372^473101+773027142418Enzo Doria05/2016
2538(13*2^472838-1)/3142340Lelio R Paula09/2015
2539(17*2^472789-1)/187347142320Lelio R Paula09/2015
254036915^7162+7162^36915142309Hans Havermann05/2021
25412^472634-109511142278Enzo Doria04/2014
254231870^28997+28997^31870142216Hans Havermann06/2021
2543(48^84589+1)/49142213Robert Price01/2014
25447*10^142189+87142190Robert Price07/2019
25452^472258+7142164Lelio R Paula08/2015
254640135^3484+3484^40135142162Hans Havermann05/2021
2547(23*10^142105+91)/3142106Robert Price08/2019
2548tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2549(11*2^471913-1)/21142060Lelio R Paula09/2015
2550(16*10^142058+197)/3142059Robert Price04/2019
25519*10^142037+91142038Robert Price10/2020
25522^471792+1880881142024Enzo Doria11/2016
2553(31*2^471580-1)/135141960Lelio R Paula08/2015
2554(4*10^141926-79)/3141927Robert Price02/2018
25552^471464-111546435141925Paul Bourdelais10/2021
2556(904*19^110984-1)/3141924Curtis Bright05/2015
2557(14*10^141853+37)/3141854Robert Price12/2018
2558(41*10^141836-59)/9141837Robert Price10/2018
25594*5^202913-9141831Lelio R Paula04/2015
25602*7^167812-3141818Lelio R Paula12/2014
25612^471043+35141799Robert Price11/2015
2562(11*2^470956-1)/7945141770Lelio R Paula08/2015
256343636^1773+1773^43636141761Hans Havermann05/2021
2564(11*10^141718-131)/3141719Robert Price09/2018
25652^470692+76771141693Enzo Doria05/2016
256650160^667+667^50160141659Hans Havermann05/2021
256731522^31181+31181^31522141657Hans Havermann05/2021
256833076^19135+19135^33076141626Hans Havermann04/2021
2569(91*10^141610+71)/9141612Robert Price01/2022
2570(21*2^470391+1)/533141601Lelio R Paula09/2015
257131932^27155+27155^31932141582Hans Havermann05/2021
257236449^7660+7660^36449141577Hans Havermann05/2021
25732^470305-459373141576Enzo Doria05/2015
257432195^24936+24936^32195141556Hans Havermann05/2021
25752^470183+72623141540Enzo Doria04/2016
25762^470173-16465141537Enzo Doria04/2013
257737297^6234+6234^37297141534Hans Havermann05/2021
257844*10^141476+9141478Robert Price10/2020
25792^469974-1841141477Enzo Doria05/2014
2580(23*2^469939+1)/25141466Lelio R Paula08/2015
25812*10^141448+63141449Robert Price05/2018
25822^469824+43141432Lelio R Paula09/2017
25832*10^141407-27141408Robert Price05/2018
2584(214*10^141385-1)/3141387Robert Price01/2021
25852^469630-59711141373Enzo Doria10/2015
258635277^10172+10172^35277141370Hans Havermann04/2021
258733397^17100+17100^33397141370Hans Havermann04/2021
2588(25*10^141366-331)/9141367Robert Price08/2018
258936986^6639+6639^36986141365Hans Havermann06/2021
259034572^12271+12271^34572141361Hans Havermann06/2021
259137179^6338+6338^37179141353Hans Havermann05/2021
2592(2^469564-3)/611141351Lelio R Paula08/2015
2593197^61601+2141342Lelio R Paula08/2017
259433420^16951+16951^33420141340Hans Havermann05/2021
259531623^29458+29458^31623141330Hans Havermann05/2021
259648112^865+865^48112141306Hans Havermann05/2021
25972^469372-112949141296Enzo Doria07/2014
25985*10^141294-63141295Robert Price04/2021
25993^296115+4141283Tyler NeSmith01/2021
2600143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2601143^65536+106^65536141253Serge Batalov03/2018
2602(11*10^141243-23)/3141244Robert Price09/2021
26042^469198+782569141243Enzo Doria10/2016
260338129^5062+5062^38129141243Hans Havermann05/2021
26052^469076-2786939141206Enzo Doria11/2015
260638630^4521+4521^38630141202Hans Havermann05/2021
260731755^27836+27836^31755141139Hans Havermann05/2021
260835554^9325+9325^35554141137Hans Havermann05/2021
26092^468804+1874941141125Enzo Doria06/2016
26102^468787+81353141119Enzo Doria08/2016
26112^468595-350407141062Enzo Doria06/2015
26122^468564+87855141052Lelio R Paula01/2016
26132^468551-21987141048Enzo Doria07/2013
26142^468523-7141040Lelio R Paula08/2015
2615(25*10^141019-13)/3141020Robert Price09/2019
26162^468405+87855141004Lelio R Paula01/2016
261739338^3831+3831^39338140961Hans Havermann05/2021
261831458^30239+30239^31458140950Hans Havermann05/2021
26198*10^140932+29140933Robert Price11/2021
262033166^17691+17691^33166140881Hans Havermann06/2021
26212^467978-113051140876Enzo Doria07/2014
26222^467780-344429140816Enzo Doria07/2015
26239*10^140802-89140803Robert Price04/2020
26242^467605-1855603140764Enzo Doria09/2015
26255*10^140744-7140745Robert Price09/2015
2626(5^201359-1)/4140744Paul Bourdelais12/2008
26272^467401-1850023140702Enzo Doria08/2015
2628(266*10^140681-17)/3140683Robert Price07/2020
2629(2^467270+78557)/23247140658Lelio R Paula07/2015
263032138^23781+23781^32138140644Hans Havermann05/2021
263131654^27735+27735^31654140640Hans Havermann05/2021
2632(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
26332^467166-1854941140631Enzo Doria09/2015
2634(203*10^140615-11)/3140617Robert Price12/2020
2635(85*10^140609+473)/9140610Robert Price01/2020
263639231^3836+3836^39231140600Hans Havermann06/2021
26372^466866-1840571140541Enzo Doria06/2015
26382^466829-459523140530Enzo Doria05/2015
26392^466692-113213140489Enzo Doria07/2014
264023*10^140464-3140466Robert Price10/2021
264131335^30364+30364^31335140455Hans Havermann05/2021
264232795^19126+19126^32795140416Hans Havermann05/2021
2643(44*10^140410-503)/9140411Robert Price12/2018
2644153^64265-2140400Lelio R Paula11/2017
2645(112*10^140357-1)/3140359Serge Batalov12/2014
2646(29*10^140337-17)/3140338Robert Price09/2019
26472^466181-112735140335Enzo Doria07/2014
2648(16*10^140290-37)/3140291Robert Price05/2021
2649(5*10^140281-119)/3140282Robert Price03/2018
265034568^11415+11415^34568140259Hans Havermann05/2021
2651(27*2^465872+1)/691140241Lelio R Paula08/2015
265233632^14781+14781^33632140236Hans Havermann05/2021
265331803^25670+25670^31803140233Hans Havermann05/2021
26542^465803-114817140221Enzo Doria05/2015
2655floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
26562^465503-112735140131Enzo Doria07/2014
2657(16*10^140091+167)/3140092Robert Price06/2019
26586^179964+179964^6-1140040Robert Price04/2014
2659(89*10^140008-179)/9140009Robert Price12/2019
2660(29*2^465077-1)/9140003Lelio R Paula08/2015
26612^465072-344789140001Enzo Doria07/2015
266234742^10683+10683^34742139965Hans Havermann05/2021
26635*10^139945+81139946Robert Price03/2019
266432648^19335+19335^32648139941Hans Havermann05/2021
26652^464864-17139939Lelio R Paula09/2017
26668*10^139920+51139921Robert Price08/2019
2667(85*10^139913-1)/3139915Robert Price02/2020
266831203^30436+30436^31203139896Hans Havermann04/2021
26694*10^139839-27139840Robert Price08/2021
267033582^14573+14573^33582139821Hans Havermann05/2021
2671(17^113621+1)/18139804Paul Bourdelais09/2011
26732*10^139800-21139801Robert Price09/2020
267232628^19261+19261^32628139801Hans Havermann04/2021
2674(13*10^139782+191)/3139783Robert Price11/2018
2675(64*10^139776+791)/9139777Robert Price01/2022
2676(695*10^139772+7)/9139774Robert Price12/2021
2677(19*2^464312-1)/3139773Lelio R Paula08/2015
2678(74*10^139723+133)/9139724Robert Price06/2019
26793*10^139722+13139723Robert Price07/2018
268031577^26592+26592^31577139721Hans Havermann05/2021
268177*10^139692+3139694Robert Price06/2020
2682(31*2^463970+1)/5139670Lelio R Paula08/2015
2683(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
268439640^3321+3321^39640139584Hans Havermann05/2021
268536663^6410+6410^36663139571Hans Havermann05/2021
26862^463633-2788423139568Enzo Doria11/2015
268733659^13978+13978^33659139532Hans Havermann05/2021
268831811^24318+24318^31811139521Hans Havermann04/2021
268934149^12172+12172^34149139512Hans Havermann04/2021
2690(29*10^139476+313)/9139477Robert Price04/2021
269131721^24940+24940^31721139474Hans Havermann05/2021
269232833^17698+17698^32833139473Hans Havermann05/2021
26932^463271-109501139459Enzo Doria04/2014
2694(5*10^139457+79)/3139458Robert Price03/2018
26952^463237-99139449Lelio R Paula09/2017
2696(49*10^139442+383)/9139443Robert Price04/2019
269731155^29902+29902^31155139441Hans Havermann05/2021
2698(7*10^139417-547)/9139417Robert Price01/2018
2699(10^139398+191)/3139398Robert Price02/2018
270023*10^139386-3139388Robert Price10/2021
27012^463019+79463139383Enzo Doria06/2016
27023^292129-112756139381Enzo Doria07/2014
2703(15*2^462951+1)/527139361Lelio R Paula08/2015
270431922^23205+23205^31922139359Hans Havermann05/2021
27062^462855-1865707139334Enzo Doria02/2016
270531237^28876+28876^31237139334Hans Havermann05/2021
2707(86*10^139315+121)/9139316Robert Price08/2019
27082^462786-292043139313Enzo Doria08/2015
270938915^3798+3798^38915139299Hans Havermann05/2021
2710(26*10^139289+1)/9139290Serge Batalov05/2010
271134065^12248+12248^34065139260Hans Havermann05/2021
271236425^6654+6654^36425139256Hans Havermann05/2021
271339252^3527+3527^39252139243Hans Havermann05/2021
2714(17*10^139239+67)/3139240Robert Price01/2019
271531887^23248+23248^31887139231Hans Havermann05/2021
2716(25*10^139210-97)/9139211Robert Price01/2022
27172^462238-935139148Yves Minet02/2014
2718(29*10^139134-119)/9139135Robert Price12/2021
2719(109*10^139100-7)/3139102Robert Price03/2021
272038744^3885+3885^38744139068Hans Havermann05/2021
272131112^29499+29499^31112139065Hans Havermann05/2021
27222*10^139043-63139044Robert Price01/2022
272336390^6613+6613^36390139025Hans Havermann04/2021
27242*10^138975+33138976Robert Price11/2021
272542437^1882+1882^42437138966Hans Havermann05/2021
272632151^20990+20990^32151138958Hans Havermann05/2021
272732154^20933+20933^32154138933Hans Havermann04/2021
272831082^29499+29499^31082138931Hans Havermann04/2021
27292^461228+1870441138844Enzo Doria05/2016
27302^461204-113675138837Enzo Doria08/2014
2731(2^461139-7)/47138815Lelio R Paula08/2015
2732(17*10^138812-521)/9138813Robert Price04/2018
27333*10^138811-11138812Robert Price07/2018
2734(28*10^138768+173)/3138769Robert Price12/2019
2735(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2736(379*10^138737-1)/9138739Robert Price02/2020
2737(43*10^138648+101)/9138649Robert Price11/2018
27382^460567-113541138645Enzo Doria08/2014
2739(10^138622+161)/9138622Robert Price09/2021
27407*10^138604+3138605Robert Price08/2015
2741(133*10^138600+17)/3138602Robert Price11/2021
274233912^12203+12203^33912138581Hans Havermann05/2021
27432^460330+69138574Lelio R Paula09/2017
2744(17*10^138569-77)/3138570Robert Price08/2019
274531186^27725+27725^31186138556Hans Havermann05/2021
2746(16*10^138545+89)/3138546Robert Price03/2021
274739753^3056+3056^39753138546Hans Havermann05/2021
274831282^26847+26847^31282138545Hans Havermann05/2021
27496*10^138520-37138521Robert Price02/2021
275031830^22447+22447^31830138498Hans Havermann05/2021


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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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