PRP Records

Probable Primes Top 10000

(291192 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 ?
2751tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2752(11*2^471913-1)/21142060Lelio R Paula09/2015
2753(16*10^142058+197)/3142059Robert Price04/2019
27549*10^142037+91142038Robert Price10/2020
27552^471792+1880881142024Enzo Doria11/2016
2756(509*10^142018+31)/9142020Robert Price08/2022
2757(31*2^471580-1)/135141960Lelio R Paula08/2015
2758(4*10^141926-79)/3141927Robert Price02/2018
27592^471464-111546435141925Paul Bourdelais10/2021
2760(904*19^110984-1)/3141924Curtis Bright05/2015
2761(14*10^141853+37)/3141854Robert Price12/2018
2762(41*10^141836-59)/9141837Robert Price10/2018
27634*5^202913-9141831Lelio R Paula04/2015
27642*7^167812-3141818Lelio R Paula12/2014
27652^471043+35141799Robert Price11/2015
2766(11*2^470956-1)/7945141770Lelio R Paula08/2015
276743636^1773+1773^43636141761Hans Havermann05/2021
2768(53*10^141722-611)/9141723Robert Price02/2022
2769(11*10^141718-131)/3141719Robert Price09/2018
2770(61*10^141716+47)/9141717Robert Price07/2022
27712^470692+76771141693Enzo Doria05/2016
277250160^667+667^50160141659Hans Havermann05/2021
277331522^31181+31181^31522141657Hans Havermann05/2021
277433076^19135+19135^33076141626Hans Havermann04/2021
2775(91*10^141610+71)/9141612Robert Price01/2022
2776(21*2^470391+1)/533141601Lelio R Paula09/2015
277731932^27155+27155^31932141582Hans Havermann05/2021
277836449^7660+7660^36449141577Hans Havermann05/2021
27792^470305-459373141576Enzo Doria05/2015
278032195^24936+24936^32195141556Hans Havermann05/2021
27812^470183+72623141540Enzo Doria04/2016
27822^470173-16465141537Enzo Doria04/2013
278337297^6234+6234^37297141534Hans Havermann05/2021
2784(509*10^141479+13)/9141481Robert Price05/2022
278544*10^141476+9141478Robert Price10/2020
27862^469974-1841141477Enzo Doria05/2014
2787(23*2^469939+1)/25141466Lelio R Paula08/2015
27882*10^141448+63141449Robert Price05/2018
27892^469824+43141432Lelio R Paula09/2017
27902*10^141407-27141408Robert Price05/2018
2791(214*10^141385-1)/3141387Robert Price01/2021
27922^469630-59711141373Enzo Doria10/2015
279335277^10172+10172^35277141370Hans Havermann04/2021
279433397^17100+17100^33397141370Hans Havermann04/2021
2795(25*10^141366-331)/9141367Robert Price08/2018
279636986^6639+6639^36986141365Hans Havermann06/2021
279734572^12271+12271^34572141361Hans Havermann06/2021
279837179^6338+6338^37179141353Hans Havermann05/2021
2799(2^469564-3)/611141351Lelio R Paula08/2015
2800197^61601+2141342Lelio R Paula08/2017
280133420^16951+16951^33420141340Hans Havermann05/2021
280231623^29458+29458^31623141330Hans Havermann05/2021
280348112^865+865^48112141306Hans Havermann05/2021
28042^469372-112949141296Enzo Doria07/2014
28055*10^141294-63141295Robert Price04/2021
28063^296115+4141283Tyler NeSmith01/2021
2807(64*10^141256+161)/9141257Robert Price08/2022
2808143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2809143^65536+106^65536141253Serge Batalov03/2018
2810(11*10^141243-23)/3141244Robert Price09/2021
28122^469198+782569141243Enzo Doria10/2016
281138129^5062+5062^38129141243Hans Havermann05/2021
28132^469076-2786939141206Enzo Doria11/2015
281438630^4521+4521^38630141202Hans Havermann05/2021
281531755^27836+27836^31755141139Hans Havermann05/2021
281635554^9325+9325^35554141137Hans Havermann05/2021
28172^468804+1874941141125Enzo Doria06/2016
28182^468787+81353141119Enzo Doria08/2016
28192^468595-350407141062Enzo Doria06/2015
28202^468564+87855141052Lelio R Paula01/2016
28212^468551-21987141048Enzo Doria07/2013
28222^468523-7141040Lelio R Paula08/2015
2823(25*10^141019-13)/3141020Robert Price09/2019
28242^468405+87855141004Lelio R Paula01/2016
282539338^3831+3831^39338140961Hans Havermann05/2021
282631458^30239+30239^31458140950Hans Havermann05/2021
28278*10^140932+29140933Robert Price11/2021
282833166^17691+17691^33166140881Hans Havermann06/2021
28292^467978-113051140876Enzo Doria07/2014
28302^467780-344429140816Enzo Doria07/2015
28319*10^140802-89140803Robert Price04/2020
28322^467605-1855603140764Enzo Doria09/2015
28335*10^140744-7140745Robert Price09/2015
2834(5^201359-1)/4140744Paul Bourdelais12/2008
28352^467401-1850023140702Enzo Doria08/2015
2836(266*10^140681-17)/3140683Robert Price07/2020
2837(2^467270+78557)/23247140658Lelio R Paula07/2015
283832138^23781+23781^32138140644Hans Havermann05/2021
283931654^27735+27735^31654140640Hans Havermann05/2021
2840(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
28412^467166-1854941140631Enzo Doria09/2015
2842(203*10^140615-11)/3140617Robert Price12/2020
2843(85*10^140609+473)/9140610Robert Price01/2020
284439231^3836+3836^39231140600Hans Havermann06/2021
28452^466866-1840571140541Enzo Doria06/2015
28462^466829-459523140530Enzo Doria05/2015
28472^466692-113213140489Enzo Doria07/2014
284823*10^140464-3140466Robert Price10/2021
284931335^30364+30364^31335140455Hans Havermann05/2021
285032795^19126+19126^32795140416Hans Havermann05/2021
2851(44*10^140410-503)/9140411Robert Price12/2018
2852153^64265-2140400Lelio R Paula11/2017
2853(112*10^140357-1)/3140359Serge Batalov12/2014
2854(29*10^140337-17)/3140338Robert Price09/2019
28552^466181-112735140335Enzo Doria07/2014
2856(16*10^140290-37)/3140291Robert Price05/2021
2857(5*10^140281-119)/3140282Robert Price03/2018
285834568^11415+11415^34568140259Hans Havermann05/2021
2859(27*2^465872+1)/691140241Lelio R Paula08/2015
286033632^14781+14781^33632140236Hans Havermann05/2021
286131803^25670+25670^31803140233Hans Havermann05/2021
28622^465803-114817140221Enzo Doria05/2015
2863floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
28642^465503-112735140131Enzo Doria07/2014
2865(16*10^140091+167)/3140092Robert Price06/2019
2866(8*10^140087-137)/3140088Robert Price03/2022
28676^179964+179964^6-1140040Robert Price04/2014
2868(89*10^140008-179)/9140009Robert Price12/2019
2869(29*2^465077-1)/9140003Lelio R Paula08/2015
28702^465072-344789140001Enzo Doria07/2015
287134742^10683+10683^34742139965Hans Havermann05/2021
28725*10^139945+81139946Robert Price03/2019
287332648^19335+19335^32648139941Hans Havermann05/2021
28742^464864-17139939Lelio R Paula09/2017
28758*10^139920+51139921Robert Price08/2019
2876(85*10^139913-1)/3139915Robert Price02/2020
287731203^30436+30436^31203139896Hans Havermann04/2021
2878(16^116139+619)/5139845Anonymous08/2022
28794*10^139839-27139840Robert Price08/2021
288033582^14573+14573^33582139821Hans Havermann05/2021
2881(17^113621+1)/18139804Paul Bourdelais09/2011
28832*10^139800-21139801Robert Price09/2020
288232628^19261+19261^32628139801Hans Havermann04/2021
2884(13*10^139782+191)/3139783Robert Price11/2018
2885(64*10^139776+791)/9139777Robert Price01/2022
2886(695*10^139772+7)/9139774Robert Price12/2021
2887(19*2^464312-1)/3139773Lelio R Paula08/2015
2888(74*10^139723+133)/9139724Robert Price06/2019
28893*10^139722+13139723Robert Price07/2018
289031577^26592+26592^31577139721Hans Havermann05/2021
289177*10^139692+3139694Robert Price06/2020
2892(31*2^463970+1)/5139670Lelio R Paula08/2015
2893(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
289439640^3321+3321^39640139584Hans Havermann05/2021
289536663^6410+6410^36663139571Hans Havermann05/2021
28962^463633-2788423139568Enzo Doria11/2015
289733659^13978+13978^33659139532Hans Havermann05/2021
289831811^24318+24318^31811139521Hans Havermann04/2021
289934149^12172+12172^34149139512Hans Havermann04/2021
2900(29*10^139476+313)/9139477Robert Price04/2021
290131721^24940+24940^31721139474Hans Havermann05/2021
290232833^17698+17698^32833139473Hans Havermann05/2021
29032^463271-109501139459Enzo Doria04/2014
2904(5*10^139457+79)/3139458Robert Price03/2018
29052^463237-99139449Lelio R Paula09/2017
2906(49*10^139442+383)/9139443Robert Price04/2019
290731155^29902+29902^31155139441Hans Havermann05/2021
2908(7*10^139417-547)/9139417Robert Price01/2018
2909(10^139398+191)/3139398Robert Price02/2018
291023*10^139386-3139388Robert Price10/2021
29112^463019+79463139383Enzo Doria06/2016
29123^292129-112756139381Enzo Doria07/2014
2913(15*2^462951+1)/527139361Lelio R Paula08/2015
291431922^23205+23205^31922139359Hans Havermann05/2021
29162^462855-1865707139334Enzo Doria02/2016
291531237^28876+28876^31237139334Hans Havermann05/2021
2917(86*10^139315+121)/9139316Robert Price08/2019
29182^462786-292043139313Enzo Doria08/2015
291938915^3798+3798^38915139299Hans Havermann05/2021
2920(26*10^139289+1)/9139290Serge Batalov05/2010
292134065^12248+12248^34065139260Hans Havermann05/2021
292236425^6654+6654^36425139256Hans Havermann05/2021
292339252^3527+3527^39252139243Hans Havermann05/2021
2924(17*10^139239+67)/3139240Robert Price01/2019
292531887^23248+23248^31887139231Hans Havermann05/2021
2926(25*10^139210-97)/9139211Robert Price01/2022
29272^462238-935139148Yves Minet02/2014
2928(29*10^139134-119)/9139135Robert Price12/2021
2929(109*10^139100-7)/3139102Robert Price03/2021
293038744^3885+3885^38744139068Hans Havermann05/2021
293131112^29499+29499^31112139065Hans Havermann05/2021
29322*10^139043-63139044Robert Price01/2022
293336390^6613+6613^36390139025Hans Havermann04/2021
29342*10^138975+33138976Robert Price11/2021
293542437^1882+1882^42437138966Hans Havermann05/2021
293632151^20990+20990^32151138958Hans Havermann05/2021
293732154^20933+20933^32154138933Hans Havermann04/2021
293831082^29499+29499^31082138931Hans Havermann04/2021
29392^461228+1870441138844Enzo Doria05/2016
29402^461204-113675138837Enzo Doria08/2014
2941(2^461139-7)/47138815Lelio R Paula08/2015
2942(17*10^138812-521)/9138813Robert Price04/2018
29433*10^138811-11138812Robert Price07/2018
2944(28*10^138768+173)/3138769Robert Price12/2019
2945(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2946(379*10^138737-1)/9138739Robert Price02/2020
2947(43*10^138648+101)/9138649Robert Price11/2018
29482^460567-113541138645Enzo Doria08/2014
2949(10^138622+161)/9138622Robert Price09/2021
29507*10^138604+3138605Robert Price08/2015
2951(133*10^138600+17)/3138602Robert Price11/2021
295233912^12203+12203^33912138581Hans Havermann05/2021
29532^460330+69138574Lelio R Paula09/2017
2954(17*10^138569-77)/3138570Robert Price08/2019
295531186^27725+27725^31186138556Hans Havermann05/2021
2956(16*10^138545+89)/3138546Robert Price03/2021
295739753^3056+3056^39753138546Hans Havermann05/2021
295831282^26847+26847^31282138545Hans Havermann05/2021
29596*10^138520-37138521Robert Price02/2021
29612^460078-69581138498Enzo Doria12/2015
296031830^22447+22447^31830138498Hans Havermann05/2021
296237384^5065+5065^37384138492Hans Havermann05/2021
296334774^9585+9585^34774138456Hans Havermann05/2021
296410^138444-5001138444Robert Price12/2021
29652^459768+1531138404Lelio R Paula06/2012
2966(266*10^138328-17)/3138330Robert Price07/2020
296732963^15696+15696^32963138306Hans Havermann05/2021
29682^459343-113611138277Enzo Doria08/2014
2969(28*10^138240+113)/3138241Robert Price03/2020
29702^459199+1874393138233Enzo Doria06/2016
297133339^14002+14002^33339138230Hans Havermann05/2021
29722^459063-345307138192Enzo Doria06/2015
29732*10^138162-43138163Robert Price04/2018
29742^458927-112747138151Enzo Doria06/2014
29752^458927-69217138151Enzo Doria11/2015
297630907^29458+29458^30907138130Hans Havermann05/2021
297732882^15837+15837^32882138094Hans Havermann05/2021
297839252^3295+3295^39252138083Hans Havermann05/2021
297933789^12190+12190^33789138062Hans Havermann06/2021
2980555555*2^458524+1513138036Darren Bedwell08/2009
298130931^29002+29002^30931138028Hans Havermann05/2021
29822^458465+2^32+1138012T. D. Noe06/2007
298332206^19275+19275^32206138003Hans Havermann05/2021
29842^458321-113053137969Enzo Doria07/2014
29852^458298+79459137962Enzo Doria06/2016
29862^458248-21815137947Enzo Doria07/2013
29872^458194+1876549137931Enzo Doria07/2016
2988(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2989(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
2990(793*10^137887+53)/9137889Robert Price01/2022
29912^457937+57137853Lelio R Paula09/2017
2992(8*10^137845+13)/3137846Robert Price06/2018
29932^457822+105137819Donovan Johnson06/2006
29942^457754-113711137798Enzo Doria09/2014
299511^132315-360137792Enzo Doria09/2012
299632072^19689+19689^32072137725Hans Havermann06/2021
299744592^1225+1225^44592137707Hans Havermann05/2021
29982^457347-37137676Lelio R Paula09/2017
29992^457322-2786393137668Enzo Doria10/2015
3000gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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