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 ?
5501(2^349111-5)/3105093Lelio R Paula12/2013
5502675^37142+37142^675105087Norbert Schneider08/2018
55032^348981-2797573105054Enzo Doria04/2016
55042^348869-6555105021Lelio R Paula01/2017
55055^150217+78104998Lelio R Paula11/2016
5506(88*10^104989-1)/3104991Robert Price04/2020
5507(28*10^104972+149)/3104973Robert Price12/2019
550824927^16262+16262^24927104972Hans Havermann10/2020
55092^348703-113005104971Enzo Doria06/2014
5510(191*10^104956-17)/3104958Robert Price11/2021
55122^348612-809104943Yves Minet05/2013
5511(73*10^104942-1)/9104943Robert Price01/2015
55132^348583-350407104934Enzo Doria06/2015
55142^348531-949104919Yves Minet05/2012
551520^80636-59104910Lelio R Paula12/2016
55168*10^104893-13104894Robert Price08/2019
55182^348437+35104890Lelio R Paula09/2011
551725208^14487+14487^25208104890Hans Havermann09/2020
55192^348348+135104864Lelio R Paula09/2011
5520(29*10^104858+349)/9104859Robert Price06/2021
55216*10^104852-31104853Robert Price07/2020
5523(2^348284+9)/25104843Lelio R Paula12/2013
552275^55914-74104843Norbert Schneider01/2015
55242^348268+255255104840Lelio R Paula01/2017
552535540^891+891^35540104839Hans Havermann09/2020
55265^149985-52104836Lelio R Paula11/2016
55272^348224-20249104826Enzo Doria06/2013
5528(2^348217+2522)/2104824Stefano Morozzi09/2020
55292^348212-20105104823Enzo Doria06/2013
553024647^17898+17898^24647104819Hans Havermann10/2020
553120^80562+19104814Lelio R Paula12/2016
55322*10^104811-87104812Robert Price04/2018
55332^348149-20053104804Enzo Doria06/2013
55342^348095-171104788Lelio R Paula09/2011
553525383^13412+13412^25383104769Hans Havermann09/2020
55362^348003-20377104760Enzo Doria06/2013
55372^347994-741104757Lelio R Paula12/2016
5538(2^347993+2234)/2104757Stefano Morozzi01/2021
5539(2^347990+790)/2104756Stefano Morozzi09/2020
554025137^14702+14702^25137104756Hans Havermann09/2020
5541(13*2^347972-1)/282309104746Lelio R Paula03/2014
55422^347910-109937104732Enzo Doria04/2014
5543(88*10^104709-637)/9104710Robert Price11/2020
5544(13*10^104702+71)/3104703Robert Price06/2021
55455^149794+28104702Lelio R Paula11/2016
5546105^51800-2104698Lelio R Paula10/2017
5547(16^86939+3^86939)/19104684Robert Price06/2013
5548(15^89009-1)/14104682Paul Bourdelais03/2010
55492^347731-18609104678Enzo Doria05/2013
55504*6^134519+7104677Lelio R Paula11/2014
5551(34*10^104672-259)/9104673Robert Price12/2021
555225321^13588+13588^25321104656Hans Havermann09/2020
55532^347612-18545104642Enzo Doria05/2013
55566^134465+95104635Lelio R Paula11/2016
5554(2^347588+3718)/2104635Stefano Morozzi09/2020
5555(166*10^104633-7)/3104635Robert Price11/2020
55572^347517-17301104614Enzo Doria05/2013
5558(2^347493+3186)/2104606Stefano Morozzi09/2020
5559(2^347490+2574)/2104605Stefano Morozzi09/2020
55603^219222-310104596Lelio R Paula11/2016
556125993^10554+10554^25993104581Hans Havermann09/2020
5562(15*2^347399-1)/13104578Lelio R Paula03/2014
55632^347372-17853104570Enzo Doria05/2013
55642^347314+99104552Lelio R Paula09/2011
55652^347300-22233104548Enzo Doria06/2013
55662^347287-19845104544Enzo Doria06/2013
55672^347258-231191104536Harrison Mesh06/2022
5568(31*2^347254-1)/891104533Lelio R Paula03/2014
55695*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
55707*2^347239-3104531Lelio R Paula09/2014
5571(3^219098-8)/514147439969104525Lelio R Paula12/2013
55725*3^219047+8104513Lelio R Paula09/2014
55732^347148-109073104502Enzo Doria04/2014
55742^347129-20145104497Enzo Doria06/2013
55754*10^104461-57104462Robert Price10/2018
5576(2^346989+590)/2104454Stefano Morozzi09/2020
55772^346923-19585104435Enzo Doria05/2013
5578(11*2^346864-1)/175104416Lelio R Paula03/2014
55792^346854+346854^2+1104414Robert Price06/2014
55802^346834+11715104408Lelio R Paula04/2015
558124276^19961+19961^24276104392Hans Havermann09/2020
558279^55009+78104387Norbert Schneider02/2015
55833^218744+58104368Lelio R Paula11/2016
55849*10^104361+89104362Robert Price11/2019
558525048^14665+14665^25048104358Hans Havermann09/2020
55862^346649+65104352Lelio R Paula09/2011
55872^346638-17265104349Enzo Doria05/2013
5588(2^346606+2082)/2104339Stefano Morozzi09/2020
5589(2^346607+2070)/2104339Stefano Morozzi09/2020
5590(2^346582+3202)/2104332Stefano Morozzi09/2020
559126092^9967+9967^26092104331Hans Havermann09/2020
55925*10^104326+77104327Robert Price12/2018
5593(2^346564+2026)/2104326Stefano Morozzi09/2020
55952^346527-111817104316Enzo Doria05/2014
55946^134055+101104316Lelio R Paula11/2016
559692105!4+8104312Robert Price09/2019
55976^134013+163104283Lelio R Paula11/2016
5598(22*10^104272-61)/3104273Robert Price03/2022
5599(2^346318+862)/2104252Stefano Morozzi02/2021
560118^83049-89104250Lelio R Paula01/2017
5600(2^346311+606)/2104250Stefano Morozzi09/2020
5602(166*10^104230+11)/3104232Robert Price03/2021
56032^346213+484049104221Enzo Doria04/2017
560418^83021-91104214Lelio R Paula01/2017
560510^104212+128779104213Patrick De Geest05/2016
560610^104212+237447104213Patrick De Geest05/2016
560710^104212+242139104213Patrick De Geest05/2016
560810^104212+269199104213Patrick De Geest05/2016
560924254^19803+19803^24254104213Hans Havermann09/2020
5610(10^104212-71)/1104212Serge Batalov12/2014
561123678^23821-23821^23678104202Norbert Schneider01/2020
56122^346078+7695104180Lelio R Paula12/2016
56132^346055-19537104173Enzo Doria05/2013
5614(3*2^346057+1)/77104173Lelio R Paula12/2013
56152^346037-20125104168Enzo Doria06/2013
5616(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
56176^133854-17993104159Enzo Doria03/2013
56182^345990+1874239104154Enzo Doria06/2016
56192^345988-20373104153Enzo Doria06/2013
5620(2^345965+2214)/2104146Stefano Morozzi09/2020
5621(26*10^104132-503)/9104133Robert Price07/2018
56223*5^148968+8104125Lelio R Paula11/2014
5623(7*10^104113+53)/3104114Robert Price05/2018
5624p(21253)#/2+8104113Robert Price01/2017
562533582^1259+1259^33582104106Hans Havermann09/2020
562632958^1441+1441^32958104104Hans Havermann09/2020
562729127^3748+3748^29127104095Hans Havermann09/2020
5628322^41507+41507^322104094Norbert Schneider12/2014
56296^133768-17423104092Enzo Doria03/2013
56302^345786-19557104092Enzo Doria05/2013
5631171^46606-2104072Lelio R Paula10/2017
5632(29*10^104071+91)/3104072Robert Price04/2020
56332^345704-149104068Lelio R Paula09/2011
563425821^10712+10712^25821104056Hans Havermann09/2020
5635(2^345662+2038)/2104055Stefano Morozzi09/2020
56366^133704-17273104042Enzo Doria02/2013
5637(3*2^345590-1)/23104033Lelio R Paula03/2014
5638(19*2^345590+1)/33859104030Lelio R Paula12/2013
56392^345547+11104021Lelio R Paula09/2011
5640(19*10^104014-49)/3104015Robert Price05/2019
5641(2^345519+1794)/2104012Stefano Morozzi01/2021
56422^345504+723104008Lelio R Paula09/2011
56432^345498-20037104006Enzo Doria06/2013
564518^82854-37104005Lelio R Paula01/2017
5644(2^345497+2070)/2104005Stefano Morozzi09/2020
56462^345486-109065104002Enzo Doria04/2014
56472^345487-1851507104002Enzo Doria08/2015
56482^345476+777103999Lelio R Paula09/2011
5649(2^345477+1554)/2103999Stefano Morozzi09/2020
56504*10^103981-83103982Robert Price10/2018
5651(2^345327+3206)/2103954Stefano Morozzi09/2020
5652(5*2^345321-1)/3103953Lelio R Paula03/2014
5653(2^345267-9)/539049127103927Lelio R Paula12/2013
5654(19*10^103907+77)/3103908Robert Price05/2019
5655(78557*2^345163+1)/78589103905Lelio R Paula07/2014
56562^345106-112181103888Enzo Doria06/2014
5657(2^345105+1326)/2103887Stefano Morozzi02/2021
56582^345079+99103880Lelio R Paula09/2011
5659(2^345034+1198)/2103866Stefano Morozzi09/2020
566011^99736-1500103865Enzo Doria12/2012
5661(569^37699-1)/568103863Serge Batalov06/2022
5662(2^345010+2082)/2103859Stefano Morozzi09/2020
566323263^23784-23784^23263103857Norbert Schneider01/2020
56643*10^103844+31103845Robert Price06/2021
566523927^21814+21814^23927103813Hans Havermann09/2020
56662^344842-20157103808Enzo Doria06/2013
5667(47*2^344822+1)/1071103801Lelio R Paula05/2015
56682^344802-20765103796Enzo Doria06/2013
56692^344794-3821103794Yves Minet05/2011
56702^344782-109103103790Enzo Doria04/2014
56713^217521-112292103784Enzo Doria06/2014
56722^344759-3505103783Lelio R Paula11/2016
56732^344735-147103776Lelio R Paula09/2011
5674L(496533)-p(496533)103770Robert Price02/2018
56752*10^103749-69103750Robert Price03/2018
5676(55459*2^344617+1)/3103745Lelio R Paula07/2014
56772^344607-108891103738Enzo Doria03/2014
5678(2^344608+3798)/2103738Stefano Morozzi02/2021
5679(1097^34123-1)/1096103738Serge Batalov06/2022
5680(148*10^103718-1)/3103720Robert Price03/2020
56812^344541-19561103718Enzo Doria05/2013
5682(1017*2^344529-1)/569103714Lelio R Paula05/2015
5683(8896^26263-1)/8895103714Serge Batalov06/2022
5684(2^344503+1758)/2103706Stefano Morozzi09/2020
5685(4*10^103703-1)/3103704Serge Batalov08/2009
56862^344444-455103688Yves Minet03/2012
5687(4*10^103678-43)/3103679Robert Price01/2022
5688(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
5689(2^344367+2738)/2103665Stefano Morozzi01/2021
56912^344317-109933103650Enzo Doria04/2014
569026055^9508+9508^26055103650Hans Havermann09/2020
56922^344309-1852033103648Enzo Doria08/2015
569325729^10672+10672^25729103643Hans Havermann09/2020
5694(2^344289+1166)/2103642Stefano Morozzi09/2020
56953*10^103637+61103638Robert Price09/2020
5696(2^344246+1614)/2103629Stefano Morozzi09/2020
56972^344213-21253103619Enzo Doria06/2013
56982^344196-465103614Lelio R Paula11/2016
56992^344187-20001103611Enzo Doria06/2013
5700(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
5701(237^43627-1)/236103601Serge Batalov06/2022
570220^79621-19^79621103590Jean-Louis Charton03/2011
5703Phi(155391,10)/1243129103586Maksym Voznyy09/2015
57042^344085-20365103580Enzo Doria06/2013
57055^148169+54103566Lelio R Paula11/2016
57062^344017-108795103560Enzo Doria03/2014
5707(2^343974+2670)/2103547Stefano Morozzi09/2020
57082^343971-5077103546Lelio R Paula09/2011
5709(7*10^103531+71)/3103532Robert Price05/2018
57102^343899+141103524Lelio R Paula08/2011
5711(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
57126^133029-67103517Lelio R Paula11/2016
5713(17*2^343877+1)/13625103515Lelio R Paula12/2013
571466*10^103507+7103509Robert Price07/2020
571526297^8614+8614^26297103485Hans Havermann09/2020
5716(2^343764+2658)/2103483Stefano Morozzi09/2020
571726499^8036+8036^26499103480Hans Havermann09/2020
5718(136*10^103474-1)/9103476Serge Batalov12/2014
57195^148014-24103458Lelio R Paula11/2016
572028316^4503+4503^28316103453Hans Havermann09/2020
5721(22*10^103450+53)/3103451Robert Price07/2019
57222^343604+9931103436Yves Minet01/2011
57232^343601-21189103435Enzo Doria06/2013
5724(10^103423+173)/3103423Robert Price05/2021
57252^343508-115229103407Enzo Doria06/2015
5726(8766^26227-1)/8765103404Serge Batalov06/2022
5727(509203*2^343491-1)/16147103403Lelio R Paula05/2015
57283^216685-113056103386Enzo Doria07/2014
572924829^14580+14580^24829103382Hans Havermann08/2020
573091355!4+1024103381Robert Price09/2019
573144^62903-43^62903103379Jean-Louis Charton08/2012
573211^99262-20103371Lelio R Paula12/2016
5733(509203*2^343357-1)/5103366Lelio R Paula05/2015
5734(2^343363+3570)/2103363Stefano Morozzi09/2020
57352^343356-2791889103361Enzo Doria03/2016
5736(25*10^103360-241)/9103361Robert Price05/2018
5737Phi(104989,10)/2939693103350Maksym Voznyy09/2015
573824826^14511+14511^24826103319Hans Havermann09/2020
57392^343182-171103309Lelio R Paula08/2011
5740(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
5741(10680^25639-1)/10679103285Serge Batalov06/2022
5742(7427^26683-1)/7426103282Serge Batalov06/2022
57432^343079-1835611103278Enzo Doria05/2015
57442^343063-1147103273Yves Minet06/2013
574524741^14930+14930^24741103271Hans Havermann09/2020
5746(16*10^103255-73)/3103256Robert Price07/2020
5747(219^44119-1)/218103256Serge Batalov06/2022
57489*6^132689+7103254Lelio R Paula11/2014
57492^342979-18085103247Enzo Doria05/2013
5750(16*10^103244-31)/3103245Robert Price03/2019


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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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