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 ?
45012^371276-461267111766Enzo Doria07/2015
45026*10^111760+43111761Robert Price07/2020
450398079!4-1024111747Robert Price11/2019
4504(2^371186+3162)/2111738Stefano Morozzi09/2020
45052^371098-113261111712Enzo Doria07/2014
4506(7*10^111706-61)/9111706Erik Branger01/2011
45072^371044+1869391111696Enzo Doria05/2016
450826310^17581+17581^26310111688Hans Havermann01/2021
450988^57416+87111645Norbert Schneider11/2015
45102^370829-109693111631Enzo Doria04/2014
451115^94906-2111619Lelio R Paula11/2013
451225835^20904+20904^25835111614Hans Havermann02/2021
4513(2^370726+1198)/2111600Stefano Morozzi09/2020
451427758^10479+10479^27758111597Hans Havermann02/2021
45152^370695-4627111591Yves Minet05/2019
45167*10^111579-87111580Robert Price06/2020
45172^370643-37111575Yves Minet01/2012
4518(2^370655-5)/2439111575Lelio R Paula03/2014
45192^370610-3911111565Yves Minet04/2017
452026200^18097+18097^26200111550Hans Havermann01/2021
4521286^45405+45405^286111532Norbert Schneider04/2015
45224*5^159563-9111531Lelio R Paula11/2014
45235*10^111528-21111529Robert Price12/2021
4524(4^185225+23)/3111517Robert Price10/2018
45252^370393-2797093111500Enzo Doria03/2016
4526(21*2^370382-1)/629111495Lelio R Paula03/2014
4527(2^370371+554)/2111493Stefano Morozzi09/2020
45286^143273-5111489Paul Bourdelais01/2021
45292^370292-2791979111469Enzo Doria03/2016
45302^370177-461551111435Enzo Doria07/2015
4531(2^370169+1706)/2111432Stefano Morozzi09/2020
4532109^54683-108111413Norbert Schneider02/2017
4533(83*10^111406-173)/9111407Robert Price04/2021
4534(2^370043+1010)/2111394Stefano Morozzi09/2020
453532961^2396+2396^32961111392Hans Havermann10/2020
4536numbpart(10^10+76282)111391Serge Batalov04/2015
45372^369974+733111374Lelio R Paula05/2013
4538121^53470+120111367Norbert Schneider10/2018
45392^369915-286267111356Enzo Doria07/2015
4540(62*10^111347-629)/9111348Robert Price07/2021
45412^369855-1615111338Lelio R Paula05/2017
45427*10^111325+3111326Robert Price08/2015
454351^65176+2111293Lelio R Paula08/2013
45442^369643-1865767111274Enzo Doria03/2016
45452^369603+885111262Lelio R Paula05/2017
454625555^22564+22564^25555111252Hans Havermann10/2020
4547L(532277)111240Renaud Lifchitz03/2004
4548105^55033-2111233Lelio R Paula10/2017
4549(35*10^111232-737)/9111233Robert Price07/2018
455026970^13307+13307^26970111227Hans Havermann10/2020
455125419^23716+23716^25419111210Hans Havermann10/2020
45529*10^111201-29111202Robert Price09/2019
45532^369392+29835111199Lelio R Paula05/2017
45543^233059+16111198Robert Price03/2020
45552^369354-3413111187Yves Minet12/2016
45562^369296-27111170Lelio R Paula02/2013
45572^369239-109837111153Enzo Doria05/2014
45582^369224-291839111148Enzo Doria07/2015
45592^369216+2798881111146Enzo Doria04/2016
456026842^13817+13817^26842111137Hans Havermann11/2020
4561(5*10^111119-191)/3111120Robert Price05/2021
456210^111111+163849111112Patrick De Geest03/2017
456310^111111-312911111111Patrick De Geest03/2017
45642^369092-216923111108Enzo Doria05/2014
45652^369081-55111105Lelio R Paula02/2013
4566(2^369047+3618)/2111094Stefano Morozzi09/2020
456788^57124-87111077Norbert Schneider11/2015
45682^368980+753111075Lelio R Paula05/2013
45692^368946-3623111064Yves Minet03/2017
45702^368929+29835111059Lelio R Paula05/2017
45714^184463-3^184463111058Jean-Louis Charton12/2004
4572111^54298+110111057Norbert Schneider04/2017
4573(4*10^111032-7)/3111033Ray Chandler04/2011
457435799^1262+1262^35799111015Hans Havermann10/2020
4575(298*10^111004+11)/3111006Robert Price11/2020
457627648^10349+10349^27648111004Hans Havermann11/2020
457728899^6932+6932^28899110997Hans Havermann11/2020
45782^368641-460303110972Enzo Doria06/2015
45792^368619-109087110966Enzo Doria04/2014
4580(74*10^110961+313)/9110962Robert Price06/2019
458125258^24711+24711^25258110956Hans Havermann11/2020
4582(2^368539+1290)/2110941Stefano Morozzi01/2021
45833*2^368489+7110927Lelio R Paula09/2014
4584(14*10^110922+61)/3110923Robert Price12/2018
458597411!4-2110913Robert Price07/2017
4586(301*10^110903+23)/9110905Robert Price06/2021
4587(9179*2^368330-1)/35110881Lelio R Paula05/2015
458825830^19619+19619^25830110880Hans Havermann10/2020
4589(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
459026022^18191+18191^26022110850Hans Havermann10/2020
4591(2^368211+2250)/2110843Stefano Morozzi01/2021
4592(37*10^110813+251)/9110814Robert Price09/2021
45932^368050-64875110795Lelio R Paula05/2017
45942^368048+25110794Lelio R Paula02/2013
4595(2^368017+2262)/2110784Stefano Morozzi02/2021
459669^60239-2110771Lelio R Paula10/2013
4597(23*2^367952+1)/15717110762Lelio R Paula03/2014
45982^367924-69110757Lelio R Paula02/2013
4599(23*10^110738+61)/3110739Robert Price01/2022
4600(2^367779+3750)/2110713Stefano Morozzi01/2021
46012^367709-109723110692Enzo Doria04/2014
4602(3*2^367644-1)/107110671Lelio R Paula03/2014
4603(2^367626+3514)/2110667Stefano Morozzi09/2020
4604(23*2^367398+1)/57963110595Lelio R Paula03/2014
4605140^51515-139110558Norbert Schneider04/2019
46062^367215+1879223110543Enzo Doria09/2016
460725782^19375+19375^25782110534Hans Havermann10/2020
460826117^17058+17058^26117110526Hans Havermann10/2020
46092^367141+41110521Lelio R Paula02/2013
46102^367126+29835110516Lelio R Paula05/2017
4611(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
4612(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
4613(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
4614(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
4615(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
4616(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
4617(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
4618(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
4619(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
4620(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
4621(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
46223*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
46233*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
46243*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
46253*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
46263*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
46273*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
46283*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
46297*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
46307*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
46317*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
46327*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
46337*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
46347*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
46357*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
46367*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
46377*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
46387*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
46397*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
46407*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
46417*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
46427*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
46437*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
4644(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
4645(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
4646(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
4647(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
4648(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
4649(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
4650(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
4651(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
4652(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
4653(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
4654(11*10^110496+49)/3110497Robert Price07/2018
465525447^21958+21958^25447110481Hans Havermann11/2020
4656(31*2^366976+1)/7110472Lelio R Paula03/2014
46577*10^110468-23110469Robert Price07/2019
46582^366853+5711110434Lelio R Paula05/2017
4659(21181*2^366833+1)/3110432Lelio R Paula07/2014
46602^366816+315110423Lelio R Paula05/2017
46612^366775-2787037110411Enzo Doria03/2016
4662(112*10^110405-1)/3110407Serge Batalov12/2014
46632^366751+2797553110404Enzo Doria03/2016
466425276^23331+23331^25276110404Hans Havermann10/2020
46652^366748+255110403Lelio R Paula05/2017
46662^366738-2985110400Yves Minet09/2014
4667(23*2^366739+1)/74575110396Lelio R Paula03/2014
4668(2^366722+1314)/2110395Stefano Morozzi02/2021
46692^366716+1871791110393Enzo Doria05/2016
46702^366649+1871687110373Enzo Doria05/2016
46712^366629-351205110367Enzo Doria06/2015
4672(31*10^110363+257)/9110364Robert Price12/2021
46742^366558+1874479110345Enzo Doria06/2016
467325132^24581+24581^25132110345Hans Havermann10/2020
4675(2^366539+770)/2110339Stefano Morozzi09/2020
467626368^15285+15285^26368110331Hans Havermann10/2020
4677(23*10^110290+19)/3110291Robert Price07/2019
467818^87853-4409110280Enzo Doria03/2013
467928490^7419+7419^28490110267Hans Havermann11/2020
46802^366218-23110243Lelio R Paula02/2013
4681(21*2^366193-1)/197110235Lelio R Paula03/2014
46822^366178-343991110231Enzo Doria07/2015
468325777^18798+18798^25777110174Hans Havermann10/2020
46842^365944+1871341110161Enzo Doria05/2016
46852^365838-461267110129Enzo Doria07/2015
468630152^4491+4491^30152110126Hans Havermann11/2020
468710^110111+464019110112Patrick De Geest05/2021
468810^110111-40001110111Robert Price01/2021
46892^365763-6555110106Lelio R Paula04/2017
4690(2^365689+2^182845+1)/511008311/2006
46912^365666-459161110077Enzo Doria05/2015
46923*10^110076-7110077Robert Price08/2015
469313^98785-72110041Lelio R Paula03/2017
4694(25^78707+1)/26110027Robert Price06/2013
4695(16*10^110014-73)/3110015Robert Price07/2020
4696(7*10^110006-151)/9110006Robert Price02/2018
46976^141361-7110001Lelio R Paula11/2014
469820^84536+81109984Lelio R Paula03/2017
46995*2^365347-9109982Lelio R Paula09/2014
47009*6^141303+7109957Lelio R Paula11/2014
470127635^9522+9522^27635109953Hans Havermann11/2020
470278^58099+77109929Norbert Schneider02/2015
47032*10^109928-7109929Robert Price10/2015
470430580^3933+3933^30580109927Hans Havermann11/2020
470526380^14689+14689^26380109926Hans Havermann11/2020
4706(2^365161+1130)/2109925Stefano Morozzi09/2020
4707(27*2^365137-1)/2021109916Lelio R Paula03/2014
4708(4441*29^75152-24)/7109905Curtis Bright05/2015
4709(2^365087+7)/6015109899Lelio R Paula01/2014
4710(2^365069+3774)/2109897Stefano Morozzi02/2021
471129652^5083+5083^29652109894Mark Rodenkirch10/2020
4712(2^365049+722)/2109891Stefano Morozzi09/2020
471318^87533-11109878Lelio R Paula04/2017
47142^364982-5109871Henri Lifchitz04/2006
47153*10^109861+59109862Robert Price08/2018
47165*10^109860-69109861Robert Price02/2021
47172^364936-1867979109857Enzo Doria04/2016
471827013^11652+11652^27013109846Hans Havermann10/2020
47192^364867-112087109836Enzo Doria06/2014
47204^182415-85061109825Mike Oakes06/2011
4721(2^364809+1034)/2109819Stefano Morozzi09/2020
4722(52*10^109807-133)/9109808Robert Price09/2021
472325708^18675+18675^25708109806Hans Havermann10/2020
4724(17^89227+16^89227)/33109788Robert Price08/2013
47252^364687-187109782Lelio R Paula01/2012
47262^364644+67109769Lelio R Paula01/2012
4727(9787*2^364625-1)/24947109763Lelio R Paula05/2015
4728(2^364616+5)/9109760Lelio R Paula01/2014
4729(55*10^109759+89)/9109760Robert Price03/2019
473012^101694+73109747Lelio R Paula03/2017
473113^98518-66109744Lelio R Paula03/2017
4732(8*10^109721-269)/9109721Robert Price09/2021
47332^364478-113261109719Enzo Doria07/2014
4734(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
4735(24737*2^364454+1)/3109716Lelio R Paula07/2014
473627814^8777+8777^27814109681Hans Havermann10/2020
4737(62*10^109673+1)/9109674Serge Batalov11/2010
47383^229824+340109654Lelio R Paula03/2017
4739(2*10^109645-71)/3109645Robert Price12/2017
47402^364169-112813109626Enzo Doria06/2014
474128822^6359+6359^28822109622Hans Havermann11/2020
474210^109615+21109616Lelio R Paula03/2017
474310^109615-456267109615Patrick De Geest03/2017
47442^364094-113109604Lelio R Paula01/2012
474525251^21898+21898^25251109600Hans Havermann11/2020
4746(4^182026+11)/3109591Robert Price02/2017
47472^364041-6883109588Lelio R Paula09/2011
474812^101545+11109586Lelio R Paula03/2017
474926536^13475+13475^26536109582Hans Havermann11/2020
47502^363842-2787101109528Enzo Doria03/2016


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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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