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 ?
2512^1493170+784129449489Enzo Doria08/2017
2522^1489873+1888277448497Enzo Doria06/2017
2532^1484671+1888463446931Enzo Doria06/2017
2542^1482867+1886783446388Enzo Doria04/2017
2552^1482148+284011446172Enzo Doria04/2017
2562^1479356+1888291445331Enzo Doria06/2017
25714^384558+3440753Paul Bourdelais01/2021
2582^1461244+784531439879Enzo Doria10/2017
259(67^239053+1)/68436527Paul Bourdelais09/2021
260(80^228419+1)/81434701Paul Bourdelais02/2021
2612^1443089+60227434414Enzo Doria10/2017
262(21^328129-1)/20433858Paul Bourdelais06/2014
263(35^280979+1)/36433850Paul Bourdelais09/2021
2642^1434400+3431798Paul Bourdelais06/2019
2652^1432308+1888801431168Enzo Doria10/2017
266(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
2672^1425483+1886813429114Enzo Doria04/2017
268(63^238481+1)/64429107Paul Bourdelais12/2020
269(17^348259+1)/18428514Paul Bourdelais05/2014
270(10^427912+89)/9427912Serge Batalov12/2014
2712^1421089+1890167427791Enzo Doria09/2017
27220^326600+3424917Paul Bourdelais01/2021
273(10^424861-7)/3424861Leonid Durman01/2012
2742^1404213+184217422711Enzo Doria09/2017
2752^1401872+1884385422006Enzo Doria04/2017
2762^1401257+6077421821Enzo Doria09/2017
277138^196873-137^196873421285Jean-Louis Charton12/2009
2782^1398269+131595420921Makoto Morimoto10/2013
2792^1397071+684443420561Enzo Doria07/2017
280953^141023-952^141023420121Jean-Louis Charton10/2016
281(3^877843-1)/2418838Paul Bourdelais07/2010
2822^1386321+60299417325Enzo Doria02/2018
2832^1386320+184531417324Enzo Doria09/2017
2842^1382074+1883587416046Enzo Doria01/2017
2852^1379907+1885223415394Enzo Doria03/2017
2862^1375574+1886719414090Enzo Doria04/2017
2872^1373111+1884833413348Enzo Doria02/2017
2882^1368632+1889731412000Enzo Doria10/2017
289(89*10^411590+1)/9411591Serge Batalov09/2014
290F(1968721)411439Henri Lifchitz11/2009
2912^1366066+683749411227Enzo Doria02/2017
2922^1355790+1888939408134Enzo Doria07/2017
2932^1355635+1884203408087Enzo Doria01/2017
294(88^208739+1)/89405888Paul Bourdelais12/2020
295(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
2962^1347744-3405712Paul Bourdelais07/2019
2971215^131072+242^131072404302Kellen Shenton08/2022
2981196^131072+595^131072403405Kellen Shenton08/2022
29910^400000+1415223400001Patrick De Geest10/2020
30010^400000-339233400000Patrick De Geest10/2020
301Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
3022^1319770+1884949397291Enzo Doria06/2017
3032^1313062+1888849395272Enzo Doria08/2017
304(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
305(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
3062^1311618+783529394837Enzo Doria01/2017
3072^1308000+1883521393748Enzo Doria02/2017
308(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
309(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
310(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
311(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
312(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
313(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
3142^1303102+1866409392273Enzo Doria09/2017
3152^1302818+283429392188Enzo Doria01/2017
316(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
3172^1299181+1886867391093Enzo Doria04/2017
318(37^249341-1)/36391016Paul Bourdelais08/2020
3192^1298304+1882891390829Enzo Doria01/2017
32095196^12497+12497^95196390000Hans Havermann12/2021
321(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
32281650^54369+54369^81650386642Yusuf AttarBashi06/2021
32380565^62824+62824^80565386561Hans Havermann08/2021
32483747^41272+41272^83747386548Hans Havermann08/2021
32515^328574+328574^15386434Serge Batalov05/2014
3262^1280078+1885099385342Enzo Doria08/2017
3272^1274941+1880717383796Enzo Doria10/2016
3282^1272632+383431383101Enzo Doria01/2017
3292^1271346+1889839382714Enzo Doria08/2017
330(10^380976-7)/3380976Leonid Durman01/2012
3312^1257787+1447761378632Makoto Morimoto10/2013
332(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
333(77^200657-1)/76378536Paul Bourdelais08/2020
334(98^189619+1)/99377573Paul Bourdelais02/2021
335F(1803059)376817Henri Lifchitz06/2009
3367^442674+4374103Paul Bourdelais02/2021
337(97^187393-1)/96372306Paul Bourdelais09/2020
33810^371696+7371697Alfred Reich05/2021
3392^1234709+883127371685Enzo Doria12/2016
340(67^203431+1)/68371479Paul Bourdelais09/2021
3412^1231466+283819370709Enzo Doria07/2017
3422^1220335+1881263367358Enzo Doria11/2016
3432^1216694+1884769366262Enzo Doria02/2017
3442^1215889-3366020Paul Bourdelais06/2019
3452^1215296+1885441365841Enzo Doria03/2017
346(80^192133+1)/81365645Paul Bourdelais01/2021
3472^1214307+1888115365543Enzo Doria05/2017
3482^1213815+3365395Paul Bourdelais06/2019
349(80^191953+1)/81365302Paul Bourdelais01/2021
3502^1207345+1882577363448Enzo Doria12/2016
3512^1207073+883727363366Enzo Doria03/2017
3523^761457-2363308Ryan Propper07/2015
353(10^363030+7)/337/443363025Alfred Reich12/2021
354(2^1200924+324730)/2361514Stefano Morozzi06/2021
355(2^1200912+274110)/2361511Stefano Morozzi01/2021
3562^1200906+165249361509Stefano Morozzi07/2022
357(2^1200887+344126)/2361503Stefano Morozzi10/2020
3582^1200877+186755361500Stefano Morozzi09/2022
3592^1200861+198521361495Stefano Morozzi11/2021
360(2^1200856+305790)/2361494Stefano Morozzi10/2020
361(2^1200853+372822)/2361493Stefano Morozzi06/2021
3622^1200812+324178)/2361481Stefano Morozzi06/2021
363(2^1200768+380458)/2361467Stefano Morozzi01/2021
3642^1200756+140917361464Stefano Morozzi05/2022
3652^1200741+184781361460Stefano Morozzi09/2022
366(2^1200741+293402)/2361459Stefano Morozzi07/2021
3682^1200672+1880881361439Enzo Doria10/2016
3672^1200672+141535361439Stefano Morozzi09/2022
3692^1200660+198555361435Stefano Morozzi12/2021
3702^1200657+164837361434Stefano Morozzi05/2022
371(2^1200603+356030)/2361418Stefano Morozzi10/2020
372(2^1200590+275854)/2361414Stefano Morozzi03/2021
3732^1200550+139297361402Stefano Morozzi10/2021
374(2^1200456+320526)/2361373Stefano Morozzi10/2020
3752^1200416+164065361362Stefano Morozzi01/2022
3762^1200331+155429361336Stefano Morozzi10/2021
377(2^1200289+348366)/2361323Stefano Morozzi10/2020
378(2^1200284+273162)/2361322Stefano Morozzi10/2020
3792^1200252+194535361312Stefano Morozzi11/2021
380(2^1200250+364230)/2361311Stefano Morozzi10/2020
3812^1200227+156881361305Stefano Morozzi05/2022
382(2^1200209+305990)/2361299Stefano Morozzi10/2020
383(2^1200210+376278)/2361299Stefano Morozzi10/2020
384(2^1200182+274462)/2361291Stefano Morozzi01/2021
3852^1200178+149193361290Stefano Morozzi07/2022
3862^1200168+140403361287Stefano Morozzi03/2022
387(2^1200162+275910)/2361285Stefano Morozzi03/2021
3882^1200134+141385361277Stefano Morozzi08/2022
389(2^1200131+360150)/2361276Stefano Morozzi10/2020
390(2^1200118+290718)/2361272Stefano Morozzi01/2021
3912^1200022+192777361243Stefano Morozzi09/2022
392(64*10^360173-1)/243360173Serge Batalov09/2014
393(59^203309+1)/60360029Paul Bourdelais09/2021
3942^1195093+1882577359759Enzo Doria12/2016
395(6^461108-11)/5358812Paul Bourdelais04/2019
3962^1191375+8543358640Phil Moore06/2008
3972^1190972+1880191358519Enzo Doria11/2016
398(45^216551-1)/44358004Paul Bourdelais08/2020
399(50^210319-1)/49357324Paul Bourdelais08/2020
400(531^131072+25^131072)/2357184Kellen Shenton03/2021
4012^1179836+1885021355167Enzo Doria02/2017
40220^271951+3353817Paul Bourdelais01/2021
403(63^195893-1)/62352477Paul Bourdelais08/2020
404numbpart(100000135540)352269Serge Batalov04/2017
405(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
4062^1168554+783529351770Enzo Doria01/2017
407(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
4082^1166152+1882411351047Enzo Doria12/2016
40910^350071+7350072Alfred Reich05/2021
4102^1162154+1890207349844Enzo Doria08/2017
411(7*10^348724-61)/9348724Erik Branger09/2016
412(127^165601-1)/126348390Alexander Zhirkov09/2015
4132^1153083+1883693347113Enzo Doria04/2017
414(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
4152^1145882+80779344945Enzo Doria09/2016
4162^1136462+1887289342110Enzo Doria05/2017
417F(1636007)341905Henri Lifchitz03/2009
4182^1133678+782569341272Enzo Doria11/2016
419(11^327001+1)/12340536Paul Bourdelais09/2013
420(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
421Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
4222^1126380-3339075Paul Bourdelais06/2019
4232^1125446+1885099338794Enzo Doria08/2017
424(63^188147+1)/64338539Paul Bourdelais12/2020
4252^1124549+143807338523Enzo Doria10/2016
4262^1121187+1886783337511Enzo Doria04/2017
427(48^200443-1)/47336992Paul Bourdelais08/2020
428(94^170371-1)/93336162Paul Bourdelais09/2020
4292^1116184+1883521336005Enzo Doria02/2017
4302^1114517+1880087335504Enzo Doria10/2016
431(101^166849+1)/102334418Paul Bourdelais12/2020
432(3^700897+1)/4334413Paul Bourdelais04/2010
4332^1104408-114539332460Enzo Doria03/2015
4342^1101921+82085331712Enzo Doria10/2016
4352^1100655+683513331331Enzo Doria01/2017
436(10^330906+71)/9330906Serge Batalov07/2015
4372^1098346+482899330636Enzo Doria11/2016
4382^1095679+1878713329833Enzo Doria09/2016
4392^1094740-1851539329550Enzo Doria08/2015
4402^1091469-379369328565Enzo Doria03/2014
441(69^178093-1)/68327485Paul Bourdelais08/2020
442(10^326884+7)/421326882Alfred Reich12/2021
4432^1085750+582349326844Enzo Doria11/2016
4442^1083596+483061326195Enzo Doria12/2016
445(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
4462^1082908+583561325988Enzo Doria05/2017
44730^220411-29^220411325574Jean-Louis Charton10/2018
4482^1078242+1881649324584Enzo Doria11/2016
4492^1077737+1880117324432Enzo Doria10/2016
4502^1075425+1880117323736Enzo Doria10/2016
451(28^223381+1)/29323267Paul Bourdelais12/2020
45210^322999+187071323000Stefano Morozzi03/2019
45310^322999-143151322999Patrick De Geest05/2020
4542^1072146+1886869322749Enzo Doria04/2017
4552^1072118-7321953322740Enzo Doria02/2015
4562^1071026+1886869322411Enzo Doria04/2017
4572^1070539+1880633322265Enzo Doria10/2016
4582^1069293-1147195321890Enzo Doria05/2015
4592^1065968+1880941320889Enzo Doria10/2016
4602^1065897-1147195320867Enzo Doria05/2015
4612^1063427+1882103320124Enzo Doria12/2016
4622^1061095-1061095319422Henri Lifchitz10/2013
4632^1060950+653119319378Enzo Doria12/2016
4642^1060363+782753319202Enzo Doria11/2016
465(71^172259-1)/70318895Paul Bourdelais08/2020
4662^1054736+483061317508Enzo Doria12/2016
4672^1053965+1879667317276Enzo Doria10/2016
468(43^194119-1)/42317086Paul Bourdelais08/2020
4692^1052186-458165316740Enzo Doria03/2015
4702^1046613-114685315062Enzo Doria04/2015
4712^1045625-459373314765Enzo Doria06/2015
472(7*10^314564-61)/9314564Erik Branger09/2016
473(7^371669-1)/6314096Paul Bourdelais02/2010
474(53^181981-1)/52313784Paul Bourdelais08/2020
4752^1041944+283051313657Enzo Doria12/2016
4762^1041153-114391313419Enzo Doria02/2015
477(74^167311+1)/75312742Paul Bourdelais12/2020
4782^1038871+1866983312732Enzo Doria04/2016
479(55^179573-1)/54312521Paul Bourdelais08/2020
4802^1037647+1881263312363Enzo Doria11/2016
4812^1037226+1879699312237Enzo Doria10/2016
4822^1036867+1865843312129Enzo Doria02/2016
483(76^165947+1)/77312114Paul Bourdelais01/2021
4842^1036020-114539311874Enzo Doria02/2015
485(90^159463-1)/89311628Paul Bourdelais08/2020
4862^1032240+1883431310736Enzo Doria01/2017
4872^1030352+1870021310167Enzo Doria06/2016
4882^1030046+1882843310075Enzo Doria11/2016
4893^648872+16309591Robert Price04/2020
4905^442281+2309142Paul Bourdelais01/2021
491A352736(16)306985Kellen Shenton05/2022
492(11^293831-1)/10305993Paul Bourdelais03/2010
493(67^167449-1)/66305773Paul Bourdelais08/2020
494(62^170539+1)/63305671Paul Bourdelais12/2020
4952^1015321-1015321305643Henri Lifchitz08/2013
4962^1014224-2791229305312Enzo Doria01/2016
497(10^304986+7)/673304984Alfred Reich11/2021
49865473^45250+45250^65473304818Hans Havermann02/2022
49966012^41423+41423^66012304794Hans Havermann03/2022
50065073^48202+48202^65073304742Hans Havermann04/2022


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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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