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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
2512^1432308+1888801431168Enzo Doria10/2017
252(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
2532^1425483+1886813429114Enzo Doria04/2017
254(63^238481+1)/64429107Paul Bourdelais12/2020
255(17^348259+1)/18428514Paul Bourdelais05/2014
256(10^427912+89)/9427912Serge Batalov12/2014
2572^1421089+1890167427791Enzo Doria09/2017
25820^326600+3424917Paul Bourdelais01/2021
259(10^424861-7)/3424861Leonid Durman01/2012
2602^1404213+184217422711Enzo Doria09/2017
2612^1401872+1884385422006Enzo Doria04/2017
2622^1401257+6077421821Enzo Doria09/2017
263138^196873-137^196873421285Jean-Louis Charton12/2009
2642^1398269+131595420921Makoto Morimoto10/2013
2652^1397071+684443420561Enzo Doria07/2017
266953^141023-952^141023420121Jean-Louis Charton10/2016
267(3^877843-1)/2418838Paul Bourdelais07/2010
2682^1386321+60299417325Enzo Doria02/2018
2692^1386320+184531417324Enzo Doria09/2017
2702^1382074+1883587416046Enzo Doria01/2017
2712^1379907+1885223415394Enzo Doria03/2017
2722^1375574+1886719414090Enzo Doria04/2017
2732^1373111+1884833413348Enzo Doria02/2017
2742^1368632+1889731412000Enzo Doria10/2017
275(89*10^411590+1)/9411591Serge Batalov09/2014
276F(1968721)411439Henri Lifchitz11/2009
2772^1366066+683749411227Enzo Doria02/2017
2782^1355790+1888939408134Enzo Doria07/2017
2792^1355635+1884203408087Enzo Doria01/2017
280(88^208739+1)/89405888Paul Bourdelais12/2020
281(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
2822^1347744-3405712Paul Bourdelais07/2019
28310^400000+1415223400001Patrick De Geest10/2020
28410^400000-339233400000Patrick De Geest10/2020
285Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
2862^1319770+1884949397291Enzo Doria06/2017
2872^1313062+1888849395272Enzo Doria08/2017
288(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
289(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
2902^1311618+783529394837Enzo Doria01/2017
2912^1308000+1883521393748Enzo Doria02/2017
292(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
293(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
294(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
295(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
296(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
297(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
2982^1303102+1866409392273Enzo Doria09/2017
2992^1302818+283429392188Enzo Doria01/2017
300(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
3012^1299181+1886867391093Enzo Doria04/2017
302(37^249341-1)/36391016Paul Bourdelais08/2020
3032^1298304+1882891390829Enzo Doria01/2017
30495196^12497+12497^95196390000Hans Havermann12/2021
305(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
30681650^54369+54369^81650386642Yusuf AttarBashi06/2021
30780565^62824+62824^80565386561Hans Havermann08/2021
30883747^41272+41272^83747386548Hans Havermann08/2021
30915^328574+328574^15386434Serge Batalov05/2014
3102^1280078+1885099385342Enzo Doria08/2017
3112^1274941+1880717383796Enzo Doria10/2016
3122^1272632+383431383101Enzo Doria01/2017
3132^1271346+1889839382714Enzo Doria08/2017
314(10^380976-7)/3380976Leonid Durman01/2012
3152^1257787+1447761378632Makoto Morimoto10/2013
316(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
317(77^200657-1)/76378536Paul Bourdelais08/2020
318(98^189619+1)/99377573Paul Bourdelais02/2021
319F(1803059)376817Henri Lifchitz06/2009
3207^442674+4374103Paul Bourdelais02/2021
321(97^187393-1)/96372306Paul Bourdelais09/2020
32210^371696+7371697Alfred Reich05/2021
3232^1234709+883127371685Enzo Doria12/2016
324(67^203431+1)/68371479Paul Bourdelais09/2021
3252^1231466+283819370709Enzo Doria07/2017
3262^1220335+1881263367358Enzo Doria11/2016
3272^1216694+1884769366262Enzo Doria02/2017
3282^1215889-3366020Paul Bourdelais06/2019
3292^1215296+1885441365841Enzo Doria03/2017
330(80^192133+1)/81365645Paul Bourdelais01/2021
3312^1214307+1888115365543Enzo Doria05/2017
3322^1213815+3365395Paul Bourdelais06/2019
333(80^191953+1)/81365302Paul Bourdelais01/2021
3342^1207345+1882577363448Enzo Doria12/2016
3352^1207073+883727363366Enzo Doria03/2017
3363^761457-2363308Ryan Propper07/2015
337(10^363030+7)/337/443363025Alfred Reich12/2021
338(2^1200924+324730)/2361514Stefano Morozzi06/2021
339(2^1200912+274110)/2361511Stefano Morozzi01/2021
340(2^1200887+344126)/2361503Stefano Morozzi10/2020
3412^1200861+198521361495Stefano Morozzi11/2021
342(2^1200856+305790)/2361494Stefano Morozzi10/2020
343(2^1200853+372822)/2361493Stefano Morozzi06/2021
3442^1200812+324178)/2361481Stefano Morozzi06/2021
345(2^1200768+380458)/2361467Stefano Morozzi01/2021
3462^1200756+140917361464Stefano Morozzi05/2022
347(2^1200741+293402)/2361459Stefano Morozzi07/2021
3482^1200672+1880881361439Enzo Doria10/2016
3492^1200660+198555361435Stefano Morozzi12/2021
3502^1200657+164837361434Stefano Morozzi05/2022
351(2^1200603+356030)/2361418Stefano Morozzi10/2020
352(2^1200590+275854)/2361414Stefano Morozzi03/2021
3532^1200550+139297361402Stefano Morozzi10/2021
354(2^1200456+320526)/2361373Stefano Morozzi10/2020
3552^1200416+164065361362Stefano Morozzi01/2022
3562^1200331+155429361336Stefano Morozzi10/2021
357(2^1200289+348366)/2361323Stefano Morozzi10/2020
358(2^1200284+273162)/2361322Stefano Morozzi10/2020
3592^1200252+194535361312Stefano Morozzi11/2021
360(2^1200250+364230)/2361311Stefano Morozzi10/2020
3612^1200227+156881361305Stefano Morozzi05/2022
362(2^1200209+305990)/2361299Stefano Morozzi10/2020
363(2^1200210+376278)/2361299Stefano Morozzi10/2020
364(2^1200182+274462)/2361291Stefano Morozzi01/2021
3652^1200168+140403361287Stefano Morozzi03/2022
366(2^1200162+275910)/2361285Stefano Morozzi03/2021
367(2^1200131+360150)/2361276Stefano Morozzi10/2020
368(2^1200118+290718)/2361272Stefano Morozzi01/2021
369(64*10^360173-1)/243360173Serge Batalov09/2014
370(59^203309+1)/60360029Paul Bourdelais09/2021
3712^1195093+1882577359759Enzo Doria12/2016
372(6^461108-11)/5358812Paul Bourdelais04/2019
3732^1191375+8543358640Phil Moore06/2008
3742^1190972+1880191358519Enzo Doria11/2016
375(45^216551-1)/44358004Paul Bourdelais08/2020
376(50^210319-1)/49357324Paul Bourdelais08/2020
377(531^131072+25^131072)/2357184Kellen Shenton03/2021
3782^1179836+1885021355167Enzo Doria02/2017
37920^271951+3353817Paul Bourdelais01/2021
380(63^195893-1)/62352477Paul Bourdelais08/2020
381numbpart(100000135540)352269Serge Batalov04/2017
382(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
3832^1168554+783529351770Enzo Doria01/2017
384(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
3852^1166152+1882411351047Enzo Doria12/2016
38610^350071+7350072Alfred Reich05/2021
3872^1162154+1890207349844Enzo Doria08/2017
388(7*10^348724-61)/9348724Erik Branger09/2016
389(127^165601-1)/126348390Alexander Zhirkov09/2015
3902^1153083+1883693347113Enzo Doria04/2017
391(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
3922^1145882+80779344945Enzo Doria09/2016
3932^1136462+1887289342110Enzo Doria05/2017
394F(1636007)341905Henri Lifchitz03/2009
3952^1133678+782569341272Enzo Doria11/2016
396(11^327001+1)/12340536Paul Bourdelais09/2013
397(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
398Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
3992^1126380-3339075Paul Bourdelais06/2019
4002^1125446+1885099338794Enzo Doria08/2017
401(63^188147+1)/64338539Paul Bourdelais12/2020
4022^1124549+143807338523Enzo Doria10/2016
4032^1121187+1886783337511Enzo Doria04/2017
404(48^200443-1)/47336992Paul Bourdelais08/2020
405(94^170371-1)/93336162Paul Bourdelais09/2020
4062^1116184+1883521336005Enzo Doria02/2017
4072^1114517+1880087335504Enzo Doria10/2016
408(101^166849+1)/102334418Paul Bourdelais12/2020
409(3^700897+1)/4334413Paul Bourdelais04/2010
4102^1104408-114539332460Enzo Doria03/2015
4112^1101921+82085331712Enzo Doria10/2016
4122^1100655+683513331331Enzo Doria01/2017
413(10^330906+71)/9330906Serge Batalov07/2015
4142^1098346+482899330636Enzo Doria11/2016
4152^1095679+1878713329833Enzo Doria09/2016
4162^1094740-1851539329550Enzo Doria08/2015
4172^1091469-379369328565Enzo Doria03/2014
418(69^178093-1)/68327485Paul Bourdelais08/2020
419(10^326884+7)/421326882Alfred Reich12/2021
4202^1085750+582349326844Enzo Doria11/2016
4212^1083596+483061326195Enzo Doria12/2016
422(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
4232^1082908+583561325988Enzo Doria05/2017
42430^220411-29^220411325574Jean-Louis Charton10/2018
4252^1078242+1881649324584Enzo Doria11/2016
4262^1077737+1880117324432Enzo Doria10/2016
4272^1075425+1880117323736Enzo Doria10/2016
428(28^223381+1)/29323267Paul Bourdelais12/2020
42910^322999+187071323000Stefano Morozzi03/2019
43010^322999-143151322999Patrick De Geest05/2020
4312^1072146+1886869322749Enzo Doria04/2017
4322^1072118-7321953322740Enzo Doria02/2015
4332^1071026+1886869322411Enzo Doria04/2017
4342^1070539+1880633322265Enzo Doria10/2016
4352^1069293-1147195321890Enzo Doria05/2015
4362^1065968+1880941320889Enzo Doria10/2016
4372^1065897-1147195320867Enzo Doria05/2015
4382^1063427+1882103320124Enzo Doria12/2016
4392^1061095-1061095319422Henri Lifchitz10/2013
4402^1060950+653119319378Enzo Doria12/2016
4412^1060363+782753319202Enzo Doria11/2016
442(71^172259-1)/70318895Paul Bourdelais08/2020
4432^1054736+483061317508Enzo Doria12/2016
4442^1053965+1879667317276Enzo Doria10/2016
445(43^194119-1)/42317086Paul Bourdelais08/2020
4462^1052186-458165316740Enzo Doria03/2015
4472^1046613-114685315062Enzo Doria04/2015
4482^1045625-459373314765Enzo Doria06/2015
449(7*10^314564-61)/9314564Erik Branger09/2016
450(7^371669-1)/6314096Paul Bourdelais02/2010
451(53^181981-1)/52313784Paul Bourdelais08/2020
4522^1041944+283051313657Enzo Doria12/2016
4532^1041153-114391313419Enzo Doria02/2015
454(74^167311+1)/75312742Paul Bourdelais12/2020
4552^1038871+1866983312732Enzo Doria04/2016
456(55^179573-1)/54312521Paul Bourdelais08/2020
4572^1037647+1881263312363Enzo Doria11/2016
4582^1037226+1879699312237Enzo Doria10/2016
4592^1036867+1865843312129Enzo Doria02/2016
460(76^165947+1)/77312114Paul Bourdelais01/2021
4612^1036020-114539311874Enzo Doria02/2015
462(90^159463-1)/89311628Paul Bourdelais08/2020
4632^1032240+1883431310736Enzo Doria01/2017
4642^1030352+1870021310167Enzo Doria06/2016
4652^1030046+1882843310075Enzo Doria11/2016
4663^648872+16309591Robert Price04/2020
4675^442281+2309142Paul Bourdelais01/2021
468A352736(16)306985Kellen Shenton05/2022
469(11^293831-1)/10305993Paul Bourdelais03/2010
470(67^167449-1)/66305773Paul Bourdelais08/2020
471(62^170539+1)/63305671Paul Bourdelais12/2020
4722^1015321-1015321305643Henri Lifchitz08/2013
4732^1014224-2791229305312Enzo Doria01/2016
474(10^304986+7)/673304984Alfred Reich11/2021
47565473^45250+45250^65473304818Hans Havermann02/2022
47666012^41423+41423^66012304794Hans Havermann03/2022
47765073^48202+48202^65073304742Hans Havermann04/2022
478238176^19+19^238176304569Hans Havermann03/2022
47973122^14615+14615^73122304539Hans Havermann05/2022
48064492^52639+52639^64492304487Hans Havermann03/2022
48165955^41288+41288^65955304437Hans Havermann04/2022
48271729^17530+17530^71729304403Hans Havermann03/2022
48370170^21733+21733^70170304336Hans Havermann03/2022
4842^1010751-107709304267Enzo Doria03/2014
48584473^3994+3994^84473304222Hans Havermann03/2022
486(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
48774442^12125+12125^74442303998Hans Havermann02/2022
48877842^8039+8039^77842303989Hans Havermann01/2022
48964209^54140+54140^64209303935Hans Havermann02/2022
4902^1009577+1869587303913Enzo Doria06/2016
49167389^32338+32338^67389303906Hans Havermann02/2022
4928^336419-7^336419303817Jean-Louis Charton01/2008
49380766^5771+5771^80766303782Hans Havermann01/2022
49466094^39385+39385^66094303724Hans Havermann01/2022
49569147^24574+24574^69147303589Hans Havermann02/2022
49678390^7459+7459^78390303580Hans Havermann01/2022
4972^1008301+1869377303529Enzo Doria06/2016
49865008^46615+46615^65008303492Hans Havermann02/2022
499(2^1007838+5)/3303389Serge Batalov08/2015
50065018^46293+46293^65018303343Hans Havermann01/2022


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!