Henri & Renaud Lifchitz's PRP Top records

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 ?
6251	(14*10^116112-101)/3	116113	Robert Price	02/2019
6252	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6253	3*10^116107+23	116108	Robert Price	03/2022
6254	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6255	2^385622+71839	116084	Enzo Doria	04/2016
6257	2^385564+781	116067	Lelio R Paula	01/2012
6256	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6258	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6259	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6260	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6261	(266*10^116024-17)/3	116026	Robert Price	07/2020
6262	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6263	2^385410+71893	116020	Enzo Doria	04/2016
6264	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6265	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6266	12^107422-11	115928	Riley Fisher	12/2023
6267	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6268	(11*10^115910-131)/3	115911	Robert Price	09/2018
6269	2^384953-111943	115883	Paul Bourdelais	02/2012
6270	43^70942-2	115882	Lelio R Paula	04/2014
6271	(94*10^115879-7)/3	115881	Robert Price	03/2020
6272	7*10^115863+3	115864	Robert Price	08/2015
6273	2^384834+93	115847	Donovan Johnson	07/2008
6274	2^384809+71297	115840	Enzo Doria	04/2016
6275	(55*10^115829+323)/9	115830	Robert Price	10/2021
6276	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6277	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6278	(793*10^115810+53)/9	115812	Robert Price	01/2022
6279	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6280	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6281	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6282	2*10^115784-27	115785	Robert Price	05/2018
6283	10^115773+126739	115774	Patrick De Geest	04/2018
6285	10^115773-1000000001	115773	Robert Price	03/2018
6284	10^115773-396221	115773	Patrick De Geest	04/2018
6286	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6287	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6288	2^384530+1874305	115756	Enzo Doria	06/2016
6289	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6290	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6291	(44*10^115697-413)/9	115698	Robert Price	03/2019
6292	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6293	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6294	2^384312+81091	115690	Yves Minet	02/2010
6295	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6296	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6297	(4*10^115668-79)/3	115669	Robert Price	02/2018
6298	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6299	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6300	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6301	18^92125-92125^18	115642	Dylan Delgado	08/2019
6302	3^242337-4042	115625	Enzo Doria	05/2014
6303	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6304	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6305	7*10^115561+79	115562	Robert Price	07/2019
6306	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6307	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6308	2^383780-3149	115530	Yves Minet	10/2014
6309	(41*10^115523-383)/9	115524	Robert Price	11/2018
6310	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6311	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6312	2^383560-455	115464	Yves Minet	03/2012
6313	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6314	(22*10^115454+119)/3	115455	Robert Price	04/2021
6315	89^59221-88^59221	115445	Robert Price	06/2015
6316	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6317	2^383347+1869413	115399	Enzo Doria	05/2016
6318	(103*10^115366+17)/3	115368	Robert Price	08/2020
6319	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6320	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6321	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6322	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6324	2^383039+1869509	115307	Enzo Doria	05/2016
6323	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6325	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6326	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6327	(22*10^115282+29)/3	115283	Robert Price	02/2021
6328	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6329	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6330	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6331	6*10^115211+79	115212	Robert Price	09/2020
6332	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6333	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6334	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6335	(22*10^115188-193)/9	115189	Robert Price	07/2022
6336	2^382633+73697	115185	Enzo Doria	04/2016
6337	2^382509-113593	115147	Enzo Doria	08/2014
6338	2^382502-2791721	115145	Enzo Doria	03/2016
6339	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6340	2^382464+22741	115134	Enzo Doria	09/2023
6341	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6342	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6343	9^120590-120590	115073	Robert Price	03/2014
6344	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6345	2^382198+9	115054	Lelio R Paula	03/2013
6346	18268*31^77131+22839	115035	Eric Chen	05/2024
6347	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6348	(89*10^115030-179)/9	115031	Robert Price	12/2019
6349	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6350	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6351	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6352	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6353	(23*10^114962+7)/3	114963	Robert Price	05/2023
6354	2^381883-59197	114959	Enzo Doria	10/2015
6355	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6356	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6358	2^381806-4481	114936	Yves Minet	07/2011
6357	2^381808-1851507	114936	Enzo Doria	08/2015
6359	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6360	2^381774-112373	114926	Enzo Doria	06/2014
6361	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6362	2^381555-109051	114860	Enzo Doria	04/2014
6363	2^381551+213683	114859	Enzo Doria	09/2023
6364	2^381546-113501	114857	Enzo Doria	08/2014
6365	(7*10^114845-19)/3	114846	Robert Price	10/2020
6366	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6367	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6368	3^240644+16	114817	Robert Price	04/2020
6369	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6370	2^381360-110429	114801	Enzo Doria	05/2014
6371	(17*10^114795+79)/3	114796	Robert Price	04/2019
6372	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6373	2^381252-115079	114769	Enzo Doria	06/2015
6374	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6375	2^381209-29323	114756	Enzo Doria	07/2015
6376	2^381207-111546435	114755	Paul Bourdelais	10/2021
6377	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6378	2^381201+1873205	114753	Enzo Doria	06/2016
6380	(85*10^114737+293)/9	114738	Robert Price	12/2019
6381	(265*10^114736+17)/3	114738	Robert Price	03/2020
6379	379*10^114735+9	114738	Jason Yuen	01/2025
6382	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6383	2^380974-112991	114685	Enzo Doria	07/2014
6384	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6385	(26*10^114658-119)/3	114659	Robert Price	07/2023
6386	88^58949-87	114626	Norbert Schneider	11/2015
6387	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6388	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6389	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6390	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6391	(331*10^114605-7)/9	114607	Robert Price	04/2022
6392	2^380700+91	114603	Lelio R Paula	03/2013
6393	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6394	7*10^114577+27	114578	Robert Price	11/2020
6396	10^114575+3^114576	114576	Mike Oakes	09/2010
6395	10^114575+66561	114576	Patrick De Geest	02/2017
6397	10^114575-581081	114575	Patrick De Geest	02/2017
6398	2^380587-115315	114569	Enzo Doria	06/2015
6399	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6400	2^380513-216925	114546	Enzo Doria	05/2014
6401	2^380451-1840087	114528	Enzo Doria	06/2015
6402	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6403	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6404	2^380279-461347	114476	Enzo Doria	07/2015
6405	(331*10^114454-7)/9	114456	Robert Price	04/2022
6406	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6407	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6408	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6409	(11*10^114400+529)/9	114401	Robert Price	09/2021
6410	2^380021+1871147	114398	Enzo Doria	05/2016
6411	2^380005+1869707	114393	Enzo Doria	05/2016
6412	2^379958-113297	114379	Enzo Doria	07/2014
6413	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6414	2^379881-109105	114356	Enzo Doria	04/2014
6415	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6416	(4*10^114340+83)/3	114341	Robert Price	02/2018
6417	(26*10^114317-77)/3	114318	Robert Price	11/2019
6418	(4*10^114296+149)/9	114296	Robert Price	04/2018
6419	88^58773-87	114284	Norbert Schneider	11/2015
6420	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6421	(132^53891-1)/131	114278	Anonymous	06/2024
6422	2^379529-2790283	114250	Enzo Doria	03/2016
6423	2^379522+1869115	114248	Enzo Doria	05/2016
6424	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6425	2^379317-115033	114186	Enzo Doria	06/2015
6426	(22*10^114178+47)/3	114179	Robert Price	06/2021
6427	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6428	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6429	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6430	6*10^114091+23	114092	Robert Price	09/2020
6431	(4*10^114076+143)/3	114077	Robert Price	03/2018
6432	332*25^81584+12357	114053	Eric Chen	10/2023
6433	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
6434	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
6435	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
6437	(46*10^113969+683)/9	113970	Robert Price	03/2019
6436	(83*10^113969+133)/9	113970	Robert Price	08/2021
6438	32226^3439+3439^32226	113966	Hans Havermann	02/2021
6439	(77*10^113963-149)/9	113964	Robert Price	03/2022
6440	78*10^113954-7	113956	Robert Price	10/2020
6441	2*10^113941+9	113942	Dmitry Domanov	11/2010
6442	10^113933+145897	113934	Patrick De Geest	02/2021
6445	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
6443	10^113933-8000000001	113933	Robert Price	11/2020
6444	10^113933-66167	113933	Patrick De Geest	02/2021
6446	2339662057597*10^113903+9	113916	Robert Price	03/2021
6447	4*10^113905+91	113906	Robert Price	08/2018
6448	10^113894+76609	113895	Patrick De Geest	02/2021
6450	10^113894-10000001	113894	Robert Price	09/2020
6449	10^113894-373947	113894	Patrick De Geest	02/2021
6451	33933^2270+2270^33933	113881	Hans Havermann	02/2021
6452	4*10^113874-21	113875	Robert Price	09/2018
6453	2^378272-16565	113872	Enzo Doria	04/2013
6454	2^378217-109075	113855	Enzo Doria	04/2014
6455	2^378198+67	113849	Lelio R Paula	03/2013
6456	2^378173-3249	113842	Yves Minet	12/2014
6457	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
6458	2^378137+1334025	113831	Henri Lifchitz	10/2024
6459	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
6460	30030^6173+6173^30030	113829	Hans Havermann	01/2021
6461	2^378128-262977	113828	Enzo Doria	05/2014
6462	2^378123-113215	113827	Enzo Doria	07/2014
6463	6^146274-18893	113824	Enzo Doria	03/2013
6464	34596^1949+1949^34596	113815	Hans Havermann	02/2021
6465	2^378078+75	113813	Lelio R Paula	03/2013
6466	(28*10^113810+449)/9	113811	Robert Price	11/2021
6467	26273^21448+21448^26273	113799	Hans Havermann	02/2021
6468	2^377966+255255	113780	Paul Bourdelais	10/2021
6469	2^377940+63	113772	Lelio R Paula	03/2013
6470	2^377941-2785843	113772	Enzo Doria	04/2016
6471	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
6472	2^377810+1875109	113733	Enzo Doria	09/2016
6473	2^377803-1838635	113731	Enzo Doria	05/2015
6474	2^377799+52223	113729	Yves Minet	08/2010
6475	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
6476	11^109190-270	113710	Enzo Doria	12/2012
6477	28206^10739+10739^28206	113698	Hans Havermann	01/2021
6478	7*10^113693+9	113694	Robert Price	09/2015
6479	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
6480	(82*10^113681+161)/9	113682	Robert Price	10/2019
6481	26121^22478+22478^26121	113673	Hans Havermann	01/2021
6482	4*10^113658+49	113659	Robert Price	01/2019
6483	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
6484	(2*10^113631+529)/9	113631	Robert Price	01/2018
6485	2^377408-2798279	113612	Enzo Doria	04/2016
6486	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
6487	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
6488	5*10^113586+57	113587	Robert Price	12/2018
6489	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
6490	2^377222+93679	113556	Yves Minet	02/2011
6492	262147#+316847	113552	Makoto Morimoto	02/2016
6491	27172^15101+15101^27172	113552	Hans Havermann	01/2021
6493	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
6494	2^377026-458903	113497	Enzo Doria	04/2015
6495	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
6496	34791^1828+1828^34791	113488	Hans Havermann	02/2021
6497	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
6498	(29*10^113468-17)/3	113469	Robert Price	09/2019
6499	35^73477-34^73477	113454	Robert Price	05/2012
6500	(14*10^113451-89)/3	113452	Robert Price	05/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301421 PRPs in the top)