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 ?
7001	43^70942-2	115882	Lelio R Paula	04/2014
7002	(94*10^115879-7)/3	115881	Robert Price	03/2020
7003	7*10^115863+3	115864	Robert Price	08/2015
7004	2^384834+93	115847	Donovan Johnson	07/2008
7005	2^384809+71297	115840	Enzo Doria	04/2016
7006	(55*10^115829+323)/9	115830	Robert Price	10/2021
7007	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
7008	31348^4951+4951^31348	115822	Hans Havermann	02/2021
7009	(793*10^115810+53)/9	115812	Robert Price	01/2022
7010	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
7011	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
7012	31115^5266+5266^31115	115794	Hans Havermann	02/2021
7013	2*10^115784-27	115785	Robert Price	05/2018
7014	10^115773+126739	115774	Patrick De Geest	04/2018
7016	10^115773-1000000001	115773	Robert Price	03/2018
7015	10^115773-396221	115773	Patrick De Geest	04/2018
7017	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
7018	30537^6178+6178^30537	115762	Hans Havermann	01/2021
7019	2^384530+1874305	115756	Enzo Doria	06/2016
7020	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
7021	28275^12406+12406^28275	115748	Hans Havermann	01/2021
7022	(44*10^115697-413)/9	115698	Robert Price	03/2019
7023	31408^4825+4825^31408	115692	Hans Havermann	02/2021
7024	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
7025	2^384312+81091	115690	Yves Minet	02/2010
7026	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
7027	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
7028	(4*10^115668-79)/3	115669	Robert Price	02/2018
7029	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
7030	994^38584+993	115652	Alfred Reich	03/2026
7031	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
7032	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
7033	18^92125-92125^18	115642	Dylan Delgado	08/2019
7034	(25^82723+3^82723)/28	115641	Robert Price	09/2025
7035	3^242337-4042	115625	Enzo Doria	05/2014
7036	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
7037	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
7038	7*10^115561+79	115562	Robert Price	07/2019
7039	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
7040	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
7041	2^383780-3149	115530	Yves Minet	10/2014
7042	(41*10^115523-383)/9	115524	Robert Price	11/2018
7043	27316^16923+16923^27316	115506	Hans Havermann	02/2021
7044	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
7045	2^383560-455	115464	Yves Minet	03/2012
7046	(2^383544+5)/3	115458	Lelio R Paula	03/2014
7047	(22*10^115454+119)/3	115455	Robert Price	04/2021
7048	89^59221-88^59221	115445	Robert Price	06/2015
7049	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
7050	2^383347+1869413	115399	Enzo Doria	05/2016
7051	(103*10^115366+17)/3	115368	Robert Price	08/2020
7052	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
7053	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
7054	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
7055	29961^7060+7060^29961	115315	Hans Havermann	01/2021
7057	2^383039+1869509	115307	Enzo Doria	05/2016
7056	32918^3183+3183^32918	115307	Hans Havermann	01/2021
7058	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
7059	36964^1315+1315^36964	115288	Hans Havermann	02/2021
7060	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
7061	(22*10^115282+29)/3	115283	Robert Price	02/2021
7062	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
7063	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
7064	30416^6141+6141^30416	115224	Hans Havermann	02/2021
7065	6*10^115211+79	115212	Robert Price	09/2020
7066	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
7067	27987^13078+13078^27987	115210	Hans Havermann	02/2021
7068	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
7069	(22*10^115188-193)/9	115189	Robert Price	07/2022
7070	2^382633+73697	115185	Enzo Doria	04/2016
7071	2^382509-113593	115147	Enzo Doria	08/2014
7072	2^382502-2791721	115145	Enzo Doria	03/2016
7073	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
7074	2^382464+22741	115134	Enzo Doria	09/2023
7075	26752^20065+20065^26752	115099	Hans Havermann	02/2021
7076	26383^23008+23008^26383	115080	Hans Havermann	02/2021
7077	9^120590-120590	115073	Robert Price	03/2014
7078	28203^12016+12016^28203	115062	Hans Havermann	02/2021
7079	2^382198+9	115054	Lelio R Paula	03/2013
7080	18268*31^77131+22839	115035	Eric Chen	05/2024
7081	30101^6630+6630^30101	115032	Hans Havermann	01/2021
7082	(89*10^115030-179)/9	115031	Robert Price	12/2019
7083	25554^26089-26089^25554	114987	Frank Doornink	02/2024
7084	25142^26129-26129^25142	114979	Frank Doornink	12/2023
7085	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
7086	27300^16271+16271^27300	114972	Hans Havermann	02/2021
7087	(23*10^114962+7)/3	114963	Robert Price	05/2023
7088	2^381883-59197	114959	Enzo Doria	10/2015
7089	27423^15542+15542^27423	114944	Hans Havermann	02/2021
7090	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
7092	2^381806-4481	114936	Yves Minet	07/2011
7091	2^381808-1851507	114936	Enzo Doria	08/2015
7093	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
7094	2^381774-112373	114926	Enzo Doria	06/2014
7095	26341^22980+22980^26341	114883	Hans Havermann	01/2021
7096	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
7097	2^381555-109051	114860	Enzo Doria	04/2014
7098	2^381551+213683	114859	Enzo Doria	09/2023
7099	2^381546-113501	114857	Enzo Doria	08/2014
7100	(7*10^114845-19)/3	114846	Robert Price	10/2020
7101	26675^20178+20178^26675	114833	Hans Havermann	02/2021
7102	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
7103	3^240644+16	114817	Robert Price	04/2020
7104	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
7105	2^381360-110429	114801	Enzo Doria	05/2014
7106	(17*10^114795+79)/3	114796	Robert Price	04/2019
7107	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
7108	2^381252-115079	114769	Enzo Doria	06/2015
7109	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
7110	2^381209-29323	114756	Enzo Doria	07/2015
7111	2^381207-111546435	114755	Paul Bourdelais	10/2021
7112	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
7113	2^381201+1873205	114753	Enzo Doria	06/2016
7115	(85*10^114737+293)/9	114738	Robert Price	12/2019
7116	(265*10^114736+17)/3	114738	Robert Price	03/2020
7114	379*10^114735+9	114738	Jason Yuen	01/2025
7117	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
7118	2^380974-112991	114685	Enzo Doria	07/2014
7119	37097^1234+1234^37097	114679	Hans Havermann	02/2021
7120	(26*10^114658-119)/3	114659	Robert Price	07/2023
7121	88^58949-87	114626	Norbert Schneider	11/2015
7122	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
7123	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
7124	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
7125	29913^6782+6782^29913	114608	Hans Havermann	02/2021
7126	(331*10^114605-7)/9	114607	Robert Price	04/2022
7127	2^380700+91	114603	Lelio R Paula	03/2013
7128	394^44151+393	114594	Alfred Reich	03/2026
7129	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
7130	7*10^114577+27	114578	Robert Price	11/2020
7132	10^114575+3^114576	114576	Mike Oakes	09/2010
7131	10^114575+66561	114576	Patrick De Geest	02/2017
7133	10^114575-581081	114575	Patrick De Geest	02/2017
7134	2^380587-115315	114569	Enzo Doria	06/2015
7135	31874^3927+3927^31874	114558	Hans Havermann	02/2021
7136	2^380513-216925	114546	Enzo Doria	05/2014
7137	2^380451-1840087	114528	Enzo Doria	06/2015
7138	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
7139	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
7140	2^380279-461347	114476	Enzo Doria	07/2015
7141	(331*10^114454-7)/9	114456	Robert Price	04/2022
7142	27121^16590+16590^27121	114447	Hans Havermann	01/2021
7143	25966^25555+25555^25966	114445	Hans Havermann	01/2021
7144	(611*32^76029-53)/31	114437	Eric Chen	11/2023
7145	(11*10^114400+529)/9	114401	Robert Price	09/2021
7146	2^380021+1871147	114398	Enzo Doria	05/2016
7147	2^380005+1869707	114393	Enzo Doria	05/2016
7148	2^379958-113297	114379	Enzo Doria	07/2014
7149	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
7150	2^379881-109105	114356	Enzo Doria	04/2014
7151	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
7152	(4*10^114340+83)/3	114341	Robert Price	02/2018
7153	(26*10^114317-77)/3	114318	Robert Price	11/2019
7154	(4*10^114296+149)/9	114296	Robert Price	04/2018
7155	88^58773-87	114284	Norbert Schneider	11/2015
7156	27764^13065+13065^27764	114280	Hans Havermann	01/2021
7157	(132^53891-1)/131	114278	Anonymous	06/2024
7158	2^379529-2790283	114250	Enzo Doria	03/2016
7159	2^379522+1869115	114248	Enzo Doria	05/2016
7160	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
7161	2^379317-115033	114186	Enzo Doria	06/2015
7162	(22*10^114178+47)/3	114179	Robert Price	06/2021
7163	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
7164	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
7165	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
7166	6*10^114091+23	114092	Robert Price	09/2020
7167	(4*10^114076+143)/3	114077	Robert Price	03/2018
7168	332*25^81584+12357	114053	Eric Chen	10/2023
7169	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
7170	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
7171	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
7173	(46*10^113969+683)/9	113970	Robert Price	03/2019
7172	(83*10^113969+133)/9	113970	Robert Price	08/2021
7174	32226^3439+3439^32226	113966	Hans Havermann	02/2021
7175	(77*10^113963-149)/9	113964	Robert Price	03/2022
7176	78*10^113954-7	113956	Robert Price	10/2020
7177	2*10^113941+9	113942	Dmitry Domanov	11/2010
7178	10^113933+145897	113934	Patrick De Geest	02/2021
7181	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
7179	10^113933-8000000001	113933	Robert Price	11/2020
7180	10^113933-66167	113933	Patrick De Geest	02/2021
7182	2339662057597*10^113903+9	113916	Robert Price	03/2021
7184	4*10^113905+91	113906	Robert Price	08/2018
7183	Phi(256695,7)	113906	Henri Lifchitz	02/2026
7185	10^113894+76609	113895	Patrick De Geest	02/2021
7187	10^113894-10000001	113894	Robert Price	09/2020
7186	10^113894-373947	113894	Patrick De Geest	02/2021
7188	33933^2270+2270^33933	113881	Hans Havermann	02/2021
7189	4*10^113874-21	113875	Robert Price	09/2018
7190	2^378272-16565	113872	Enzo Doria	04/2013
7191	2^378217-109075	113855	Enzo Doria	04/2014
7192	2^378198+67	113849	Lelio R Paula	03/2013
7193	2^378173-3249	113842	Yves Minet	12/2014
7194	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
7195	2^378137+1334025	113831	Henri Lifchitz	10/2024
7196	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
7197	30030^6173+6173^30030	113829	Hans Havermann	01/2021
7198	2^378128-262977	113828	Enzo Doria	05/2014
7199	2^378123-113215	113827	Enzo Doria	07/2014
7200	6^146274-18893	113824	Enzo Doria	03/2013
7201	34596^1949+1949^34596	113815	Hans Havermann	02/2021
7202	2^378078+75	113813	Lelio R Paula	03/2013
7203	(28*10^113810+449)/9	113811	Robert Price	11/2021
7204	26273^21448+21448^26273	113799	Hans Havermann	02/2021
7205	2^377966+255255	113780	Paul Bourdelais	10/2021
7206	2^377940+63	113772	Lelio R Paula	03/2013
7207	2^377941-2785843	113772	Enzo Doria	04/2016
7208	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
7209	2^377810+1875109	113733	Enzo Doria	09/2016
7210	2^377803-1838635	113731	Enzo Doria	05/2015
7211	2^377799+52223	113729	Yves Minet	08/2010
7212	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
7213	11^109190-270	113710	Enzo Doria	12/2012
7214	28206^10739+10739^28206	113698	Hans Havermann	01/2021
7215	7*10^113693+9	113694	Robert Price	09/2015
7216	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
7217	(82*10^113681+161)/9	113682	Robert Price	10/2019
7218	26121^22478+22478^26121	113673	Hans Havermann	01/2021
7219	4*10^113658+49	113659	Robert Price	01/2019
7220	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
7221	(2*10^113631+529)/9	113631	Robert Price	01/2018
7222	2^377408-2798279	113612	Enzo Doria	04/2016
7223	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
7224	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
7225	5*10^113586+57	113587	Robert Price	12/2018
7226	Phi(150733,-7)	113582	Henri Lifchitz	12/2025
7227	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
7228	2^377222+93679	113556	Yves Minet	02/2011
7230	262147#+316847	113552	Makoto Morimoto	02/2016
7229	27172^15101+15101^27172	113552	Hans Havermann	01/2021
7231	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
7232	2^377026-458903	113497	Enzo Doria	04/2015
7233	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
7234	34791^1828+1828^34791	113488	Hans Havermann	02/2021
7235	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
7236	(29*10^113468-17)/3	113469	Robert Price	09/2019
7237	35^73477-34^73477	113454	Robert Price	05/2012
7238	(14*10^113451-89)/3	113452	Robert Price	05/2020
7239	2^376790+27	113426	Lelio R Paula	03/2013
7240	2^376786-112701	113424	Enzo Doria	06/2014
7241	2^376731+21	113408	Lelio R Paula	03/2013
7242	9*10^113394-73	113395	Robert Price	01/2021
7243	29660^6651+6651^29660	113387	Hans Havermann	01/2021
7245	2^376634+1871245	113379	Enzo Doria	05/2016
7244	(4^188318+17)/3	113379	Robert Price	02/2017
7246	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
7247	2^376576-344369	113361	Enzo Doria	07/2015
7248	2^376549-4543	113353	Yves Minet	03/2019
7249	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
7250	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303258 PRPs in the top)