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) !!!

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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 ?
7001	(10^117059-71)/1	117059	Serge Batalov	12/2014
7002	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
7003	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
7004	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
7005	(30^79231+29^79231)/59	117033	Robert Price	10/2026
7006	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
7007	(693^41189-1)/692	117005	Michael Stocker	05/2020
7008	(26*10^116999-503)/9	117000	Robert Price	07/2018
7009	20^89917-21	116985	Anonymous	09/2024
7010	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
7011	38496^1093+1093^38496	116975	Hans Havermann	02/2021
7012	3^245154-6256	116969	Enzo Doria	05/2014
7013	5*10^116966-43	116967	Robert Price	01/2019
7014	(748^40699-1)/747	116963	Tom Wu	08/2025
7015	2^388536-113495	116961	Enzo Doria	08/2014
7016	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
7017	(8*32^77701+271)/31	116952	Eric Chen	11/2023
7018	2^388469-43	116941	Lelio R Paula	03/2013
7019	27417^18416+18416^27417	116939	Hans Havermann	02/2021
7020	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
7021	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
7022	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
7023	2^388180+93	116854	Donovan Johnson	07/2008
7024	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
7025	(85*10^116842+293)/9	116843	Robert Price	12/2019
7026	35296^2043+2043^35296	116840	Hans Havermann	02/2021
7027	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
7028	38633^1056+1056^38633	116814	Hans Havermann	02/2021
7029	2^387946-113261	116784	Enzo Doria	07/2014
7030	28*36^75009+305	116739	Eric Chen	12/2022
7031	28363^13056+13056^28363	116737	Hans Havermann	02/2021
7032	2^387745+75557	116723	Enzo Doria	04/2016
7033	(29*10^116719+313)/9	116720	Robert Price	04/2021
7034	29622^8699+8699^29622	116695	Hans Havermann	02/2021
7035	(206*10^116687-17)/9	116689	Robert Price	01/2020
7036	(7*10^116684+179)/3	116685	Robert Price	09/2018
7037	2^387554+71455	116666	Enzo Doria	04/2016
7038	(602*10^116647-71)/9	116649	Robert Price	12/2021
7039	3^244461-10	116638	Tyler NeSmith	09/2022
7040	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
7041	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
7042	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
7043	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
7044	(25*10^116601-331)/9	116602	Robert Price	08/2018
7045	25791^26428-26428^25791	116587	Frank Doornink	03/2024
7047	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
7046	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
7048	2^387211+111546435	116563	Paul Bourdelais	10/2021
7049	10^116557+987654321	116558	Robert Price	12/2019
7050	10^116557+9141	116558	Patrick De Geest	02/2020
7051	10^116557-609431	116557	Patrick De Geest	02/2020
7052	209^50234-50234^209	116551	Norman Luhn	09/2024
7053	(28*10^116546+41)/3	116547	Robert Price	07/2021
7054	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
7055	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
7056	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
7057	(7*10^116514-1)/3	116515	Robert Price	08/2022
7058	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
7059	28846^10931+10931^28846	116500	Hans Havermann	02/2021
7060	10^116496+3593037	116497	Paul Bourdelais	10/2021
7061	272^47851-47851^272	116497	Norman Luhn	09/2024
7062	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
7063	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
7064	998^38840+997	116487	Alfred Reich	03/2026
7065	2^386947+1869143	116483	Enzo Doria	05/2016
7066	(30^78857-1)/29	116480	Robert Price	12/2011
7067	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
7068	(2^386903-3)/5	116469	Lelio R Paula	03/2014
7069	28107^13892+13892^28107	116441	Hans Havermann	02/2021
7070	29110^9957+9957^29110	116386	Hans Havermann	02/2021
7071	26469^24838+24838^26469	116335	Hans Havermann	01/2021
7072	2^386389-1864783	116315	Enzo Doria	03/2016
7073	993^38799+992	116279	Alfred Reich	03/2026
7074	(8*32^77250-163)/31	116273	Eric Chen	11/2023
7075	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
7076	297^47012+47012^297	116250	Norbert Schneider	07/2018
7077	(35*10^116223-341)/9	116224	Robert Price	08/2021
7078	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
7079	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
7080	(10^116201+7)/39623	116197	Alfred Reich	06/2021
7081	2^385969-823	116189	Yves Minet	05/2012
7082	57^66162+2	116173	Lelio R Paula	08/2013
7083	2^385854+75049	116154	Enzo Doria	04/2016
7084	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
7085	2^385775-109587	116130	Enzo Doria	04/2014
7086	(14*10^116112-101)/3	116113	Robert Price	02/2019
7087	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
7088	3*10^116107+23	116108	Robert Price	03/2022
7089	28729^10990+10990^28729	116094	Hans Havermann	02/2021
7090	2^385622+71839	116084	Enzo Doria	04/2016
7091	2^385564+781	116067	Lelio R Paula	01/2012
7092	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
7093	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
7094	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
7095	29431^8776+8776^29431	116056	Hans Havermann	01/2021
7096	(266*10^116024-17)/3	116026	Robert Price	07/2020
7097	30263^6820+6820^30263	116022	Hans Havermann	02/2021
7098	2^385410+71893	116020	Enzo Doria	04/2016
7099	38225^1084+1084^38225	116014	Hans Havermann	02/2021
7100	26548^23433+23433^26548	116011	Hans Havermann	02/2021
7101	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
7102	12^107422-11	115928	Riley Fisher	12/2023
7103	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
7104	(11*10^115910-131)/3	115911	Robert Price	09/2018
7105	2^384953-111943	115883	Paul Bourdelais	02/2012
7106	43^70942-2	115882	Lelio R Paula	04/2014
7107	(94*10^115879-7)/3	115881	Robert Price	03/2020
7108	7*10^115863+3	115864	Robert Price	08/2015
7109	2^384834+93	115847	Donovan Johnson	07/2008
7110	2^384809+71297	115840	Enzo Doria	04/2016
7111	(55*10^115829+323)/9	115830	Robert Price	10/2021
7112	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
7113	31348^4951+4951^31348	115822	Hans Havermann	02/2021
7114	(793*10^115810+53)/9	115812	Robert Price	01/2022
7115	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
7116	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
7117	31115^5266+5266^31115	115794	Hans Havermann	02/2021
7118	2*10^115784-27	115785	Robert Price	05/2018
7119	10^115773+126739	115774	Patrick De Geest	04/2018
7120	10^115773-1000000001	115773	Robert Price	03/2018
7121	10^115773-396221	115773	Patrick De Geest	04/2018
7122	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
7123	30537^6178+6178^30537	115762	Hans Havermann	01/2021
7124	2^384530+1874305	115756	Enzo Doria	06/2016
7125	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
7126	28275^12406+12406^28275	115748	Hans Havermann	01/2021
7127	(44*10^115697-413)/9	115698	Robert Price	03/2019
7128	31408^4825+4825^31408	115692	Hans Havermann	02/2021
7129	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
7130	2^384312+81091	115690	Yves Minet	02/2010
7131	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
7132	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
7133	(4*10^115668-79)/3	115669	Robert Price	02/2018
7134	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
7135	994^38584+993	115652	Alfred Reich	03/2026
7136	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
7137	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
7138	18^92125-92125^18	115642	Dylan Delgado	08/2019
7139	(25^82723+3^82723)/28	115641	Robert Price	09/2025
7140	3^242337-4042	115625	Enzo Doria	05/2014
7141	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
7142	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
7143	7*10^115561+79	115562	Robert Price	07/2019
7144	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
7145	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
7146	2^383780-3149	115530	Yves Minet	10/2014
7147	(41*10^115523-383)/9	115524	Robert Price	11/2018
7148	27316^16923+16923^27316	115506	Hans Havermann	02/2021
7149	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
7150	2^383560-455	115464	Yves Minet	03/2012
7151	(2^383544+5)/3	115458	Lelio R Paula	03/2014
7152	(22*10^115454+119)/3	115455	Robert Price	04/2021
7153	89^59221-88^59221	115445	Robert Price	06/2015
7154	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
7155	2^383347+1869413	115399	Enzo Doria	05/2016
7156	(103*10^115366+17)/3	115368	Robert Price	08/2020
7157	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
7158	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
7159	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
7160	29961^7060+7060^29961	115315	Hans Havermann	01/2021
7162	2^383039+1869509	115307	Enzo Doria	05/2016
7161	32918^3183+3183^32918	115307	Hans Havermann	01/2021
7163	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
7164	36964^1315+1315^36964	115288	Hans Havermann	02/2021
7165	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
7166	(22*10^115282+29)/3	115283	Robert Price	02/2021
7167	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
7168	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
7169	30416^6141+6141^30416	115224	Hans Havermann	02/2021
7170	6*10^115211+79	115212	Robert Price	09/2020
7171	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
7172	27987^13078+13078^27987	115210	Hans Havermann	02/2021
7173	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
7174	(22*10^115188-193)/9	115189	Robert Price	07/2022
7175	2^382633+73697	115185	Enzo Doria	04/2016
7176	2^382509-113593	115147	Enzo Doria	08/2014
7177	2^382502-2791721	115145	Enzo Doria	03/2016
7178	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
7179	2^382464+22741	115134	Enzo Doria	09/2023
7180	26752^20065+20065^26752	115099	Hans Havermann	02/2021
7181	(41^71363+4^71363)/45	115092	Robert Price	09/2026
7182	26383^23008+23008^26383	115080	Hans Havermann	02/2021
7183	9^120590-120590	115073	Robert Price	03/2014
7184	28203^12016+12016^28203	115062	Hans Havermann	02/2021
7185	2^382198+9	115054	Lelio R Paula	03/2013
7186	18268*31^77131+22839	115035	Eric Chen	05/2024
7187	30101^6630+6630^30101	115032	Hans Havermann	01/2021
7188	(89*10^115030-179)/9	115031	Robert Price	12/2019
7189	25554^26089-26089^25554	114987	Frank Doornink	02/2024
7190	25142^26129-26129^25142	114979	Frank Doornink	12/2023
7191	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
7192	27300^16271+16271^27300	114972	Hans Havermann	02/2021
7193	(23*10^114962+7)/3	114963	Robert Price	05/2023
7194	2^381883-59197	114959	Enzo Doria	10/2015
7195	27423^15542+15542^27423	114944	Hans Havermann	02/2021
7196	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
7197	2^381806-4481	114936	Yves Minet	07/2011
7198	2^381808-1851507	114936	Enzo Doria	08/2015
7199	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
7200	2^381774-112373	114926	Enzo Doria	06/2014
7201	26341^22980+22980^26341	114883	Hans Havermann	01/2021
7202	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
7203	2^381555-109051	114860	Enzo Doria	04/2014
7204	2^381551+213683	114859	Enzo Doria	09/2023
7205	2^381546-113501	114857	Enzo Doria	08/2014
7206	(7*10^114845-19)/3	114846	Robert Price	10/2020
7207	26675^20178+20178^26675	114833	Hans Havermann	02/2021
7208	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
7209	3^240644+16	114817	Robert Price	04/2020
7210	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
7211	2^381360-110429	114801	Enzo Doria	05/2014
7212	(17*10^114795+79)/3	114796	Robert Price	04/2019
7213	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
7214	2^381252-115079	114769	Enzo Doria	06/2015
7215	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
7216	2^381209-29323	114756	Enzo Doria	07/2015
7217	2^381207-111546435	114755	Paul Bourdelais	10/2021
7218	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
7219	2^381201+1873205	114753	Enzo Doria	06/2016
7221	(85*10^114737+293)/9	114738	Robert Price	12/2019
7222	(265*10^114736+17)/3	114738	Robert Price	03/2020
7220	379*10^114735+9	114738	Jason Yuen	01/2025
7223	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
7224	2^380974-112991	114685	Enzo Doria	07/2014
7225	37097^1234+1234^37097	114679	Hans Havermann	02/2021
7226	(26*10^114658-119)/3	114659	Robert Price	07/2023
7227	88^58949-87	114626	Norbert Schneider	11/2015
7228	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
7229	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
7230	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
7231	29913^6782+6782^29913	114608	Hans Havermann	02/2021
7232	(331*10^114605-7)/9	114607	Robert Price	04/2022
7233	2^380700+91	114603	Lelio R Paula	03/2013
7234	394^44151+393	114594	Alfred Reich	03/2026
7235	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
7236	7*10^114577+27	114578	Robert Price	11/2020
7238	10^114575+3^114576	114576	Mike Oakes	09/2010
7237	10^114575+66561	114576	Patrick De Geest	02/2017
7239	10^114575-581081	114575	Patrick De Geest	02/2017
7240	2^380587-115315	114569	Enzo Doria	06/2015
7241	31874^3927+3927^31874	114558	Hans Havermann	02/2021
7242	2^380513-216925	114546	Enzo Doria	05/2014
7243	2^380451-1840087	114528	Enzo Doria	06/2015
7244	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
7245	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
7246	2^380279-461347	114476	Enzo Doria	07/2015
7247	(331*10^114454-7)/9	114456	Robert Price	04/2022
7248	27121^16590+16590^27121	114447	Hans Havermann	01/2021
7249	25966^25555+25555^25966	114445	Hans Havermann	01/2021
7250	(611*32^76029-53)/31	114437	Eric Chen	11/2023

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Probable Primes Top 10000

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