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	2^360706-458903	108584	Enzo Doria	04/2015
7002	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7003	2^360641-113185	108564	Enzo Doria	07/2014
7004	(29*10^108559-71)/3	108560	Robert Price	07/2021
7006	2^360618+75019	108557	Enzo Doria	04/2016
7005	2^360618+2025	108557	Henri Lifchitz	01/2025
7007	2^360607-216367	108554	Harrison Mesh	06/2022
7008	(14*10^108545-221)/9	108546	Robert Price	04/2018
7009	(44*10^108544-233)/9	108545	Robert Price	01/2019
7010	3*5^155286+2	108541	Lelio R Paula	11/2014
7011	7^128422+4	108530	Lelio R Paula	11/2014
7012	7^128421-80	108529	Lelio R Paula	03/2017
7013	2^360497+53807	108521	Yves Minet	07/2010
7014	2^360468-4559	108512	Yves Minet	03/2019
7015	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7016	2^360366+1459	108481	Lelio R Paula	09/2011
7017	2^360364-1499	108481	Yves Minet	05/2013
7018	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7019	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7020	14^94642-23	108472	Lelio R Paula	05/2017
7021	(197*10^108446-11)/3	108448	Robert Price	03/2020
7022	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7023	4*10^108412+9	108413	Robert Price	05/2015
7024	(259*10^108409-1)/3	108411	Robert Price	12/2020
7025	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7026	133^51042-132	108406	Norbert Schneider	02/2019
7027	2^360093-351103	108399	Enzo Doria	06/2015
7028	2^360042+723	108384	Lelio R Paula	01/2012
7029	85^56164-2	108364	Lelio R Paula	10/2013
7030	2^359937-29323	108352	Enzo Doria	07/2015
7031	22^80712-23	108350	Anonymous	09/2024
7032	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7033	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7034	2^359898-19997	108341	Enzo Doria	06/2013
7035	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
7036	2*5^154948-7	108305	Lelio R Paula	11/2014
7037	10^108303+13	108304	Lelio R Paula	02/2017
7038	10^108303-207959	108303	Patrick De Geest	03/2017
7039	7*10^108300+69	108301	Robert Price	07/2019
7040	198^47155-47155^198	108300	Norman Luhn	09/2024
7041	2^359730+753	108290	Lelio R Paula	12/2011
7042	(8*10^108273+13)/3	108274	Robert Price	06/2018
7043	2^359650-19797	108266	Enzo Doria	06/2013
7044	(47*10^108261+259)/9	108262	Robert Price	03/2022
7045	91^55259-90^55259	108255	Robert Price	07/2015
7046	10^108251+85749	108252	Patrick De Geest	02/2021
7047	10^108251-50000000001	108251	Robert Price	12/2020
7048	10^108251-252081	108251	Patrick De Geest	02/2021
7049	4*10^108238-71	108239	Robert Price	12/2018
7050	3^226845+68	108233	Lelio R Paula	03/2017
7051	31836^2509+2509^31836	108227	Hans Havermann	10/2020
7052	5^154822-12866	108216	Enzo Doria	05/2014
7053	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
7054	2^359454-177	108207	Lelio R Paula	12/2011
7055	(19*10^108184+191)/3	108185	Robert Price	05/2019
7056	6^139022-59	108181	Lelio R Paula	02/2017
7057	(19*10^108176-43)/3	108177	Robert Price	05/2019
7058	2^359352-179	108176	Lelio R Paula	12/2011
7059	2^359338-1858781	108172	Enzo Doria	04/2016
7060	12^100230-97	108167	Lelio R Paula	03/2017
7061	27028^10043+10043^27028	108163	Hans Havermann	11/2020
7062	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
7063	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7064	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7065	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7066	6^138956-59	108129	Lelio R Paula	02/2017
7067	2^359184+30285	108126	Lelio R Paula	04/2017
7068	13^97059+10	108119	Lelio R Paula	03/2017
7069	2^359137-81	108112	Lelio R Paula	12/2011
7071	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7070	2^359110-11655	108103	Lelio R Paula	04/2017
7072	2^359069-933075	108091	Paul Bourdelais	06/2021
7073	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7074	8*6^138875+5	108067	Lelio R Paula	11/2014
7075	2^358987-216919	108066	Enzo Doria	05/2014
7076	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7077	39^67918-67918^39	108062	Norbert Schneider	02/2017
7078	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7079	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7080	2^358785-16933	108006	Enzo Doria	05/2013
7081	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7082	6^138770-77	107985	Lelio R Paula	02/2017
7083	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7084	10^107976+19	107977	Lelio R Paula	02/2017
7085	10^107976-202103	107976	Patrick De Geest	03/2017
7086	2^358684+75781	107975	Enzo Doria	04/2016
7087	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7088	99^54094+2	107952	Lelio R Paula	06/2013
7089	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7090	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7091	2^358538+55	107931	Lelio R Paula	12/2011
7092	2^358517-109009	107925	Enzo Doria	03/2014
7093	26395^12258+12258^26395	107914	Hans Havermann	10/2020
7094	3^226159+104	107906	Lelio R Paula	03/2017
7095	7*10^107870+39	107871	Robert Price	01/2023
7096	2^358310-11655	107863	Lelio R Paula	03/2017
7097	(68*10^107852-329)/9	107853	Robert Price	03/2021
7098	2^358275-112987	107852	Enzo Doria	07/2014
7099	3^226038+4	107848	Tyler NeSmith	01/2021
7100	2^358233-20005	107839	Enzo Doria	06/2013
7101	2^358194+175	107828	Lelio R Paula	12/2011
7102	107^53125-106	107812	Norbert Schneider	12/2016
7103	(25*10^107804+161)/3	107805	Robert Price	09/2019
7104	3^225922-2	107793	Lelio R Paula	10/2013
7105	12^99874-95	107783	Lelio R Paula	03/2017
7106	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
7107	2^358030-171	107778	Lelio R Paula	12/2011
7108	11^103488-4170	107772	Enzo Doria	12/2012
7109	2^357930-4547	107748	Yves Minet	03/2019
7110	2^357911-20089	107742	Enzo Doria	06/2013
7111	2^357885+12857	107735	Yves Minet	07/2010
7112	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
7113	7^127473+40	107728	Lelio R Paula	03/2017
7114	5*2^357850+9	107725	Lelio R Paula	09/2014
7115	2^357786-291191	107705	Enzo Doria	06/2015
7116	28907^5320+5320^28907	107705	Hans Havermann	10/2020
7117	18^85798-23	107700	Lelio R Paula	04/2017
7118	3*10^107697+61	107698	Robert Price	09/2020
7119	(14*10^107694-83)/3	107695	Robert Price	12/2018
7120	2^357688-1854269	107675	Enzo Doria	09/2015
7121	2^357671-112225	107670	Enzo Doria	06/2014
7122	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7123	2^357618-21005	107654	Enzo Doria	06/2013
7124	2^357615-17505	107653	Enzo Doria	05/2013
7125	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7126	(30^72871-1)/29	107638	Robert Price	12/2011
7127	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7128	2^357521+1870217	107625	Enzo Doria	05/2016
7129	2^357477-1203	107612	Lelio R Paula	03/2017
7130	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7131	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7132	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7133	5^153894-18	107568	Lelio R Paula	02/2017
7134	2^357324-69059	107566	Enzo Doria	11/2015
7135	467^40296+40296^467	107563	Norbert Schneider	03/2019
7136	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7137	(8*10^107556-149)/3	107557	Robert Price	12/2021
7138	2^357283-869688105	107553	Lelio R Paula	01/2017
7139	2^357280-16805	107552	Enzo Doria	05/2013
7140	10^107547+481719	107548	Patrick De Geest	03/2017
7141	10^107547-47	107547	Lelio R Paula	02/2017
7142	(23*10^107540+37)/3	107541	Robert Price	02/2022
7143	17^87396-32	107537	Lelio R Paula	04/2017
7144	(746*10^107505+1)/9	107507	Robert Price	03/2020
7145	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7146	2^357081+107	107493	Lelio R Paula	12/2011
7147	2^357058-3911	107486	Yves Minet	04/2017
7148	3^225274+64	107484	Lelio R Paula	03/2017
7149	5*10^107482-57	107483	Robert Price	03/2021
7150	18^85619-95	107476	Lelio R Paula	04/2017
7151	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7152	3^225248-130	107471	Lelio R Paula	03/2017
7153	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7154	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7155	2^356935-18085	107449	Enzo Doria	05/2013
7156	55396^87+87^55396	107442	Hans Havermann	10/2020
7157	(14*10^107439-137)/3	107440	Robert Price	04/2021
7158	164^48505-48505^164	107432	Norman Luhn	09/2024
7159	10^107409+37	107410	Lelio R Paula	02/2017
7160	10^107409-329633	107409	Patrick De Geest	03/2017
7161	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7162	2^356787-109027	107404	Enzo Doria	04/2014
7163	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7164	3*10^107389+77	107390	Robert Price	09/2018
7165	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7166	5^153622-42	107378	Lelio R Paula	02/2017
7167	2^356699-97305	107378	Lelio R Paula	03/2017
7168	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
7169	2^356654+85	107364	Lelio R Paula	11/2011
7170	2^356641-19921	107360	Enzo Doria	06/2013
7171	5*10^107355+11	107356	Robert Price	08/2019
7172	2^356623-465	107355	Lelio R Paula	03/2017
7173	19^83945-92	107345	Lelio R Paula	02/2017
7174	25491^16246+16246^25491	107337	Hans Havermann	11/2020
7175	10^107334+28149	107335	Patrick De Geest	03/2017
7176	10^107334-83	107334	Lelio R Paula	02/2017
7177	2^356518+885	107323	Lelio R Paula	03/2017
7178	(59*10^107322+391)/9	107323	Robert Price	03/2021
7179	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
7180	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
7181	2^356442-114713	107300	Enzo Doria	04/2015
7182	2^356425+72257	107295	Enzo Doria	04/2016
7183	2^356351-112237	107273	Enzo Doria	06/2014
7185	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
7184	2^356322+74539	107264	Enzo Doria	04/2016
7186	2^356274+1874479	107250	Enzo Doria	06/2016
7187	24606^22819+22819^24606	107241	Hans Havermann	10/2020
7188	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
7189	20^82422-93	107234	Lelio R Paula	02/2017
7190	2^356157-20365	107214	Enzo Doria	06/2013
7191	8*10^107209+99	107210	Robert Price	03/2021
7192	2^356129-18949	107206	Enzo Doria	05/2013
7193	2^356100-109587	107197	Enzo Doria	04/2014
7194	2*10^107173-37	107174	Robert Price	11/2021
7195	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
7196	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
7197	2^355968-64875	107158	Lelio R Paula	01/2017
7198	2^355952+1870321	107153	Enzo Doria	05/2016
7199	27069^9088+9088^27069	107152	Hans Havermann	11/2020
7200	2^355915-117	107142	Lelio R Paula	11/2011
7201	(16*10^107140+77)/3	107141	Robert Price	03/2019
7202	24628^22369+22369^24628	107124	Hans Havermann	11/2020
7203	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
7204	3^224495-8	107112	Lelio R Paula	12/2013
7205	3*10^107096+23	107097	Robert Price	03/2022
7206	25077^18632+18632^25077	107086	Hans Havermann	10/2020
7207	7^126691-44	107067	Lelio R Paula	03/2017
7208	4^177830-8243	107065	Mike Oakes	02/2011
7209	(509*10^107057+13)/9	107059	Robert Price	05/2022
7210	2^355604+214051	107048	Enzo Doria	10/2023
7211	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
7212	10^107028+3593037	107029	Paul Bourdelais	10/2021
7213	10^107028-43301	107028	Alfred Reich	08/2024
7214	2^355524-21237	107024	Enzo Doria	06/2013
7216	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
7215	24843^20320+20320^24843	107022	Hans Havermann	10/2020
7217	2^355494-19901	107015	Enzo Doria	06/2013
7218	2^355454-869688105	107003	Lelio R Paula	01/2017
7219	4*10^106997+13	106998	Robert Price	02/2021
7220	(8*10^106985-629)/9	106985	Robert Price	01/2022
7221	2^355366+54615	106976	Lelio R Paula	01/2017
7222	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
7223	2^355275-19861	106949	Enzo Doria	06/2013
7224	27503^7738+7738^27503	106949	Hans Havermann	11/2020
7225	(85*10^106943+77)/9	106944	Robert Price	07/2022
7226	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
7227	4*10^106914-93	106915	Robert Price	07/2020
7228	4*10^106892-3	106893	Robert Price	10/2015
7229	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
7230	2^355001+335931	106866	Enzo Doria	08/2024
7231	2^354946-3	106850	M. Frind & P. Underwood	08/2002
7232	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
7233	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
7234	2^354873-18693	106828	Enzo Doria	05/2013
7235	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
7237	2^354828+4257	106814	Lelio R Paula	01/2017
7236	25216^17217+17217^25216	106814	Hans Havermann	10/2020
7238	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
7239	436^40459+40459^436	106791	Norbert Schneider	03/2019
7240	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
7241	(115*10^106772-7)/9	106774	Robert Price	02/2020
7242	2^354640-354640+1	106758	Robert Price	10/2014
7243	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
7244	2^354585+95	106741	Lelio R Paula	10/2011
7245	(206*10^106737+1)/9	106739	Robert Price	04/2022
7246	2^354553+189	106732	Lelio R Paula	10/2011
7248	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
7247	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
7249	2^354514-109031	106720	Enzo Doria	04/2014
7250	2^354509-109465	106718	Enzo Doria	04/2014

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Probable Primes Top 10000

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