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	2^344444-455	103688	Yves Minet	03/2012
7002	(4*10^103678-43)/3	103679	Robert Price	01/2022
7003	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
7004	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
7006	2^344317-109933	103650	Enzo Doria	04/2014
7005	26055^9508+9508^26055	103650	Hans Havermann	09/2020
7007	2^344309-1852033	103648	Enzo Doria	08/2015
7008	25729^10672+10672^25729	103643	Hans Havermann	09/2020
7009	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
7010	3*10^103637+61	103638	Robert Price	09/2020
7011	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
7012	2^344213-21253	103619	Enzo Doria	06/2013
7013	2^344196-465	103614	Lelio R Paula	11/2016
7014	2^344187-20001	103611	Enzo Doria	06/2013
7015	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
7016	(237^43627-1)/236	103601	Serge Batalov	06/2022
7017	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
7018	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
7019	(9^108553-2^108553)/7	103586	Jon Grantham	07/2023
7020	2^344085-20365	103580	Enzo Doria	06/2013
7021	5^148169+54	103566	Lelio R Paula	11/2016
7022	2^344017-108795	103560	Enzo Doria	03/2014
7023	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
7024	2^343971-5077	103546	Lelio R Paula	09/2011
7025	(7*10^103531+71)/3	103532	Robert Price	05/2018
7026	2^343899+141	103524	Lelio R Paula	08/2011
7027	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
7028	6^133029-67	103517	Lelio R Paula	11/2016
7029	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
7030	66*10^103507+7	103509	Robert Price	07/2020
7031	26297^8614+8614^26297	103485	Hans Havermann	09/2020
7032	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
7033	26499^8036+8036^26499	103480	Hans Havermann	09/2020
7034	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
7035	5^148014-24	103458	Lelio R Paula	11/2016
7036	28316^4503+4503^28316	103453	Hans Havermann	09/2020
7037	(22*10^103450+53)/3	103451	Robert Price	07/2019
7038	2^343604+9931	103436	Yves Minet	01/2011
7039	2^343601-21189	103435	Enzo Doria	06/2013
7040	(10^103423+173)/3	103423	Robert Price	05/2021
7041	2^343508-115229	103407	Enzo Doria	06/2015
7042	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
7043	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
7044	3^216685-113056	103386	Enzo Doria	07/2014
7045	24829^14580+14580^24829	103382	Hans Havermann	08/2020
7046	91355!4+1024	103381	Robert Price	09/2019
7047	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
7048	11^99262-20	103371	Lelio R Paula	12/2016
7049	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
7050	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
7051	2^343356-2791889	103361	Enzo Doria	03/2016
7052	(25*10^103360-241)/9	103361	Robert Price	05/2018
7053	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
7054	(371*33^68040-19)/32	103321	Eric Chen	05/2023
7055	24826^14511+14511^24826	103319	Hans Havermann	09/2020
7056	2^343182-171	103309	Lelio R Paula	08/2011
7057	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
7058	(16487^24649-1)/(16487^157-1)	103287	Ryan Propper	11/2023
7059	(10680^25639-1)/10679	103285	Serge Batalov	06/2022
7060	(7427^26683-1)/7426	103282	Serge Batalov	06/2022
7061	2^343079-1835611	103278	Enzo Doria	05/2015
7062	2^343063-1147	103273	Yves Minet	06/2013
7063	24741^14930+14930^24741	103271	Hans Havermann	09/2020
7064	(16*10^103255-73)/3	103256	Robert Price	07/2020
7065	(219^44119-1)/218	103256	Serge Batalov	06/2022
7066	9*6^132689+7	103254	Lelio R Paula	11/2014
7067	2^342979-18085	103247	Enzo Doria	05/2013
7068	(16*10^103244-31)/3	103245	Robert Price	03/2019
7069	2^342966-16995	103244	Lelio R Paula	11/2016
7070	23797^21774+21774^23797	103230	Hans Havermann	09/2020
7071	25388^11637+11637^25388	103224	Hans Havermann	09/2020
7072	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
7073	(16*10^103214-31)/3	103215	Robert Price	03/2019
7075	(37*10^103211+611)/9	103212	Robert Price	11/2018
7074	(238*10^103210-1)/3	103212	Robert Price	04/2020
7076	5^147650+16	103203	Lelio R Paula	11/2016
7077	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
7078	2^342817+2707067	103199	Enzo Doria	03/2016
7079	43^63177-42	103198	Theodore Burton	02/2007
7080	2^342805-21025	103195	Enzo Doria	06/2013
7081	24129^18890+18890^24129	103182	Hans Havermann	09/2020
7082	(622*10^103171-1)/9	103173	Robert Price	11/2021
7083	2^342714+12285	103168	Lelio R Paula	11/2016
7084	(2*10^103161-17)/3	103161	Serge Batalov	11/2022
7085	18^82178-4481	103156	Enzo Doria	03/2013
7086	2^342665-17349	103153	Enzo Doria	05/2013
7087	30408^2467+2467^30408	103150	Hans Havermann	09/2020
7088	(5^147571-3^147571)/2	103148	Kellen Shenton	05/2022
7089	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
7090	2^342612+175	103137	Lelio R Paula	08/2011
7091	5*2^342585-3	103130	Lelio R Paula	09/2014
7092	(16*10^103127+77)/3	103128	Robert Price	03/2019
7093	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
7094	2^342503-19209	103104	Enzo Doria	05/2013
7095	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
7096	2^342476+51	103096	Lelio R Paula	08/2011
7097	2^342460-18885	103091	Enzo Doria	05/2013
7098	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
7099	(194*10^103074-17)/3	103076	Robert Price	09/2020
7100	7^121968+82	103075	Lelio R Paula	10/2016
7101	2^342392-108863	103071	Enzo Doria	03/2014
7102	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
7103	3^216014+28	103065	Lelio R Paula	11/2016
7104	2^342353-108879	103059	Enzo Doria	03/2014
7105	10^103055+276081	103056	Patrick De Geest	12/2016
7106	10^103055-53	103055	Lelio R Paula	11/2016
7107	(58*10^103046+419)/9	103047	Robert Price	05/2019
7108	7^121933+4	103046	Lelio R Paula	11/2014
7109	(71*10^103028-143)/9	103029	Robert Price	10/2021
7110	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
7111	19^80560-68	103017	Lelio R Paula	10/2016
7112	2^342209+76607	103016	Enzo Doria	05/2016
7114	328^40945+40945^328	103013	Norbert Schneider	12/2014
7113	12^95454-91	103013	Lelio R Paula	10/2016
7115	25833^9716+9716^25833	103009	Hans Havermann	01/2019
7116	(893*10^103004+7)/9	103006	Robert Price	06/2021
7117	(1475^32503-1)/1474	102993	Serge Batalov	06/2022
7118	65^56809-64^56809	102990	Robert Price	08/2013
7119	5^147338-6	102985	Lelio R Paula	11/2014
7120	2^342084-112739	102978	Enzo Doria	06/2014
7121	9*6^132330+7	102974	Lelio R Paula	11/2014
7122	2^342034-16737	102963	Enzo Doria	05/2013
7123	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
7124	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
7125	2^341991-17421	102950	Enzo Doria	05/2013
7126	2^341969-112225	102943	Enzo Doria	06/2014
7127	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
7128	2^341859+1869413	102910	Enzo Doria	05/2016
7129	10^102909+61	102910	Lelio R Paula	11/2016
7130	10^102909-67049	102909	Patrick De Geest	12/2016
7131	23814^20935+20935^23814	102898	Hans Havermann	02/2019
7132	28345^4264+4264^28345	102888	Hans Havermann	02/2019
7133	25665^10204+10204^25665	102886	Hans Havermann	02/2019
7134	26288^8181+8181^26288	102860	Hans Havermann	02/2019
7135	2^341659+1836773	102850	Enzo Doria	03/2016
7136	2^341608-110639	102835	Enzo Doria	05/2014
7137	10^102824+49	102825	Lelio R Paula	11/2016
7138	10^102824-168011	102824	Patrick De Geest	12/2016
7139	11^98708-8	102794	Lelio R Paula	10/2016
7140	2^341466+4429	102792	Lelio R Paula	09/2011
7141	2^341460-107	102790	Lelio R Paula	08/2011
7142	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
7143	2^341355+21	102759	Lelio R Paula	08/2011
7144	(6496^26947-1)/6495	102736	Serge Batalov	06/2022
7145	2^341246+40755	102726	Lelio R Paula	11/2016
7146	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
7147	7^121547+78	102720	Lelio R Paula	10/2016
7148	2^341223-461197	102719	Enzo Doria	06/2015
7149	27838^4893+4893^27838	102711	Hans Havermann	03/2019
7151	2^341190-20577	102709	Enzo Doria	06/2013
7150	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
7152	(25*10^102698+77)/3	102699	Robert Price	09/2022
7153	6^131976-65	102698	Lelio R Paula	10/2016
7154	2^341134+2533	102692	Henri Lifchitz	09/2005
7155	13^92184-54	102688	Lelio R Paula	10/2016
7156	2^341116-20873	102687	Enzo Doria	06/2013
7157	2^341094-19953	102680	Enzo Doria	06/2013
7158	23761^20950+20950^23761	102676	Hans Havermann	03/2019
7160	2^341053+129	102668	Lelio R Paula	08/2011
7159	(4724^27943-1)/4723	102668	Serge Batalov	06/2022
7162	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
7161	7^121471+94	102655	Lelio R Paula	10/2016
7164	2^341004-173	102653	Lelio R Paula	08/2011
7163	20^78901+3	102653	Lelio R Paula	10/2016
7165	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
7166	5^146853-52	102646	Lelio R Paula	10/2016
7167	2^340969-216931	102642	Enzo Doria	05/2014
7168	122^49196+121	102641	Norbert Schneider	10/2018
7169	2^340952+1870021	102637	Enzo Doria	05/2016
7170	5*2^340940-3	102634	Lelio R Paula	08/2014
7171	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
7172	(11*10^102629-23)/3	102630	Robert Price	09/2021
7173	3^215094+5*2^215094	102626	Jon Grantham	08/2023
7174	25876^9239+9239^25876	102615	Hans Havermann	02/2019
7175	(4*10^102612+83)/3	102613	Robert Price	02/2018
7176	75^54717+74	102598	Norbert Schneider	01/2015
7177	(17*10^102597+13)/3	102598	Robert Price	01/2019
7178	2^340806-20393	102593	Enzo Doria	06/2013
7179	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
7180	6^131821+77	102577	Lelio R Paula	10/2016
7181	(203*10^102561-11)/3	102563	Robert Price	12/2020
7182	2^340688-29	102558	Henri Lifchitz	05/2005
7183	2^340685-109101	102557	Enzo Doria	04/2014
7184	65^56567-64	102552	Norbert Schneider	11/2014
7185	26230^8121+8121^26230	102550	Hans Havermann	03/2019
7186	(64*10^102547+161)/9	102548	Robert Price	08/2022
7187	(8*10^102541+49)/3	102542	Robert Price	05/2020
7188	(536*10^102533-23)/9	102535	Robert Price	02/2020
7189	2^340547-108897	102515	Enzo Doria	03/2014
7190	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
7191	25592^10119+10119^25592	102500	Hans Havermann	02/2019
7192	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
7193	7^121268+82	102484	Lelio R Paula	10/2016
7194	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
7195	2^340434-5955	102481	Lelio R Paula	11/2016
7196	(7*10^102480-19)/3	102481	Robert Price	10/2020
7197	(2^340381+47)/7	102465	Lelio R Paula	12/2013
7198	111^50095+110	102461	Norbert Schneider	04/2017
7199	2^340291-20301	102438	Enzo Doria	06/2013
7200	12^94915+89	102431	Lelio R Paula	10/2016
7201	(106*10^102422+17)/3	102424	Robert Price	04/2021
7202	24466^15349+15349^24466	102417	Hans Havermann	03/2019
7203	2^340212+111546435	102415	Paul Bourdelais	10/2021
7204	2^340208-20373	102413	Enzo Doria	06/2013
7205	6^131598-17273	102404	Enzo Doria	02/2013
7206	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
7207	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
7208	2^340115-21181	102385	Enzo Doria	06/2013
7209	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
7210	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
7211	9348*31^68638+13	102369	Eric Chen	04/2024
7212	89^52511-88^52511	102365	Robert Price	06/2015
7213	3^214539-112756	102362	Enzo Doria	07/2014
7214	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
7215	2^340000-19877	102351	Enzo Doria	06/2013
7216	2^339990-114845	102348	Enzo Doria	05/2015
7217	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
7218	20^78661-99	102341	Lelio R Paula	09/2016
7220	2^339951-19585	102336	Enzo Doria	05/2013
7219	(17*10^102335-167)/3	102336	Robert Price	05/2022
7221	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
7222	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
7223	5*10^102323-91	102324	Robert Price	03/2021
7225	2^339889+29327	102317	Yves Minet	06/2010
7224	(167*10^102315-17)/3	102317	Robert Price	03/2020
7226	26348^7641+7641^26348	102314	Hans Havermann	03/2019
7227	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
7228	2^339834-109493	102301	Enzo Doria	04/2014
7229	(16*10^102299-19)/3	102300	Robert Price	02/2019
7230	(11^98221-5^98221)/6	102286	Robert Price	01/2013
7231	3^214365+1820	102279	Lelio R Paula	10/2016
7232	31978^1579+1579^31978	102278	Hans Havermann	03/2019
7233	(89*10^102262-467)/9	102263	Robert Price	04/2022
7234	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
7235	2^339694-16995	102259	Lelio R Paula	09/2016
7236	(56*10^102255+691)/9	102256	Robert Price	05/2019
7237	122^49008+121	102249	Norbert Schneider	10/2018
7238	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
7239	7^120985-38	102245	Lelio R Paula	10/2016
7240	10^102244+122961	102245	Patrick De Geest	12/2016
7241	10^102244-27	102244	Lelio R Paula	09/2016
7242	7^120982-62	102242	Lelio R Paula	10/2016
7243	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
7244	4*6^131382-5	102236	Lelio R Paula	11/2014
7245	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
7246	2^339586-1091	102226	Yves Minet	11/2012
7247	11^98161-3072000	102225	Enzo Doria	12/2012
7248	9*7^120961-4	102225	Lelio R Paula	11/2014
7249	5*3^214250+2	102224	Serge Batalov	10/2010
7250	12^94713-59	102213	Lelio R Paula	10/2016

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