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	6^134465+95	104635	Lelio R Paula	11/2016
7002	2^347517-17301	104614	Enzo Doria	05/2013
7003	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
7004	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
7005	3^219222-310	104596	Lelio R Paula	11/2016
7006	25993^10554+10554^25993	104581	Hans Havermann	09/2020
7007	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
7008	2^347372-17853	104570	Enzo Doria	05/2013
7009	2^347314+99	104552	Lelio R Paula	09/2011
7010	2^347300-22233	104548	Enzo Doria	06/2013
7011	2^347287-19845	104544	Enzo Doria	06/2013
7012	2^347258-231191	104536	Harrison Mesh	06/2022
7013	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
7014	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
7015	7*2^347239-3	104531	Lelio R Paula	09/2014
7016	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
7017	5*3^219047+8	104513	Lelio R Paula	09/2014
7018	2^347148-109073	104502	Enzo Doria	04/2014
7019	2^347129-20145	104497	Enzo Doria	06/2013
7020	4*10^104461-57	104462	Robert Price	10/2018
7021	(710^(252227+1)+9*10^52227-7)/9	104455	Robert Price	10/2023
7022	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
7023	2^346923-19585	104435	Enzo Doria	05/2013
7024	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
7025	2^346854+346854^2+1	104414	Robert Price	06/2014
7026	2^346834+11715	104408	Lelio R Paula	04/2015
7027	24276^19961+19961^24276	104392	Hans Havermann	09/2020
7028	79^55009+78	104387	Norbert Schneider	02/2015
7029	3^218744+58	104368	Lelio R Paula	11/2016
7030	9*10^104361+89	104362	Robert Price	11/2019
7031	25048^14665+14665^25048	104358	Hans Havermann	09/2020
7032	2^346649+65	104352	Lelio R Paula	09/2011
7033	(19*33^68718-600883)/32	104350	Eric Chen	05/2023
7034	2^346638-17265	104349	Enzo Doria	05/2013
7035	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
7036	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
7037	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
7038	26092^9967+9967^26092	104331	Hans Havermann	09/2020
7039	5*10^104326+77	104327	Robert Price	12/2018
7040	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
7041	(8925^26569-1)/(8925^163-1)	104320	Ryan Propper	11/2023
7044	2^346527-111817	104316	Enzo Doria	05/2014
7043	6^134055+101	104316	Lelio R Paula	11/2016
7042	fibonacci(499147)-4	104316	Jon Grantham	08/2023
7045	92105!4+8	104312	Robert Price	09/2019
7046	(7^123407-5^123407)/2	104291	Jon Grantham	08/2023
7047	6^134013+163	104283	Lelio R Paula	11/2016
7048	10^(2*52140+1)-10^52140-1	104281	Robert Price	07/2023
7049	(22*10^104272-61)/3	104273	Robert Price	03/2022
7050	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
7052	18^83049-89	104250	Lelio R Paula	01/2017
7051	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
7053	(166*10^104230+11)/3	104232	Robert Price	03/2021
7054	2^346213+484049	104221	Enzo Doria	04/2017
7055	18^83021-91	104214	Lelio R Paula	01/2017
7056	10^104212+128779	104213	Patrick De Geest	05/2016
7057	10^104212+237447	104213	Patrick De Geest	05/2016
7058	10^104212+242139	104213	Patrick De Geest	05/2016
7059	10^104212+269199	104213	Patrick De Geest	05/2016
7060	24254^19803+19803^24254	104213	Hans Havermann	09/2020
7061	(10^104212-71)/1	104212	Serge Batalov	12/2014
7062	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
7063	(13*31^69863+12407)/30	104191	Eric Chen	04/2024
7064	2^346078+7695	104180	Lelio R Paula	12/2016
7065	2^346055-19537	104173	Enzo Doria	05/2013
7066	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
7067	2^346037-20125	104168	Enzo Doria	06/2013
7068	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
7069	6^133854-17993	104159	Enzo Doria	03/2013
7070	2^345990+1874239	104154	Enzo Doria	06/2016
7071	2^345988-20373	104153	Enzo Doria	06/2013
7072	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
7073	(26*10^104132-503)/9	104133	Robert Price	07/2018
7074	3*5^148968+8	104125	Lelio R Paula	11/2014
7075	(7*10^104113+53)/3	104114	Robert Price	05/2018
7076	p(21253)#/2+8	104113	Robert Price	01/2017
7077	33582^1259+1259^33582	104106	Hans Havermann	09/2020
7078	32958^1441+1441^32958	104104	Hans Havermann	09/2020
7079	29127^3748+3748^29127	104095	Hans Havermann	09/2020
7080	322^41507+41507^322	104094	Norbert Schneider	12/2014
7081	6^133768-17423	104092	Enzo Doria	03/2013
7082	2^345786-19557	104092	Enzo Doria	05/2013
7083	171^46606-2	104072	Lelio R Paula	10/2017
7084	(29*10^104071+91)/3	104072	Robert Price	04/2020
7085	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
7086	2^345704-149	104068	Lelio R Paula	09/2011
7087	25821^10712+10712^25821	104056	Hans Havermann	09/2020
7088	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
7089	6^133704-17273	104042	Enzo Doria	02/2013
7090	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
7091	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
7092	2^345547+11	104021	Lelio R Paula	09/2011
7093	(19*10^104014-49)/3	104015	Robert Price	05/2019
7094	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
7095	2^345504+723	104008	Lelio R Paula	09/2011
7096	2^345498-20037	104006	Enzo Doria	06/2013
7098	18^82854-37	104005	Lelio R Paula	01/2017
7097	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
7099	2^345486-109065	104002	Enzo Doria	04/2014
7100	2^345487-1851507	104002	Enzo Doria	08/2015
7101	2^345476+777	103999	Lelio R Paula	09/2011
7102	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
7103	4*10^103981-83	103982	Robert Price	10/2018
7104	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
7105	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
7106	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
7107	(19*10^103907+77)/3	103908	Robert Price	05/2019
7108	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
7109	2^345106-112181	103888	Enzo Doria	06/2014
7110	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
7111	2^345079+99	103880	Lelio R Paula	09/2011
7112	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
7113	11^99736-1500	103865	Enzo Doria	12/2012
7114	(569^37699-1)/568	103863	Serge Batalov	06/2022
7115	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
7116	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
7117	3*10^103844+31	103845	Robert Price	06/2021
7118	444*33^68368+19	103821	Eric Chen	05/2023
7119	23927^21814+21814^23927	103813	Hans Havermann	09/2020
7120	2^344842-20157	103808	Enzo Doria	06/2013
7121	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
7122	2^344802-20765	103796	Enzo Doria	06/2013
7123	2^344794-3821	103794	Yves Minet	05/2011
7124	2^344782-109103	103790	Enzo Doria	04/2014
7125	3^217521-112292	103784	Enzo Doria	06/2014
7126	2^344759-3505	103783	Lelio R Paula	11/2016
7127	2^344735-147	103776	Lelio R Paula	09/2011
7128	L(496533)-p(496533)	103770	Robert Price	02/2018
7129	2*10^103749-69	103750	Robert Price	03/2018
7130	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
7131	2^344607-108891	103738	Enzo Doria	03/2014
7133	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
7132	(1097^34123-1)/1096	103738	Serge Batalov	06/2022
7134	2^344560+22411	103723	Enzo Doria	09/2023
7135	(148*10^103718-1)/3	103720	Robert Price	03/2020
7136	2^344541-19561	103718	Enzo Doria	05/2013
7137	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
7138	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
7139	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
7140	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
7141	2^344444-455	103688	Yves Minet	03/2012
7142	(4*10^103678-43)/3	103679	Robert Price	01/2022
7143	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
7144	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
7146	2^344317-109933	103650	Enzo Doria	04/2014
7145	26055^9508+9508^26055	103650	Hans Havermann	09/2020
7147	2^344309-1852033	103648	Enzo Doria	08/2015
7148	25729^10672+10672^25729	103643	Hans Havermann	09/2020
7149	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
7150	3*10^103637+61	103638	Robert Price	09/2020
7151	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
7152	2^344213-21253	103619	Enzo Doria	06/2013
7153	2^344196-465	103614	Lelio R Paula	11/2016
7154	2^344187-20001	103611	Enzo Doria	06/2013
7155	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
7156	(237^43627-1)/236	103601	Serge Batalov	06/2022
7157	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
7158	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
7159	(9^108553-2^108553)/7	103586	Jon Grantham	07/2023
7160	2^344085-20365	103580	Enzo Doria	06/2013
7161	5^148169+54	103566	Lelio R Paula	11/2016
7162	2^344017-108795	103560	Enzo Doria	03/2014
7163	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
7164	2^343971-5077	103546	Lelio R Paula	09/2011
7165	(7*10^103531+71)/3	103532	Robert Price	05/2018
7166	2^343899+141	103524	Lelio R Paula	08/2011
7167	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
7168	6^133029-67	103517	Lelio R Paula	11/2016
7169	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
7170	66*10^103507+7	103509	Robert Price	07/2020
7171	26297^8614+8614^26297	103485	Hans Havermann	09/2020
7172	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
7173	26499^8036+8036^26499	103480	Hans Havermann	09/2020
7174	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
7175	5^148014-24	103458	Lelio R Paula	11/2016
7176	28316^4503+4503^28316	103453	Hans Havermann	09/2020
7177	(22*10^103450+53)/3	103451	Robert Price	07/2019
7178	2^343604+9931	103436	Yves Minet	01/2011
7179	2^343601-21189	103435	Enzo Doria	06/2013
7180	(10^103423+173)/3	103423	Robert Price	05/2021
7181	2^343508-115229	103407	Enzo Doria	06/2015
7182	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
7183	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
7184	3^216685-113056	103386	Enzo Doria	07/2014
7185	24829^14580+14580^24829	103382	Hans Havermann	08/2020
7186	91355!4+1024	103381	Robert Price	09/2019
7187	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
7188	11^99262-20	103371	Lelio R Paula	12/2016
7189	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
7190	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
7191	2^343356-2791889	103361	Enzo Doria	03/2016
7192	(25*10^103360-241)/9	103361	Robert Price	05/2018
7193	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
7194	(371*33^68040-19)/32	103321	Eric Chen	05/2023
7195	24826^14511+14511^24826	103319	Hans Havermann	09/2020
7196	2^343182-171	103309	Lelio R Paula	08/2011
7197	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
7198	(16487^24649-1)/(16487^157-1)	103287	Ryan Propper	11/2023
7199	(10680^25639-1)/10679	103285	Serge Batalov	06/2022
7200	(7427^26683-1)/7426	103282	Serge Batalov	06/2022
7201	2^343079-1835611	103278	Enzo Doria	05/2015
7202	2^343063-1147	103273	Yves Minet	06/2013
7203	24741^14930+14930^24741	103271	Hans Havermann	09/2020
7204	(16*10^103255-73)/3	103256	Robert Price	07/2020
7205	(219^44119-1)/218	103256	Serge Batalov	06/2022
7206	9*6^132689+7	103254	Lelio R Paula	11/2014
7207	2^342979-18085	103247	Enzo Doria	05/2013
7208	(16*10^103244-31)/3	103245	Robert Price	03/2019
7209	2^342966-16995	103244	Lelio R Paula	11/2016
7210	23797^21774+21774^23797	103230	Hans Havermann	09/2020
7211	25388^11637+11637^25388	103224	Hans Havermann	09/2020
7212	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
7213	(16*10^103214-31)/3	103215	Robert Price	03/2019
7215	(37*10^103211+611)/9	103212	Robert Price	11/2018
7214	(238*10^103210-1)/3	103212	Robert Price	04/2020
7216	5^147650+16	103203	Lelio R Paula	11/2016
7217	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
7218	2^342817+2707067	103199	Enzo Doria	03/2016
7219	43^63177-42	103198	Theodore Burton	02/2007
7220	2^342805-21025	103195	Enzo Doria	06/2013
7221	24129^18890+18890^24129	103182	Hans Havermann	09/2020
7222	(622*10^103171-1)/9	103173	Robert Price	11/2021
7223	2^342714+12285	103168	Lelio R Paula	11/2016
7224	(2*10^103161-17)/3	103161	Serge Batalov	11/2022
7225	18^82178-4481	103156	Enzo Doria	03/2013
7226	2^342665-17349	103153	Enzo Doria	05/2013
7227	30408^2467+2467^30408	103150	Hans Havermann	09/2020
7228	(5^147571-3^147571)/2	103148	Kellen Shenton	05/2022
7229	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
7230	2^342612+175	103137	Lelio R Paula	08/2011
7231	5*2^342585-3	103130	Lelio R Paula	09/2014
7232	(16*10^103127+77)/3	103128	Robert Price	03/2019
7233	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
7234	2^342503-19209	103104	Enzo Doria	05/2013
7235	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
7236	2^342476+51	103096	Lelio R Paula	08/2011
7237	2^342460-18885	103091	Enzo Doria	05/2013
7238	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
7239	(194*10^103074-17)/3	103076	Robert Price	09/2020
7240	7^121968+82	103075	Lelio R Paula	10/2016
7241	2^342392-108863	103071	Enzo Doria	03/2014
7242	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
7243	3^216014+28	103065	Lelio R Paula	11/2016
7244	2^342353-108879	103059	Enzo Doria	03/2014
7245	10^103055+276081	103056	Patrick De Geest	12/2016
7246	10^103055-53	103055	Lelio R Paula	11/2016
7247	(58*10^103046+419)/9	103047	Robert Price	05/2019
7248	7^121933+4	103046	Lelio R Paula	11/2014
7249	(71*10^103028-143)/9	103029	Robert Price	10/2021
7250	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020

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Probable Primes Top 10000

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