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	13^66628+46	74220	Lelio R Paula	01/2015
7002	2^246476-17295	74197	Lelio R Paula	05/2013
7003	(61*10^74189-1)/3	74191	Robert Price	11/2017
7004	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
7005	5*2^246413-3	74179	Lelio R Paula	05/2014
7006	2^246386-28635	74170	Lelio R Paula	05/2013
7007	2^246334-111245	74154	Enzo Doria	05/2014
7008	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
7009	15^63045+82	74147	Lelio R Paula	01/2015
7010	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
7011	2^246268-110507	74135	Enzo Doria	05/2014
7012	3^155328+2660	74111	Lelio R Paula	01/2015
7013	2^246148-2786249	74098	Enzo Doria	03/2016
7014	(16*10^74092-19)/3	74093	Robert Price	03/2016
7015	2^246115-110767	74088	Enzo Doria	05/2014
7016	7^87666-68	74087	Lelio R Paula	08/2014
7017	10^74079+1145141919	74080	Marisa Kirisame	03/2015
7018	10^74079+6219	74080	Patrick De Geest	03/2016
7019	10^74079-282707	74079	Patrick De Geest	03/2016
7020	129^35098+2	74078	Lelio R Paula	05/2013
7021	2^246025-112123	74061	Enzo Doria	06/2014
7022	(67*10^74045+17)/3	74047	Robert Price	02/2017
7023	2^245823+66831	74001	Marek Hubal	02/2017
7024	5^105869+42	74000	Lelio R Paula	08/2014
7025	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
7026	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
7027	(3^155048-7)/262	73975	Lelio R Paula	06/2012
7028	9998*2^245696+3	73966	Donovan Johnson	10/2004
7029	13^66400-80	73966	Lelio R Paula	01/2015
7031	(2^245704+9)/25	73963	Lelio R Paula	07/2012
7032	11^71023-7170	73963	Enzo Doria	01/2013
7030	3*10^73962+13	73963	Robert Price	08/2017
7033	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
7034	2^245629-2797813	73942	Eric Chen	03/2016
7035	2^245557-153	73921	Lelio R Paula	03/2012
7037	(77*10^73917-59)/9	73918	Robert Price	11/2017
7036	15010^17699+17699^15010	73918	Norbert Schneider	11/2019
7038	2^245525+1869881	73911	Enzo Doria	06/2016
7039	2^245522+159	73910	Lelio R Paula	03/2012
7040	(13*10^73891-43)/3	73892	Robert Price	08/2017
7041	19^57783-56	73891	Lelio R Paula	01/2015
7042	7*10^73888+79	73889	Robert Price	02/2017
7043	6^94948+174281	73884	Mike Oakes	02/2011
7044	11^70939-4860	73876	Enzo Doria	01/2013
7045	2^245372+54615	73865	Lelio R Paula	05/2013
7046	2^245362-143	73862	Lelio R Paula	03/2012
7047	7^87396+6^(87396-1)	73859	Robert Price	03/2016
7048	(22*10^73853-37)/3	73854	Robert Price	05/2017
7049	5^105646-14246	73844	Enzo Doria	02/2013
7051	2^245290-41	73840	Lelio R Paula	03/2012
7050	2^245290-94395	73840	Lelio R Paula	05/2013
7052	15770^17589+17589^15770	73836	Norbert Schneider	10/2019
7053	12352^18043+18043^12352	73828	Norbert Schneider	11/2019
7054	8*5^105600-7	73813	Lelio R Paula	10/2014
7055	7*5^105573-4	73794	Lelio R Paula	10/2014
7056	18^58742-4805	73738	Enzo Doria	03/2013
7057	13^66179+66	73720	Lelio R Paula	01/2015
7058	(82*10^73714-1)/9	73715	Robert Price	12/2014
7059	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
7060	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
7061	(13*10^73701+17)/3	73702	Robert Price	06/2015
7062	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
7063	(3^154421-4)/23	73677	Lelio R Paula	06/2012
7064	14596^17691+17691^14596	73670	Norbert Schneider	11/2019
7065	8*7^87170+5	73669	Lelio R Paula	10/2014
7066	(29*10^73659-113)/3	73660	Robert Price	11/2017
7067	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
7068	(4*10^73647-19)/3	73648	Robert Price	06/2017
7069	2^244618-2297	73638	Yves Minet	10/2009
7070	3*5^105344+8	73633	Lelio R Paula	10/2014
7071	5^105334-14096	73626	Enzo Doria	02/2013
7072	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
7073	2^244465-110185	73592	Enzo Doria	05/2014
7074	2^244443+40755	73585	Lelio R Paula	05/2013
7075	2^244404+3841	73573	Yves Minet	03/2011
7076	2^244372-110627	73564	Enzo Doria	05/2014
7077	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
7078	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
7079	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
7080	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
7081	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
7082	18^58521+65	73460	Lelio R Paula	01/2015
7083	13^65940+36	73454	Lelio R Paula	01/2015
7084	(625^26267+1)/626	73437	Richard Fischer	12/2017
7085	5^105050-14	73427	Lelio R Paula	08/2014
7086	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
7087	15^62410-46	73400	Lelio R Paula	01/2015
7088	2^243733+1869707	73371	Enzo Doria	05/2016
7089	11^70439-5430	73355	Enzo Doria	01/2013
7090	2^243676-87	73354	Lelio R Paula	03/2012
7091	(101*10^73346-17)/3	73348	Robert Price	08/2016
7092	2^243621-113185	73338	Enzo Doria	07/2014
7093	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
7094	2*5^104888-7	73314	Lelio R Paula	10/2014
7095	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
7096	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
7097	18^58376-5255	73278	Enzo Doria	03/2013
7098	11^70363+32	73276	Lelio R Paula	02/2015
7099	2^243413+4257	73275	Lelio R Paula	05/2013
7100	104824^5+5^104824	73269	Andrey Kulsha	07/2010
7101	7^86689-6^86689	73261	Predrag Minovic	09/2004
7102	2^243296+90195	73240	Lelio R Paula	05/2013
7103	2^243281-4843	73235	Yves Minet	05/2019
7104	p(15433)#/2-4	73218	Robert Price	12/2016
7105	(59*10^73217-77)/9	73218	Robert Price	11/2017
7106	2^243127+71355	73189	Lelio R Paula	05/2013
7107	2^243116-249419	73186	Paul Bourdelais	03/2013
7108	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
7109	11^70262-98	73171	Lelio R Paula	02/2015
7110	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
7111	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
7112	(43^44773-1)/42	73134	Robert Price	04/2014
7113	6^93980-158359	73131	Mike Oakes	02/2011
7114	19953^4616+4616^19953	73114	Hans Havermann	11/2019
7115	6^93915+53	73081	Lelio R Paula	01/2015
7116	(5*10^73079+211)/9	73079	Robert Price	12/2017
7117	(74*10^73076+43)/9	73077	Robert Price	10/2015
7118	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
7119	2^242632-112199	73040	Enzo Doria	06/2014
7120	V(351646)	73029	Serge Batalov	03/2015
7121	18^58175-85	73026	Lelio R Paula	01/2015
7122	p(15395)#/2-4	73019	Robert Price	12/2016
7123	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
7124	8*6^93825-5	73011	Lelio R Paula	10/2014
7126	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
7125	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
7127	6^93815+143	73003	Lelio R Paula	01/2015
7128	6^93812+5	73000	Wojciech Florek	03/2006
7129	19^57078-62	72989	Lelio R Paula	01/2015
7130	(29*10^72985+91)/3	72986	Robert Price	03/2016
7131	20691^3368+3368^20691	72985	Hans Havermann	10/2019
7132	11^70082-2520	72983	Enzo Doria	12/2012
7133	6^93773+133	72970	Lelio R Paula	01/2015
7134	2^242328-59	72948	Lelio R Paula	03/2012
7135	5^104358-13016	72944	Enzo Doria	02/2013
7136	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
7137	12^67585-95	72937	Lelio R Paula	02/2015
7138	2^242230-113285	72919	Enzo Doria	07/2014
7139	(5*10^72916-11)/3	72917	Erik Branger	12/2013
7140	2^242220-110399	72916	Enzo Doria	05/2014
7141	2^242205-113413	72911	Enzo Doria	07/2014
7142	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
7143	2^242175+74243	72902	Yves Minet	03/2011
7144	2^242150+17659	72895	Lelio R Paula	11/2009
7145	11^69982-2340	72879	Enzo Doria	12/2012
7146	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
7147	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
7148	2^242032+87	72859	Lelio R Paula	03/2012
7149	2^241968-110595	72840	Enzo Doria	05/2014
7150	18850^7313+7313^18850	72839	Hans Havermann	11/2019
7151	(10^72821+71)/9	72821	Robert Price	11/2014
7152	2^241852-64875	72805	Lelio R Paula	05/2013
7153	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
7154	13952^17559+17559^13952	72776	Norbert Schneider	09/2019
7155	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
7156	(8*10^72759+67)/3	72760	Robert Price	01/2017
7157	2^241670+145	72750	Lelio R Paula	03/2012
7158	5^104074+52	72745	Lelio R Paula	08/2014
7159	(3^152466-5)/724	72742	Lelio R Paula	06/2012
7160	20^55908-41	72738	Lelio R Paula	01/2015
7161	(73*10^72735+53)/9	72736	Robert Price	10/2015
7162	10^72730+224011	72731	Patrick De Geest	05/2013
7163	10^72730-99	72730	Robert Price	05/2011
7164	3*10^72723+67	72724	Robert Price	11/2017
7166	(11^69833+3^69833)/14	72723	Robert Price	03/2013
7165	(10^72723-79)/3	72723	Robert Price	10/2017
7167	(88*10^72711-43)/9	72712	Robert Price	11/2015
7168	3^152379+280	72704	Lelio R Paula	01/2015
7169	(25*10^72703-241)/9	72704	Robert Price	01/2017
7170	(47*10^72696+133)/9	72697	Robert Price	04/2017
7171	17^59077-90	72692	Lelio R Paula	01/2015
7172	65^40096+58	72691	Lelio R Paula	01/2016
7173	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
7175	11^69783-38400000	72672	Enzo Doria	01/2013
7174	2^241409-112903	72672	Enzo Doria	06/2014
7176	18895^7014+7014^18895	72670	Hans Havermann	11/2019
7177	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
7178	3^152249-56	72642	Lelio R Paula	01/2015
7179	10^72631+37	72632	Robert Price	01/2011
7180	10^72631-8813	72631	Patrick De Geest	05/2013
7181	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
7182	(9^76103+8^76103)/17	72620	Robert Price	12/2012
7183	2^241220-112337	72615	Enzo Doria	06/2014
7184	(82*10^72612+449)/9	72613	Robert Price	02/2017
7185	2^241169-15793	72600	Enzo Doria	04/2013
7186	9*10^72595+11	72596	Robert Kinser	01/2017
7187	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
7188	(22*10^72560+17)/3	72561	Robert Price	09/2015
7189	2^241032-23	72558	Lelio R Paula	02/2012
7190	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
7191	2^241004-3	72550	M. Frind & P. Underwood	07/2002
7192	22061^1942+1942^22061	72543	Hans Havermann	11/2019
7193	97*10^72522-3	72524	Robert Price	01/2017
7194	(68*10^72516+7)/3	72518	Robert Price	03/2016
7195	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
7196	67^39701-66	72497	Norbert Schneider	11/2014
7197	(185*10^72484+7)/3	72486	Robert Price	02/2017
7199	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
7198	103^36005-102	72473	Norbert Schneider	10/2016
7200	15^61616+88	72467	Lelio R Paula	01/2015
7201	45^43831+2	72462	Lelio R Paula	05/2013
7202	2^240692-492389	72456	Paul Bourdelais	03/2013
7203	(646*10^72446-7)/9	72448	Robert Price	07/2016
7204	9*6^93083+7	72434	Lelio R Paula	10/2014
7205	2^240617-3645	72433	Lelio R Paula	05/2013
7206	11^69531-24000	72410	Enzo Doria	12/2012
7207	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
7208	6^92995+13	72365	Lelio R Paula	01/2015
7209	(11*10^72362-149)/3	72363	Robert Price	01/2017
7210	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
7211	6^92974-55	72348	Lelio R Paula	01/2015
7212	2^240295+11	72337	Lelio R Paula	02/2012
7213	(14*10^72326-53)/3	72327	Robert Price	12/2016
7214	15^61493-46	72322	Lelio R Paula	01/2015
7215	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
7216	5*10^72302+9	72303	Dmitry Domanov	11/2010
7217	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
7218	11^69419-3120	72293	Enzo Doria	12/2012
7219	4*10^72274-83	72275	Robert Price	10/2017
7220	10^72267+33	72268	Robert Price	01/2011
7221	10^72267-553947	72267	Patrick De Geest	05/2013
7222	11^69389-1380	72262	Enzo Doria	12/2012
7223	(16^60013-5^60013)/11	72262	Robert Price	07/2013
7224	7^85507-30	72262	Lelio R Paula	08/2014
7225	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
7226	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
7227	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
7228	2^239863-112267	72206	Enzo Doria	06/2014
7229	2^239853-114853	72203	Enzo Doria	05/2015
7230	(4*10^72174+149)/9	72174	Robert Price	03/2017
7232	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
7231	2^239651-110665	72143	Enzo Doria	05/2014
7233	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
7234	241^30280+30280^241	72128	Norbert Schneider	11/2014
7235	(68*10^72120-23)/9	72121	Robert Price	10/2015
7236	(9^75571+8^75571)/17	72112	Robert Price	12/2012
7237	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
7238	2^239513-112519	72101	Enzo Doria	06/2014
7239	(10^72097+149)/3	72097	Serge Batalov	12/2014
7240	2^239442-6555	72080	Lelio R Paula	05/2012
7241	2*5^103106+3	72069	Lelio R Paula	10/2014
7242	2^239402-197	72068	Lelio R Paula	02/2012
7243	2^239356-111875	72054	Enzo Doria	05/2014
7244	(38*10^72050-119)/9	72051	Robert Price	11/2016
7245	2^239339+15015	72049	Lelio R Paula	01/2013
7246	159^32728+2	72048	Lelio R Paula	05/2013
7247	15^61259-38	72047	Lelio R Paula	01/2015
7248	92^36683-91^36683	72038	Robert Price	08/2015
7249	2^239280+54615	72031	Lelio R Paula	05/2012
7250	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015

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Probable Primes Top 10000

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