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	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
7002	6^93815+143	73003	Lelio R Paula	01/2015
7003	6^93812+5	73000	Wojciech Florek	03/2006
7004	19^57078-62	72989	Lelio R Paula	01/2015
7005	(29*10^72985+91)/3	72986	Robert Price	03/2016
7006	11^70082-2520	72983	Enzo Doria	12/2012
7007	6^93773+133	72970	Lelio R Paula	01/2015
7008	2^242328-59	72948	Lelio R Paula	03/2012
7009	5^104358-13016	72944	Enzo Doria	02/2013
7010	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
7011	12^67585-95	72937	Lelio R Paula	02/2015
7012	2^242230-113285	72919	Enzo Doria	07/2014
7013	(5*10^72916-11)/3	72917	Erik Branger	12/2013
7014	2^242220-110399	72916	Enzo Doria	05/2014
7015	2^242205-113413	72911	Enzo Doria	07/2014
7016	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
7017	2^242175+74243	72902	Yves Minet	03/2011
7018	2^242150+17659	72895	Lelio R Paula	11/2009
7019	11^69982-2340	72879	Enzo Doria	12/2012
7020	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
7021	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
7022	2^242032+87	72859	Lelio R Paula	03/2012
7023	2^241968-110595	72840	Enzo Doria	05/2014
7024	(10^72821+71)/9	72821	Robert Price	11/2014
7025	2^241852-64875	72805	Lelio R Paula	05/2013
7026	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
7027	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
7028	(8*10^72759+67)/3	72760	Robert Price	01/2017
7029	2^241670+145	72750	Lelio R Paula	03/2012
7030	5^104074+52	72745	Lelio R Paula	08/2014
7031	(3^152466-5)/724	72742	Lelio R Paula	06/2012
7032	20^55908-41	72738	Lelio R Paula	01/2015
7033	(73*10^72735+53)/9	72736	Robert Price	10/2015
7034	10^72730+224011	72731	Patrick De Geest	05/2013
7035	10^72730-99	72730	Robert Price	05/2011
7036	3*10^72723+67	72724	Robert Price	11/2017
7037	(11^69833+3^69833)/14	72723	Robert Price	03/2013
7038	(10^72723-79)/3	72723	Robert Price	10/2017
7039	(88*10^72711-43)/9	72712	Robert Price	11/2015
7040	3^152379+280	72704	Lelio R Paula	01/2015
7041	(25*10^72703-241)/9	72704	Robert Price	01/2017
7042	(47*10^72696+133)/9	72697	Robert Price	04/2017
7043	17^59077-90	72692	Lelio R Paula	01/2015
7044	65^40096+58	72691	Lelio R Paula	01/2016
7045	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
7047	11^69783-38400000	72672	Enzo Doria	01/2013
7046	2^241409-112903	72672	Enzo Doria	06/2014
7048	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
7049	3^152249-56	72642	Lelio R Paula	01/2015
7050	10^72631+37	72632	Robert Price	01/2011
7051	10^72631-8813	72631	Patrick De Geest	05/2013
7052	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
7053	(9^76103+8^76103)/17	72620	Robert Price	12/2012
7054	2^241220-112337	72615	Enzo Doria	06/2014
7055	(82*10^72612+449)/9	72613	Robert Price	02/2017
7056	2^241169-15793	72600	Enzo Doria	04/2013
7057	9*10^72595+11	72596	Robert Kinser	01/2017
7058	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
7059	(22*10^72560+17)/3	72561	Robert Price	09/2015
7060	2^241032-23	72558	Lelio R Paula	02/2012
7061	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
7062	2^241004-3	72550	M. Frind & P. Underwood	07/2002
7063	97*10^72522-3	72524	Robert Price	01/2017
7064	(68*10^72516+7)/3	72518	Robert Price	03/2016
7065	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
7066	67^39701-66	72497	Norbert Schneider	11/2014
7067	(185*10^72484+7)/3	72486	Robert Price	02/2017
7069	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
7068	103^36005-102	72473	Norbert Schneider	10/2016
7070	15^61616+88	72467	Lelio R Paula	01/2015
7071	45^43831+2	72462	Lelio R Paula	05/2013
7072	2^240692-492389	72456	Paul Bourdelais	03/2013
7073	(646*10^72446-7)/9	72448	Robert Price	07/2016
7074	9*6^93083+7	72434	Lelio R Paula	10/2014
7075	2^240617-3645	72433	Lelio R Paula	05/2013
7076	11^69531-24000	72410	Enzo Doria	12/2012
7077	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
7078	6^92995+13	72365	Lelio R Paula	01/2015
7079	(11*10^72362-149)/3	72363	Robert Price	01/2017
7080	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
7081	6^92974-55	72348	Lelio R Paula	01/2015
7082	2^240295+11	72337	Lelio R Paula	02/2012
7083	(14*10^72326-53)/3	72327	Robert Price	12/2016
7084	15^61493-46	72322	Lelio R Paula	01/2015
7085	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
7086	5*10^72302+9	72303	Dmitry Domanov	11/2010
7087	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
7088	11^69419-3120	72293	Enzo Doria	12/2012
7089	4*10^72274-83	72275	Robert Price	10/2017
7090	10^72267+33	72268	Robert Price	01/2011
7091	10^72267-553947	72267	Patrick De Geest	05/2013
7092	11^69389-1380	72262	Enzo Doria	12/2012
7093	(16^60013-5^60013)/11	72262	Robert Price	07/2013
7094	7^85507-30	72262	Lelio R Paula	08/2014
7095	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
7096	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
7097	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
7098	2^239863-112267	72206	Enzo Doria	06/2014
7099	2^239853-114853	72203	Enzo Doria	05/2015
7100	(4*10^72174+149)/9	72174	Robert Price	03/2017
7102	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
7101	2^239651-110665	72143	Enzo Doria	05/2014
7103	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
7104	241^30280+30280^241	72128	Norbert Schneider	11/2014
7105	(68*10^72120-23)/9	72121	Robert Price	10/2015
7106	(9^75571+8^75571)/17	72112	Robert Price	12/2012
7107	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
7108	2^239513-112519	72101	Enzo Doria	06/2014
7109	(10^72097+149)/3	72097	Serge Batalov	12/2014
7110	2^239442-6555	72080	Lelio R Paula	05/2012
7111	2*5^103106+3	72069	Lelio R Paula	10/2014
7112	2^239402-197	72068	Lelio R Paula	02/2012
7113	2^239356-111875	72054	Enzo Doria	05/2014
7114	(38*10^72050-119)/9	72051	Robert Price	11/2016
7115	2^239339+15015	72049	Lelio R Paula	01/2013
7116	159^32728+2	72048	Lelio R Paula	05/2013
7117	15^61259-38	72047	Lelio R Paula	01/2015
7118	92^36683-91^36683	72038	Robert Price	08/2015
7119	2^239280+54615	72031	Lelio R Paula	05/2012
7120	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
7121	(85*10^72025-1)/3	72027	Robert Price	07/2017
7122	2^239236-97305	72018	Lelio R Paula	05/2012
7123	144^33361-143	72006	Norbert Schneider	11/2018
7124	2^239169+59	71998	Lelio R Paula	02/2012
7125	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
7126	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
7127	(29^49211-1)/28	71965	Robert Price	04/2012
7128	(299*10^71963+1)/3	71965	Robert Price	11/2017
7130	L(344293)	71953	Renaud Lifchitz	09/2003
7129	V(344293)	71953	Serge Batalov	03/2015
7131	6*10^71951+7	71952	Dmitry Domanov	11/2010
7132	3^150798+40	71949	Lelio R Paula	01/2015
7133	2^238961+95	71935	Lelio R Paula	02/2012
7134	2^238936-407	71927	Yves Minet	02/2012
7135	2^238923-28635	71923	Lelio R Paula	05/2012
7136	10^71910+25119	71911	Patrick De Geest	05/2016
7137	10^71910-801	71910	Robert Price	04/2016
7138	2^238845-112651	71900	Enzo Doria	06/2014
7139	2^238792-111245	71884	Enzo Doria	05/2014
7140	6*7^85059+5	71884	Lelio R Paula	10/2014
7141	2^238752-110589	71872	Enzo Doria	05/2014
7142	12^66581+7	71853	Lelio R Paula	07/2014
7143	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
7144	4*3^150568-5	71840	Lelio R Paula	04/2014
7145	6^92301+67	71825	Lelio R Paula	01/2015
7146	2^238568+98765331	71817	Jason Earls	01/2009
7147	2^238541-112723	71808	Enzo Doria	06/2014
7148	2^238529-15949	71805	Enzo Doria	04/2013
7149	9*5^102721-8	71800	Lelio R Paula	10/2014
7150	2^238494-165	71794	Lelio R Paula	02/2012
7151	2^238389-110905	71763	Enzo Doria	05/2014
7152	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
7153	7^84913+5062	71760	Mike Oakes	02/2010
7154	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
7155	2^238268-97305	71726	Lelio R Paula	05/2012
7156	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
7157	2^238235-113247	71716	Enzo Doria	07/2014
7158	2*12^66450-5^66450	71712	Mike Oakes	11/2010
7159	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
7160	2^238199-111817	71706	Enzo Doria	05/2014
7161	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
7162	2^238144+98765331	71689	Jason Earls	01/2009
7163	18^57102-4265	71679	Enzo Doria	03/2013
7164	(73*10^71670-1)/9	71671	Robert Price	01/2015
7165	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
7166	2^238067-111925	71666	Enzo Doria	05/2014
7167	36^46030+35	71637	Norbert Schneider	04/2014
7168	(74*10^71621+313)/9	71622	Robert Price	11/2017
7169	2^237905-91	71617	Lelio R Paula	02/2012
7170	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
7171	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
7172	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
7173	2^237846+1299	71599	Lelio R Paula	05/2012
7174	6^92004+199801	71594	Mike Oakes	02/2011
7175	159^32516+2	71581	Lelio R Paula	05/2013
7176	2^237781+855	71580	Lelio R Paula	05/2012
7177	2^237720-4079	71561	Yves Minet	06/2011
7178	2^237698-110945	71555	Enzo Doria	05/2014
7179	2^237695-113239	71554	Enzo Doria	07/2014
7180	8*5^102362-9	71549	Lelio R Paula	10/2014
7181	(4*10^71546-31)/9	71546	Erik Branger	05/2011
7182	2^237650+37	71540	Lelio R Paula	02/2012
7183	18^56977-4391	71522	Enzo Doria	03/2013
7184	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
7185	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
7186	(26*10^71503+7)/3	71504	Erik Branger	11/2013
7187	(4*10^71498+173)/3	71499	Robert Price	01/2017
7188	3^149848+110	71496	Lelio R Paula	11/2014
7189	2^237498+513	71495	Lelio R Paula	05/2012
7190	2^237485+107	71491	Lelio R Paula	02/2012
7191	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
7192	2^237439-112237	71477	Enzo Doria	06/2014
7193	2^237407-9787	71467	Lelio R Paula	11/2009
7194	2^237383+72953	71460	Enzo Doria	04/2016
7195	82^37337-81^37337	71457	Robert Price	01/2015
7196	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
7197	2^237311+191	71438	Lelio R Paula	02/2012
7198	2^237280-59	71429	Lelio R Paula	02/2012
7199	11^68564-98	71403	Lelio R Paula	01/2015
7200	2^237173+74801	71397	Enzo Doria	04/2016
7201	15^60697+56	71386	Lelio R Paula	01/2015
7202	2^237118+177	71380	Lelio R Paula	02/2012
7203	2^237110+69	71378	Lelio R Paula	02/2012
7204	15^60690-58	71377	Lelio R Paula	01/2015
7205	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
7206	(3^149567+2)/539	71359	Lelio R Paula	06/2012
7207	(5*10^71357-143)/3	71358	Robert Price	04/2016
7208	2^237039-114621	71356	Enzo Doria	05/2015
7209	12^66116-37	71352	Lelio R Paula	02/2015
7210	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
7211	2^236941-66945	71327	Lelio R Paula	05/2012
7212	2^236911-1147	71318	Yves Minet	10/2009
7213	65^39337+42	71315	Lelio R Paula	01/2016
7214	6*10^71299+7	71300	Dmitry Domanov	11/2010
7215	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
7216	10^71291+15187	71292	Patrick De Geest	03/2016
7218	10^71291-5587309119	71291	Robert Price	03/2015
7217	10^71291-273581	71291	Patrick De Geest	03/2016
7219	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
7220	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
7221	(2^236738+9)/13	71265	Lelio R Paula	05/2012
7222	5^101949+42	71260	Lelio R Paula	07/2014
7223	5*10^71237+9	71238	Dmitry Domanov	11/2010
7224	2^236634-16025	71234	Enzo Doria	04/2013
7225	71^38478+70	71233	Norbert Schneider	12/2014
7226	9*7^84280+8	71226	Lelio R Paula	10/2014
7227	(10^71223+59)/3	71223	Serge Batalov	12/2014
7228	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
7229	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
7230	2^236528-173	71203	Lelio R Paula	02/2012
7231	3*2^236511-5	71198	Lelio R Paula	04/2014
7232	2^236477-99	71187	Lelio R Paula	02/2012
7233	11^68356-2130	71186	Enzo Doria	12/2012
7234	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
7235	11^68355-3120	71185	Enzo Doria	12/2012
7236	36^45737-35^45737	71181	Robert Price	10/2012
7237	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
7238	2^236432+25	71174	Lelio R Paula	02/2012
7239	5^101818-12806	71168	Enzo Doria	02/2013
7240	(7*10^71166-457)/9	71166	Robert Price	09/2017
7241	65^39253+62	71163	Lelio R Paula	01/2016
7242	39^44718+38	71150	Norbert Schneider	05/2014
7243	2^236296-407	71133	Yves Minet	02/2012
7244	2^236286-117	71130	Lelio R Paula	02/2012
7245	2^236257-111193	71121	Enzo Doria	05/2014
7246	7^84149-36	71115	Lelio R Paula	08/2014
7247	164176#-p(164176)	71108	Henri Lifchitz	12/2018
7248	2^236209-112123	71106	Enzo Doria	06/2014
7249	18^56644-4985	71104	Enzo Doria	03/2013
7250	(46*10^71077+521)/9	71078	Robert Price	08/2017

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Probable Primes Top 10000

(253476 PRPs in the top)