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 (> 30000)	Who ?	When ?
7001	2^206506+427	62165	Henri Lifchitz	01/2005
7002	2^206465+7695	62153	Lelio R Paula	02/2013
7003	2^206464-1649	62152	Yves Minet	03/2013
7004	5^88917+56	62151	Lelio R Paula	04/2013
7005	2^206444-111569	62146	Enzo Doria	05/2014
7006	5^88908-42	62145	Lelio R Paula	04/2013
7007	18^49495-29	62130	Lelio R Paula	05/2013
7008	3*6^79842-5	62130	Lelio R Paula	09/2014
7009	7*10^62127-17	62128	Robert Price	01/2017
7010	2^206373+8415	62125	Lelio R Paula	02/2013
7011	20^47745-9583	62118	Enzo Doria	03/2013
7012	41^38516-2	62118	Lelio R Paula	08/2013
7013	2^206332-58695	62113	Lelio R Paula	09/2011
7014	11^59639-1260	62108	Enzo Doria	11/2012
7015	2^206232-15893	62083	Enzo Doria	04/2013
7016	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
7017	2^206206+75799	62075	Enzo Doria	04/2016
7018	(74*10^62072+43)/9	62073	Robert Price	10/2015
7019	2^206194-185	62071	Lelio R Paula	08/2011
7020	6^79757-103	62064	Lelio R Paula	04/2013
7021	p(13285)#/2-64	62063	Robert Price	04/2017
7022	(29*10^62030-41)/3	62031	Robert Price	07/2016
7023	20^47675-81	62027	Lelio R Paula	06/2013
7024	3^129972+98	62013	Lelio R Paula	04/2013
7025	2^205962+3	62001	Donovan Johnson	02/2006
7026	2^205933-205933^2	61993	Henri Lifchitz	05/2005
7027	(68*10^61991+7)/3	61993	Robert Price	03/2016
7028	20^47641-663	61983	Enzo Doria	03/2013
7029	3^129861+2660	61960	Lelio R Paula	04/2013
7030	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
7031	18^49354-97	61953	Lelio R Paula	05/2013
7032	(209*10^61947-17)/3	61949	Robert Price	05/2017
7034	14*10^61937+1089	61939	Jens K. Andersen	11/2007
7033	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
7035	20^47600+63	61930	Lelio R Paula	06/2013
7036	44117!3+243	61918	Robert Price	09/2014
7037	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
7038	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
7039	20^47575-81	61897	Lelio R Paula	06/2013
7040	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
7041	87^31909+86	61889	Norbert Schneider	10/2015
7042	2^205568+141	61883	Lelio R Paula	08/2011
7043	10^61868+58927	61869	Patrick De Geest	12/2012
7044	10^61868-39	61868	Robert Price	05/2011
7045	5^88505-88	61863	Lelio R Paula	04/2013
7046	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
7047	13^55528-98	61856	Lelio R Paula	05/2013
7048	30535!2-8	61844	Robert Price	06/2015
7049	11^59371-1200	61829	Enzo Doria	11/2012
7050	7*2^205370-5	61824	Lelio R Paula	04/2014
7051	(47*10^61821+403)/9	61822	Robert Price	04/2017
7052	2^205275+7695	61794	Lelio R Paula	02/2013
7053	2^205269+12915	61793	Lelio R Paula	02/2013
7054	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
7055	19^48309+40	61776	Lelio R Paula	05/2013
7056	2^205192-4079	61769	Yves Minet	06/2011
7057	2^205184+16095	61767	Lelio R Paula	09/2011
7058	20^47472-3423	61763	Enzo Doria	03/2013
7059	2^205149-1795	61757	Lelio R Paula	09/2011
7060	2^205110-17	61745	Lelio R Paula	08/2011
7061	(2^205025-7)/25	61718	Lelio R Paula	03/2012
7062	27^43117-26^43117	61717	Robert Price	08/2012
7063	2^205016+37	61716	Lelio R Paula	08/2011
7064	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
7065	1263^19898+19898^1263	61712	Serge Batalov	05/2014
7066	135^28963-134	61701	Norbert Schneider	04/2015
7067	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
7068	(46*10^61693+17)/9	61694	Robert Price	06/2015
7069	((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768	61684	Phil Carmody	09/2004
7070	1850^18879+18879^1850	61681	Serge Batalov	05/2014
7071	2^204891-1005	61679	Lelio R Paula	09/2011
7072	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
7073	15937^7408+7408^15937	61672	Hans Havermann	02/2017
7074	5^88216-12	61661	Lelio R Paula	04/2013
7075	18185^2454+2454^18185	61645	Hans Havermann	01/2017
7077	2^204767-15865	61642	Enzo Doria	04/2013
7076	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
7078	7*2^204751-9	61638	Lelio R Paula	04/2014
7080	4*10^61625+21	61626	Robert Price	08/2016
7079	15369^10226+10226^15369	61626	Hans Havermann	02/2017
7081	2^204702-18125	61622	Enzo Doria	05/2013
7082	5*3^129146+8	61620	Lelio R Paula	04/2014
7083	2^204673+129	61613	Lelio R Paula	08/2011
7084	18^49079+97	61608	Lelio R Paula	05/2013
7085	106^30416+105	61602	Norbert Schneider	12/2016
7086	2^204590-33	61588	Lelio R Paula	08/2011
7087	2^204586-111975	61587	Enzo Doria	06/2014
7088	2^204580-16077	61585	Enzo Doria	04/2013
7089	2^204574-16041	61583	Enzo Doria	04/2013
7090	15^52358+56	61578	Lelio R Paula	05/2013
7091	(28*10^61574+11)/3	61575	Robert Price	11/2015
7092	2^204516-17493	61566	Enzo Doria	05/2013
7093	4*5^88076-3	61564	Lelio R Paula	09/2014
7094	11^59110-2520	61557	Enzo Doria	12/2012
7095	2^204477-58695	61554	Lelio R Paula	09/2011
7096	12^57026-73	61542	Lelio R Paula	05/2013
7097	17^50013+90	61539	Lelio R Paula	05/2013
7098	56^35201-55^35201	61538	Robert Price	10/2013
7099	8*7^72810+5	61533	Lelio R Paula	09/2014
7101	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
7100	43867!3-6561	61531	Robert Price	11/2015
7104	10^61525+9^(61525-1)	61526	Robert Price	03/2016
7102	10^61525+62257	61526	Patrick De Geest	12/2016
7103	14821^14166+14166^14821	61526	Hans Havermann	01/2017
7106	12^57010-85	61525	Lelio R Paula	05/2013
7105	10^61525-213579	61525	Patrick De Geest	12/2016
7107	2^204332-99	61511	Lelio R Paula	08/2011
7108	2^204323-2221	61508	Yves Minet	08/2013
7110	2^204317-195	61506	Lelio R Paula	08/2011
7109	3^128910-86	61506	Lelio R Paula	04/2013
7111	2^204318+74539	61506	Enzo Doria	04/2016
7112	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
7113	2^204297-1036093	61500	Paul Bourdelais	11/2012
7114	3^128880+58	61492	Lelio R Paula	04/2013
7115	2^204216-111677	61476	Enzo Doria	05/2014
7116	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
7117	2^204129+204129	61449	Henri Lifchitz	04/2002
7118	3^128787+2^(128787-1)	61448	Robert Price	05/2016
7119	11^58999-78	61442	Lelio R Paula	05/2013
7120	2^204083-111967	61436	Enzo Doria	05/2014
7121	(45^37159+1)/46	61431	Robert Price	11/2013
7122	677^21702+21702^677	61430	Norbert Schneider	06/2016
7123	14837^13810+13810^14837	61429	Hans Havermann	02/2017
7124	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
7125	11^58976-1740	61418	Enzo Doria	11/2012
7126	2^204016-16085	61415	Enzo Doria	04/2013
7127	V(379967)	61393	Serge Batalov	03/2015
7128	43777!3-3^43777	61392	Robert Price	08/2015
7129	7^72642+88	61390	Lelio R Paula	04/2013
7130	3^128656+32	61385	Lelio R Paula	04/2013
7131	2^203916-17493	61385	Enzo Doria	05/2013
7132	6^78880+23	61381	Lelio R Paula	04/2013
7133	2^203877-111799	61374	Enzo Doria	05/2014
7134	2^203867-1615	61371	Lelio R Paula	10/2011
7135	4*10^61367+19	61368	Robert Price	04/2016
7136	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
7137	2^203825-15805	61358	Enzo Doria	04/2013
7138	2^203816-15825	61355	Enzo Doria	04/2013
7139	5*10^61348+59	61349	Robert Price	09/2016
7140	21^46395-2	61345	Lelio R Paula	08/2013
7141	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
7142	7*6^78826+5	61340	Lelio R Paula	09/2014
7143	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
7144	2^203706-111	61322	Lelio R Paula	08/2011
7145	17567^3094+3094^17567	61318	Hans Havermann	02/2017
7146	2^203689-31	61317	Thomas Masser	10/2005
7147	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014
7149	2^203642+39	61303	Lelio R Paula	08/2011
7148	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012
7150	11^58849-6040	61285	Enzo Doria	02/2013
7151	43694!3-3	61264	Robert Price	10/2014
7152	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
7153	2^203490+12909	61257	Lelio R Paula	10/2011
7154	(16*10^61251-31)/3	61252	Robert Price	03/2016
7155	20^47077-5703	61249	Enzo Doria	03/2013
7156	2^203434-113081	61240	Enzo Doria	07/2014
7157	5^87606+4	61234	Wojciech Florek	11/2005
7158	2^203412-167	61234	Lelio R Paula	08/2011
7159	2^203402+1089	61231	Lelio R Paula	10/2011
7160	(8*10^61230+67)/3	61231	Robert Price	01/2017
7161	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
7162	1265^19732+19732^1265	61211	Serge Batalov	05/2014
7163	2^203330+145	61209	Lelio R Paula	08/2011
7164	6^78647-137	61200	Lelio R Paula	04/2013
7165	85^31718+84	61198	Norbert Schneider	10/2015
7166	11^58763-270	61196	Enzo Doria	07/2012
7167	2^203285-112321	61195	Enzo Doria	06/2014
7168	2^203253-995143	61186	Paul Bourdelais	11/2012
7169	15319^9862+9862^15319	61184	Hans Havermann	07/2016
7170	7^72395-44	61181	Lelio R Paula	04/2013
7171	5*2^203176-7	61163	Lelio R Paula	04/2014
7173	7^72358+54	61150	Lelio R Paula	04/2013
7172	2^203133-111775	61150	Enzo Doria	05/2014
7174	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
7175	2^203112-18009	61143	Enzo Doria	05/2013
7176	43607!3+729	61129	Robert Price	09/2014
7177	2^203065-114853	61129	Enzo Doria	05/2015
7178	3^128111+196	61125	Lelio R Paula	04/2013
7179	128^29007+29007^128	61124	Serge Batalov	05/2014
7180	22355*2^203009-3	61117	Donovan Johnson	03/2004
7181	2^203018+33	61115	Lelio R Paula	08/2011
7182	2^203017-1615	61115	Lelio R Paula	10/2011
7183	16697^4570+4570^16697	61110	Hans Havermann	12/2016
7184	2^202998-17241	61109	Enzo Doria	05/2013
7185	20^46964+93	61102	Lelio R Paula	06/2013
7186	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
7187	20^46960-5463	61097	Enzo Doria	03/2013
7188	(11*10^61095+49)/3	61096	Robert Price	05/2016
7189	2^202934-5955	61090	Lelio R Paula	10/2011
7190	19^47772-68	61089	Lelio R Paula	05/2013
7191	2^202877-499423	61073	Paul Bourdelais	03/2013
7192	2^202763-17125	61038	Enzo Doria	05/2013
7193	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
7194	14788^13355+13355^14788	61011	Hans Havermann	12/2016
7195	16069^6258+6258^16069	61005	Hans Havermann	12/2016
7196	5^87276-14336	61004	Enzo Doria	02/2013
7197	50^35899-49^35899	60992	Robert Price	12/2012
7198	2^202599-3049	60989	Yves Minet	10/2014
7199	2^202535-111571	60970	Enzo Doria	05/2014
7200	10^60959+57	60960	Patrick De Geest	12/2008
7202	10^60959-60959	60959	Henri Lifchitz	08/2002
7201	10^60959-29177	60959	Patrick De Geest	08/2008
7203	5^87206+4^(87206+1)	60955	Robert Price	07/2016
7204	2^202476-15909	60952	Enzo Doria	04/2013
7205	2^202472-17513	60951	Enzo Doria	05/2013
7206	14858^12651+12651^14858	60950	Hans Havermann	12/2016
7207	2^202389-58695	60926	Lelio R Paula	09/2011
7208	3^127597-34	60880	Lelio R Paula	04/2013
7209	15088^10831+10831^15088	60876	Hans Havermann	12/2016
7210	2^202198-113261	60868	Enzo Doria	07/2014
7211	2^202182+135	60863	Lelio R Paula	08/2011
7212	2^202176+85	60862	Lelio R Paula	08/2011
7213	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
7214	(31*2^202163+1)/3	60859	Lelio R Paula	03/2012
7215	14708^13707+13707^14708	60847	Hans Havermann	12/2016
7216	2^202112+202112^2-1	60842	Robert Price	04/2014
7217	(13*2^202142-1)/405984274257	60841	Lelio R Paula	01/2014
7218	64743*10^60832+(6^78175-11)/5	60837	Gilbert Mozzo	05/2012
7219	(19*2^202098-1)/6795	60836	Lelio R Paula	01/2014
7220	(6^78175-11)/5	60832	Paul Bourdelais	11/2011
7221	2^202063+1605	60828	Lelio R Paula	09/2011
7222	2^202058+859	60826	Lelio R Paula	09/2011
7223	1576^19021+19021^1576	60821	Serge Batalov	05/2014
7224	(2^202009+3)/6005	60807	Lelio R Paula	03/2012
7225	10^60776+3	60777	Robert Price	01/2011
7226	10^60776-14819	60776	Patrick De Geest	12/2012
7227	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
7228	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
7229	2^201822-177	60755	Lelio R Paula	08/2011
7230	(13*10^60744+17)/3	60745	Robert Price	06/2015
7231	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
7232	(26*10^60717-71)/9	60718	Robert Price	03/2015
7233	37^38712-2	60709	Lelio R Paula	08/2013
7234	2^201657-112003	60705	Enzo Doria	05/2014
7235	(10^60703+3^60703)/13	60702	Robert Price	01/2013
7236	2^201622-112817	60695	Enzo Doria	06/2014
7237	2^201620-17177	60694	Enzo Doria	05/2013
7238	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
7239	2^201609-49789	60691	Henri Lifchitz	03/2005
7240	2^201582-19061	60683	Enzo Doria	05/2013
7241	43316!3+27	60679	Robert Price	09/2014
7242	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
7243	2^201560+105	60676	Lelio R Paula	08/2011
7244	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
7245	2^201545-18021	60672	Enzo Doria	05/2013
7246	2^201543+11715	60671	Lelio R Paula	09/2011
7248	2^201512-111755	60662	Enzo Doria	05/2014
7247	p(13013)#/2+64	60662	Robert Price	03/2017
7249	11^58248+16	60660	Lelio R Paula	05/2013
7250	2^201496-27	60657	Lelio R Paula	08/2011

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PRP Records

Probable Primes Top 10000

(173006 PRPs in the top)