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	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7002	(79*10^62387-61)/9	62388	Robert Price	10/2015
7003	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7004	6^80160-13	62377	Lelio R Paula	04/2013
7005	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7006	(17*10^62328-11)/3	62329	Robert Price	07/2015
7007	2^207023+11715	62321	Lelio R Paula	09/2011
7008	(265*10^62298+11)/3	62300	Robert Price	03/2017
7009	2^206947-69	62298	Lelio R Paula	08/2011
7010	2^206938+29835	62295	Lelio R Paula	02/2013
7011	2^206911-726877	62287	Paul Bourdelais	03/2013
7012	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7013	2^206892-112817	62281	Enzo Doria	06/2014
7014	3^130523+46	62276	Lelio R Paula	04/2013
7015	2^206872-113453	62275	Enzo Doria	07/2014
7016	2^206840-93	62266	Lelio R Paula	08/2011
7017	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7018	96^31406+95	62256	Norbert Schneider	03/2016
7019	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7020	2^206765-941683	62243	Paul Bourdelais	11/2012
7021	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7022	2^206755-1579	62240	Yves Minet	03/2013
7023	11^59764-5820	62238	Enzo Doria	01/2013
7024	5*10^62233+3	62234	Dmitry Domanov	11/2010
7025	8*3^130421+7	62228	Lelio R Paula	04/2014
7026	19^48661+10	62226	Lelio R Paula	05/2013
7028	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
7027	2^206705-112635	62225	Enzo Doria	06/2014
7029	3^130403+8680	62219	Lelio R Paula	04/2013
7030	11^59740-7110	62213	Enzo Doria	01/2013
7032	2^206596-167	62192	Lelio R Paula	08/2011
7031	2^206597+18915	62192	Lelio R Paula	02/2013
7033	6^79918+137	62189	Lelio R Paula	04/2013
7034	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
7035	2^206574+613	62185	Jason Earls	04/2008
7036	3^130328+80	62183	Lelio R Paula	04/2013
7037	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
7038	2^206550+76819	62178	Enzo Doria	05/2016
7039	11^59703-24	62175	Lelio R Paula	05/2013
7040	2^206524+75781	62170	Enzo Doria	04/2016
7041	2^206506+427	62165	Henri Lifchitz	01/2005
7042	2^206465+7695	62153	Lelio R Paula	02/2013
7043	2^206464-1649	62152	Yves Minet	03/2013
7044	5^88917+56	62151	Lelio R Paula	04/2013
7045	2^206444-111569	62146	Enzo Doria	05/2014
7046	5^88908-42	62145	Lelio R Paula	04/2013
7047	18^49495-29	62130	Lelio R Paula	05/2013
7048	3*6^79842-5	62130	Lelio R Paula	09/2014
7049	7*10^62127-17	62128	Robert Price	01/2017
7050	2^206373+8415	62125	Lelio R Paula	02/2013
7051	20^47745-9583	62118	Enzo Doria	03/2013
7052	41^38516-2	62118	Lelio R Paula	08/2013
7053	2^206332-58695	62113	Lelio R Paula	09/2011
7054	11^59639-1260	62108	Enzo Doria	11/2012
7055	2^206232-15893	62083	Enzo Doria	04/2013
7056	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
7057	2^206206+75799	62075	Enzo Doria	04/2016
7058	(74*10^62072+43)/9	62073	Robert Price	10/2015
7059	2^206194-185	62071	Lelio R Paula	08/2011
7060	6^79757-103	62064	Lelio R Paula	04/2013
7061	p(13285)#/2-64	62063	Robert Price	04/2017
7062	(29*10^62030-41)/3	62031	Robert Price	07/2016
7063	20^47675-81	62027	Lelio R Paula	06/2013
7064	3^129972+98	62013	Lelio R Paula	04/2013
7065	2^205962+3	62001	Donovan Johnson	02/2006
7066	2^205933-205933^2	61993	Henri Lifchitz	05/2005
7067	(68*10^61991+7)/3	61993	Robert Price	03/2016
7068	20^47641-663	61983	Enzo Doria	03/2013
7069	3^129861+2660	61960	Lelio R Paula	04/2013
7070	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
7071	18^49354-97	61953	Lelio R Paula	05/2013
7072	(209*10^61947-17)/3	61949	Robert Price	05/2017
7074	14*10^61937+1089	61939	Jens K. Andersen	11/2007
7073	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
7075	20^47600+63	61930	Lelio R Paula	06/2013
7076	44117!3+243	61918	Robert Price	09/2014
7077	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
7078	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
7079	20^47575-81	61897	Lelio R Paula	06/2013
7080	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
7081	87^31909+86	61889	Norbert Schneider	10/2015
7082	2^205568+141	61883	Lelio R Paula	08/2011
7083	10^61868+58927	61869	Patrick De Geest	12/2012
7084	10^61868-39	61868	Robert Price	05/2011
7085	5^88505-88	61863	Lelio R Paula	04/2013
7086	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
7087	13^55528-98	61856	Lelio R Paula	05/2013
7088	30535!2-8	61844	Robert Price	06/2015
7089	11^59371-1200	61829	Enzo Doria	11/2012
7090	7*2^205370-5	61824	Lelio R Paula	04/2014
7091	(47*10^61821+403)/9	61822	Robert Price	04/2017
7092	2^205275+7695	61794	Lelio R Paula	02/2013
7093	2^205269+12915	61793	Lelio R Paula	02/2013
7094	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
7095	19^48309+40	61776	Lelio R Paula	05/2013
7096	2^205192-4079	61769	Yves Minet	06/2011
7097	2^205184+16095	61767	Lelio R Paula	09/2011
7098	20^47472-3423	61763	Enzo Doria	03/2013
7099	2^205149-1795	61757	Lelio R Paula	09/2011
7100	2^205110-17	61745	Lelio R Paula	08/2011
7101	(2^205025-7)/25	61718	Lelio R Paula	03/2012
7102	27^43117-26^43117	61717	Robert Price	08/2012
7103	2^205016+37	61716	Lelio R Paula	08/2011
7104	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
7105	1263^19898+19898^1263	61712	Serge Batalov	05/2014
7106	135^28963-134	61701	Norbert Schneider	04/2015
7107	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
7108	(46*10^61693+17)/9	61694	Robert Price	06/2015
7109	((((((((((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
7110	1850^18879+18879^1850	61681	Serge Batalov	05/2014
7111	2^204891-1005	61679	Lelio R Paula	09/2011
7112	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
7113	15937^7408+7408^15937	61672	Hans Havermann	02/2017
7114	5^88216-12	61661	Lelio R Paula	04/2013
7115	18185^2454+2454^18185	61645	Hans Havermann	01/2017
7117	2^204767-15865	61642	Enzo Doria	04/2013
7116	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
7118	7*2^204751-9	61638	Lelio R Paula	04/2014
7120	4*10^61625+21	61626	Robert Price	08/2016
7119	15369^10226+10226^15369	61626	Hans Havermann	02/2017
7121	2^204702-18125	61622	Enzo Doria	05/2013
7122	5*3^129146+8	61620	Lelio R Paula	04/2014
7123	2^204673+129	61613	Lelio R Paula	08/2011
7124	18^49079+97	61608	Lelio R Paula	05/2013
7125	106^30416+105	61602	Norbert Schneider	12/2016
7126	2^204590-33	61588	Lelio R Paula	08/2011
7127	2^204586-111975	61587	Enzo Doria	06/2014
7128	2^204580-16077	61585	Enzo Doria	04/2013
7129	2^204574-16041	61583	Enzo Doria	04/2013
7130	15^52358+56	61578	Lelio R Paula	05/2013
7131	(28*10^61574+11)/3	61575	Robert Price	11/2015
7132	2^204516-17493	61566	Enzo Doria	05/2013
7133	4*5^88076-3	61564	Lelio R Paula	09/2014
7134	11^59110-2520	61557	Enzo Doria	12/2012
7135	2^204477-58695	61554	Lelio R Paula	09/2011
7136	12^57026-73	61542	Lelio R Paula	05/2013
7137	17^50013+90	61539	Lelio R Paula	05/2013
7138	56^35201-55^35201	61538	Robert Price	10/2013
7139	8*7^72810+5	61533	Lelio R Paula	09/2014
7141	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
7140	43867!3-6561	61531	Robert Price	11/2015
7144	10^61525+9^(61525-1)	61526	Robert Price	03/2016
7142	10^61525+62257	61526	Patrick De Geest	12/2016
7143	14821^14166+14166^14821	61526	Hans Havermann	01/2017
7146	12^57010-85	61525	Lelio R Paula	05/2013
7145	10^61525-213579	61525	Patrick De Geest	12/2016
7147	2^204332-99	61511	Lelio R Paula	08/2011
7148	2^204323-2221	61508	Yves Minet	08/2013
7150	2^204317-195	61506	Lelio R Paula	08/2011
7149	3^128910-86	61506	Lelio R Paula	04/2013
7151	2^204318+74539	61506	Enzo Doria	04/2016
7152	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
7153	2^204297-1036093	61500	Paul Bourdelais	11/2012
7154	3^128880+58	61492	Lelio R Paula	04/2013
7155	2^204216-111677	61476	Enzo Doria	05/2014
7156	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
7157	2^204129+204129	61449	Henri Lifchitz	04/2002
7158	3^128787+2^(128787-1)	61448	Robert Price	05/2016
7159	11^58999-78	61442	Lelio R Paula	05/2013
7160	2^204083-111967	61436	Enzo Doria	05/2014
7161	(45^37159+1)/46	61431	Robert Price	11/2013
7162	677^21702+21702^677	61430	Norbert Schneider	06/2016
7163	14837^13810+13810^14837	61429	Hans Havermann	02/2017
7164	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
7165	11^58976-1740	61418	Enzo Doria	11/2012
7166	2^204016-16085	61415	Enzo Doria	04/2013
7167	V(379967)	61393	Serge Batalov	03/2015
7168	43777!3-3^43777	61392	Robert Price	08/2015
7169	7^72642+88	61390	Lelio R Paula	04/2013
7170	3^128656+32	61385	Lelio R Paula	04/2013
7171	2^203916-17493	61385	Enzo Doria	05/2013
7172	6^78880+23	61381	Lelio R Paula	04/2013
7173	2^203877-111799	61374	Enzo Doria	05/2014
7174	2^203867-1615	61371	Lelio R Paula	10/2011
7175	4*10^61367+19	61368	Robert Price	04/2016
7176	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
7177	2^203825-15805	61358	Enzo Doria	04/2013
7178	2^203816-15825	61355	Enzo Doria	04/2013
7179	5*10^61348+59	61349	Robert Price	09/2016
7180	21^46395-2	61345	Lelio R Paula	08/2013
7181	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
7182	7*6^78826+5	61340	Lelio R Paula	09/2014
7183	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
7184	2^203706-111	61322	Lelio R Paula	08/2011
7185	17567^3094+3094^17567	61318	Hans Havermann	02/2017
7186	2^203689-31	61317	Thomas Masser	10/2005
7187	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014
7189	2^203642+39	61303	Lelio R Paula	08/2011
7188	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012
7190	11^58849-6040	61285	Enzo Doria	02/2013
7191	43694!3-3	61264	Robert Price	10/2014
7192	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
7193	2^203490+12909	61257	Lelio R Paula	10/2011
7194	(16*10^61251-31)/3	61252	Robert Price	03/2016
7195	20^47077-5703	61249	Enzo Doria	03/2013
7196	2^203434-113081	61240	Enzo Doria	07/2014
7198	5^87606+4	61234	Wojciech Florek	11/2005
7197	2^203412-167	61234	Lelio R Paula	08/2011
7200	2^203402+1089	61231	Lelio R Paula	10/2011
7199	(8*10^61230+67)/3	61231	Robert Price	01/2017
7201	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
7202	1265^19732+19732^1265	61211	Serge Batalov	05/2014
7203	2^203330+145	61209	Lelio R Paula	08/2011
7204	6^78647-137	61200	Lelio R Paula	04/2013
7205	85^31718+84	61198	Norbert Schneider	10/2015
7206	11^58763-270	61196	Enzo Doria	07/2012
7207	2^203285-112321	61195	Enzo Doria	06/2014
7208	2^203253-995143	61186	Paul Bourdelais	11/2012
7209	15319^9862+9862^15319	61184	Hans Havermann	07/2016
7210	7^72395-44	61181	Lelio R Paula	04/2013
7211	5*2^203176-7	61163	Lelio R Paula	04/2014
7213	7^72358+54	61150	Lelio R Paula	04/2013
7212	2^203133-111775	61150	Enzo Doria	05/2014
7214	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
7215	2^203112-18009	61143	Enzo Doria	05/2013
7216	43607!3+729	61129	Robert Price	09/2014
7217	2^203065-114853	61129	Enzo Doria	05/2015
7218	3^128111+196	61125	Lelio R Paula	04/2013
7219	128^29007+29007^128	61124	Serge Batalov	05/2014
7220	22355*2^203009-3	61117	Donovan Johnson	03/2004
7221	2^203018+33	61115	Lelio R Paula	08/2011
7222	2^203017-1615	61115	Lelio R Paula	10/2011
7223	16697^4570+4570^16697	61110	Hans Havermann	12/2016
7224	2^202998-17241	61109	Enzo Doria	05/2013
7225	20^46964+93	61102	Lelio R Paula	06/2013
7226	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
7227	20^46960-5463	61097	Enzo Doria	03/2013
7228	(11*10^61095+49)/3	61096	Robert Price	05/2016
7229	2^202934-5955	61090	Lelio R Paula	10/2011
7230	19^47772-68	61089	Lelio R Paula	05/2013
7231	2^202877-499423	61073	Paul Bourdelais	03/2013
7232	2^202763-17125	61038	Enzo Doria	05/2013
7233	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
7234	14788^13355+13355^14788	61011	Hans Havermann	12/2016
7235	16069^6258+6258^16069	61005	Hans Havermann	12/2016
7236	5^87276-14336	61004	Enzo Doria	02/2013
7237	50^35899-49^35899	60992	Robert Price	12/2012
7238	2^202599-3049	60989	Yves Minet	10/2014
7239	2^202535-111571	60970	Enzo Doria	05/2014
7240	10^60959+57	60960	Patrick De Geest	12/2008
7242	10^60959-60959	60959	Henri Lifchitz	08/2002
7241	10^60959-29177	60959	Patrick De Geest	08/2008
7243	5^87206+4^(87206+1)	60955	Robert Price	07/2016
7244	2^202476-15909	60952	Enzo Doria	04/2013
7245	2^202472-17513	60951	Enzo Doria	05/2013
7246	14858^12651+12651^14858	60950	Hans Havermann	12/2016
7247	2^202389-58695	60926	Lelio R Paula	09/2011
7248	3^127597-34	60880	Lelio R Paula	04/2013
7249	15088^10831+10831^15088	60876	Hans Havermann	12/2016
7250	2^202198-113261	60868	Enzo Doria	07/2014

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Probable Primes Top 10000

(174961 PRPs in the top)