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	2^208993+77	62914	Lelio R Paula	08/2011
7002	(2^208948-7)/261	62898	Lelio R Paula	03/2012
7003	(151*10^62879-1)/3	62881	Robert Price	04/2017
7004	15^53464-82	62879	Lelio R Paula	05/2013
7005	2^208843-112921	62869	Enzo Doria	06/2014
7006	2^208779+81	62849	Henri Lifchitz	01/2007
7007	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
7008	(73*10^62824+17)/9	62825	Robert Price	10/2015
7009	3^131670-82	62823	Lelio R Paula	04/2013
7010	19^49128-90	62823	Lelio R Paula	05/2013
7011	11^60314-4410	62811	Enzo Doria	01/2013
7012	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
7013	2^208594+93	62794	Donovan Johnson	06/2008
7014	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
7015	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
7016	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
7017	10^62750+57	62751	Robert Price	01/2011
7018	10^62750-267429	62750	Patrick De Geest	01/2013
7019	2^208427-69	62743	Lelio R Paula	08/2011
7020	2^208421-111775	62741	Enzo Doria	05/2014
7021	2^208404-112079	62736	Enzo Doria	06/2014
7022	2^208343-2221	62718	Yves Minet	08/2013
7023	2^208335+513	62716	Lelio R Paula	10/2011
7025	(2^208328+47)/3	62713	Lelio R Paula	03/2012
7024	11^60220-2040	62713	Enzo Doria	12/2012
7026	2^208292+81	62703	Henri Lifchitz	10/2005
7027	15013^15012-15012	62698	Henri Lifchitz	10/2014
7028	2^208271-112747	62696	Enzo Doria	06/2014
7029	11^60202-4380	62694	Enzo Doria	01/2013
7030	(3^131403-4)/157	62693	Lelio R Paula	04/2012
7031	2^208127-126667	62653	Paul Bourdelais	01/2012
7032	71^33843+2	62653	Lelio R Paula	05/2013
7033	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
7034	2^208019+119	62620	Lelio R Paula	08/2011
7035	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
7036	11^60126-11370	62615	Enzo Doria	12/2012
7037	2^207976-2489	62608	Yves Minet	07/2014
7038	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7039	4*21^47335+205	62588	Curtis Bright	05/2015
7040	15^53210+8	62580	Lelio R Paula	05/2013
7041	2^207865+29	62574	Henri Lifchitz	08/2005
7042	15^53199-38	62567	Lelio R Paula	05/2013
7043	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
7044	2^207782+58905	62549	Lelio R Paula	10/2011
7045	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
7046	(2^207711+5)/13	62527	Lelio R Paula	03/2012
7047	10^62523+63	62524	Robert Price	01/2011
7048	10^62523-292373	62523	Patrick De Geest	01/2013
7049	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
7050	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
7051	2^207626-112157	62502	Enzo Doria	06/2014
7052	3^130987+52	62497	Lelio R Paula	04/2013
7053	8*6^80299-7	62486	Lelio R Paula	09/2014
7054	11^59997-2670	62481	Enzo Doria	12/2012
7055	93^31740+2	62480	Lelio R Paula	05/2013
7056	(10^62451+119)/3	62451	Serge Batalov	12/2014
7057	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
7058	2^207364+115	62423	Lelio R Paula	08/2011
7059	3^130815-46	62415	Lelio R Paula	04/2013
7060	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
7061	20^47968-9483	62408	Enzo Doria	03/2013
7062	(10^62402+101)/3	62402	Robert Price	04/2016
7063	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7064	(79*10^62387-61)/9	62388	Robert Price	10/2015
7065	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7066	6^80160-13	62377	Lelio R Paula	04/2013
7067	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7068	(17*10^62328-11)/3	62329	Robert Price	07/2015
7069	2^207023+11715	62321	Lelio R Paula	09/2011
7070	(265*10^62298+11)/3	62300	Robert Price	03/2017
7071	2^206947-69	62298	Lelio R Paula	08/2011
7072	2^206938+29835	62295	Lelio R Paula	02/2013
7073	2^206911-726877	62287	Paul Bourdelais	03/2013
7074	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7075	2^206892-112817	62281	Enzo Doria	06/2014
7076	3^130523+46	62276	Lelio R Paula	04/2013
7077	2^206872-113453	62275	Enzo Doria	07/2014
7078	2^206840-93	62266	Lelio R Paula	08/2011
7079	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7080	96^31406+95	62256	Norbert Schneider	03/2016
7081	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7082	2^206765-941683	62243	Paul Bourdelais	11/2012
7083	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7084	2^206755-1579	62240	Yves Minet	03/2013
7085	11^59764-5820	62238	Enzo Doria	01/2013
7086	5*10^62233+3	62234	Dmitry Domanov	11/2010
7087	8*3^130421+7	62228	Lelio R Paula	04/2014
7088	19^48661+10	62226	Lelio R Paula	05/2013
7090	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
7089	2^206705-112635	62225	Enzo Doria	06/2014
7091	3^130403+8680	62219	Lelio R Paula	04/2013
7092	11^59740-7110	62213	Enzo Doria	01/2013
7094	2^206596-167	62192	Lelio R Paula	08/2011
7093	2^206597+18915	62192	Lelio R Paula	02/2013
7095	6^79918+137	62189	Lelio R Paula	04/2013
7096	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
7097	2^206574+613	62185	Jason Earls	04/2008
7098	3^130328+80	62183	Lelio R Paula	04/2013
7099	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
7100	2^206550+76819	62178	Enzo Doria	05/2016
7101	11^59703-24	62175	Lelio R Paula	05/2013
7102	2^206524+75781	62170	Enzo Doria	04/2016
7103	2^206506+427	62165	Henri Lifchitz	01/2005
7104	2^206465+7695	62153	Lelio R Paula	02/2013
7105	2^206464-1649	62152	Yves Minet	03/2013
7106	5^88917+56	62151	Lelio R Paula	04/2013
7107	2^206444-111569	62146	Enzo Doria	05/2014
7108	5^88908-42	62145	Lelio R Paula	04/2013
7109	18^49495-29	62130	Lelio R Paula	05/2013
7110	3*6^79842-5	62130	Lelio R Paula	09/2014
7111	7*10^62127-17	62128	Robert Price	01/2017
7112	2^206373+8415	62125	Lelio R Paula	02/2013
7113	20^47745-9583	62118	Enzo Doria	03/2013
7114	41^38516-2	62118	Lelio R Paula	08/2013
7115	2^206332-58695	62113	Lelio R Paula	09/2011
7116	11^59639-1260	62108	Enzo Doria	11/2012
7117	2^206232-15893	62083	Enzo Doria	04/2013
7118	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
7119	2^206206+75799	62075	Enzo Doria	04/2016
7120	(74*10^62072+43)/9	62073	Robert Price	10/2015
7121	2^206194-185	62071	Lelio R Paula	08/2011
7122	6^79757-103	62064	Lelio R Paula	04/2013
7123	p(13285)#/2-64	62063	Robert Price	04/2017
7124	(29*10^62030-41)/3	62031	Robert Price	07/2016
7125	20^47675-81	62027	Lelio R Paula	06/2013
7126	3^129972+98	62013	Lelio R Paula	04/2013
7127	2^205962+3	62001	Donovan Johnson	02/2006
7128	2^205933-205933^2	61993	Henri Lifchitz	05/2005
7129	(68*10^61991+7)/3	61993	Robert Price	03/2016
7130	20^47641-663	61983	Enzo Doria	03/2013
7131	3^129861+2660	61960	Lelio R Paula	04/2013
7132	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
7133	18^49354-97	61953	Lelio R Paula	05/2013
7134	(209*10^61947-17)/3	61949	Robert Price	05/2017
7136	14*10^61937+1089	61939	Jens K. Andersen	11/2007
7135	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
7137	20^47600+63	61930	Lelio R Paula	06/2013
7138	44117!3+243	61918	Robert Price	09/2014
7139	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
7140	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
7141	20^47575-81	61897	Lelio R Paula	06/2013
7142	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
7143	87^31909+86	61889	Norbert Schneider	10/2015
7144	2^205568+141	61883	Lelio R Paula	08/2011
7145	10^61868+58927	61869	Patrick De Geest	12/2012
7146	10^61868-39	61868	Robert Price	05/2011
7147	5^88505-88	61863	Lelio R Paula	04/2013
7148	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
7149	13^55528-98	61856	Lelio R Paula	05/2013
7150	30535!2-8	61844	Robert Price	06/2015
7151	11^59371-1200	61829	Enzo Doria	11/2012
7152	7*2^205370-5	61824	Lelio R Paula	04/2014
7153	(47*10^61821+403)/9	61822	Robert Price	04/2017
7154	2^205275+7695	61794	Lelio R Paula	02/2013
7155	2^205269+12915	61793	Lelio R Paula	02/2013
7156	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
7157	19^48309+40	61776	Lelio R Paula	05/2013
7158	2^205192-4079	61769	Yves Minet	06/2011
7159	2^205184+16095	61767	Lelio R Paula	09/2011
7160	20^47472-3423	61763	Enzo Doria	03/2013
7161	2^205149-1795	61757	Lelio R Paula	09/2011
7162	2^205110-17	61745	Lelio R Paula	08/2011
7163	(2^205025-7)/25	61718	Lelio R Paula	03/2012
7164	27^43117-26^43117	61717	Robert Price	08/2012
7165	2^205016+37	61716	Lelio R Paula	08/2011
7166	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
7167	1263^19898+19898^1263	61712	Serge Batalov	05/2014
7168	135^28963-134	61701	Norbert Schneider	04/2015
7169	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
7170	(46*10^61693+17)/9	61694	Robert Price	06/2015
7171	((((((((((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
7172	1850^18879+18879^1850	61681	Serge Batalov	05/2014
7173	2^204891-1005	61679	Lelio R Paula	09/2011
7174	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
7175	15937^7408+7408^15937	61672	Hans Havermann	02/2017
7176	5^88216-12	61661	Lelio R Paula	04/2013
7177	18185^2454+2454^18185	61645	Hans Havermann	01/2017
7179	2^204767-15865	61642	Enzo Doria	04/2013
7178	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
7180	7*2^204751-9	61638	Lelio R Paula	04/2014
7182	4*10^61625+21	61626	Robert Price	08/2016
7181	15369^10226+10226^15369	61626	Hans Havermann	02/2017
7183	2^204702-18125	61622	Enzo Doria	05/2013
7184	5*3^129146+8	61620	Lelio R Paula	04/2014
7185	2^204673+129	61613	Lelio R Paula	08/2011
7186	18^49079+97	61608	Lelio R Paula	05/2013
7187	106^30416+105	61602	Norbert Schneider	12/2016
7188	2^204590-33	61588	Lelio R Paula	08/2011
7189	2^204586-111975	61587	Enzo Doria	06/2014
7190	2^204580-16077	61585	Enzo Doria	04/2013
7191	2^204574-16041	61583	Enzo Doria	04/2013
7192	15^52358+56	61578	Lelio R Paula	05/2013
7193	(28*10^61574+11)/3	61575	Robert Price	11/2015
7194	2^204516-17493	61566	Enzo Doria	05/2013
7195	4*5^88076-3	61564	Lelio R Paula	09/2014
7196	11^59110-2520	61557	Enzo Doria	12/2012
7197	2^204477-58695	61554	Lelio R Paula	09/2011
7198	12^57026-73	61542	Lelio R Paula	05/2013
7199	17^50013+90	61539	Lelio R Paula	05/2013
7200	56^35201-55^35201	61538	Robert Price	10/2013
7201	8*7^72810+5	61533	Lelio R Paula	09/2014
7203	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
7202	43867!3-6561	61531	Robert Price	11/2015
7204	10^61525+9^(61525-1)	61526	Robert Price	03/2016
7205	10^61525+62257	61526	Patrick De Geest	12/2016
7206	14821^14166+14166^14821	61526	Hans Havermann	01/2017
7208	12^57010-85	61525	Lelio R Paula	05/2013
7207	10^61525-213579	61525	Patrick De Geest	12/2016
7209	2^204332-99	61511	Lelio R Paula	08/2011
7210	2^204323-2221	61508	Yves Minet	08/2013
7212	2^204317-195	61506	Lelio R Paula	08/2011
7211	3^128910-86	61506	Lelio R Paula	04/2013
7213	2^204318+74539	61506	Enzo Doria	04/2016
7214	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
7215	2^204297-1036093	61500	Paul Bourdelais	11/2012
7216	3^128880+58	61492	Lelio R Paula	04/2013
7217	2^204216-111677	61476	Enzo Doria	05/2014
7218	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
7219	2^204129+204129	61449	Henri Lifchitz	04/2002
7220	3^128787+2^(128787-1)	61448	Robert Price	05/2016
7221	11^58999-78	61442	Lelio R Paula	05/2013
7222	2^204083-111967	61436	Enzo Doria	05/2014
7223	(45^37159+1)/46	61431	Robert Price	11/2013
7224	677^21702+21702^677	61430	Norbert Schneider	06/2016
7225	14837^13810+13810^14837	61429	Hans Havermann	02/2017
7226	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
7227	11^58976-1740	61418	Enzo Doria	11/2012
7228	2^204016-16085	61415	Enzo Doria	04/2013
7229	V(379967)	61393	Serge Batalov	03/2015
7230	43777!3-3^43777	61392	Robert Price	08/2015
7231	7^72642+88	61390	Lelio R Paula	04/2013
7232	3^128656+32	61385	Lelio R Paula	04/2013
7233	2^203916-17493	61385	Enzo Doria	05/2013
7234	6^78880+23	61381	Lelio R Paula	04/2013
7235	2^203877-111799	61374	Enzo Doria	05/2014
7236	2^203867-1615	61371	Lelio R Paula	10/2011
7237	4*10^61367+19	61368	Robert Price	04/2016
7238	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
7239	L(293659)/76528122719	61361	Serge Batalov	07/2017
7240	2^203825-15805	61358	Enzo Doria	04/2013
7241	2^203816-15825	61355	Enzo Doria	04/2013
7242	5*10^61348+59	61349	Robert Price	09/2016
7243	21^46395-2	61345	Lelio R Paula	08/2013
7244	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
7245	7*6^78826+5	61340	Lelio R Paula	09/2014
7246	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
7247	2^203706-111	61322	Lelio R Paula	08/2011
7248	17567^3094+3094^17567	61318	Hans Havermann	02/2017
7249	2^203689-31	61317	Thomas Masser	10/2005
7250	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014

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Probable Primes Top 10000

(180278 PRPs in the top)