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	35^41359+2	63862	Lelio R Paula	05/2013
7002	(61*10^63857-43)/9	63858	Robert Price	09/2015
7003	(2^212131-3)/485	63856	Lelio R Paula	04/2012
7004	2^212112-459995	63853	Enzo Doria	06/2015
7005	15^54290+58	63850	Lelio R Paula	05/2013
7006	3*2^212097-7	63849	Lelio R Paula	04/2014
7007	55^36683-54	63842	Norbert Schneider	08/2014
7008	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
7009	(3^133805-7)/172	63839	Lelio R Paula	04/2012
7010	2^212049+149	63834	Lelio R Paula	08/2011
7011	5^91318-18	63829	Lelio R Paula	04/2013
7012	18468^2857+2857^18468	63824	Hans Havermann	03/2017
7013	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
7014	2^211961+12915	63807	Lelio R Paula	02/2013
7015	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
7016	747^22198+22198^747	63782	Norbert Schneider	07/2016
7017	2^211800-17169	63759	Enzo Doria	05/2013
7018	(85*10^63757-1)/3	63759	Robert Price	07/2017
7019	(14*10^63747-11)/3	63748	Erik Branger	09/2014
7020	91*19^49848+6	63746	Curtis Bright	05/2015
7021	18855^2402+2402^18855	63741	Hans Havermann	03/2017
7022	(142*10^63734-7)/9	63736	Robert Price	02/2017
7023	2^211699-111	63728	Lelio R Paula	08/2011
7024	11^61192-5550	63725	Enzo Doria	01/2013
7025	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
7026	6^81872-13	63709	Lelio R Paula	04/2013
7027	3^133522+98	63707	Lelio R Paula	05/2013
7029	2^211607-61	63701	Lelio R Paula	08/2011
7028	5^91135+8	63701	Lelio R Paula	04/2013
7030	11^61157-270	63689	Enzo Doria	07/2012
7031	10^63685+1145141919	63686	Marisa Kirisame	03/2015
7032	10^63685+103837	63686	Patrick De Geest	03/2016
7033	10^63685-130797	63685	Patrick De Geest	03/2016
7034	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
7035	2^211543+45	63681	Lelio R Paula	08/2011
7036	2^211534+43	63679	Lelio R Paula	08/2011
7037	11^61140-60	63671	Enzo Doria	07/2012
7038	2^211491-112321	63666	Enzo Doria	06/2014
7039	19085^2164+2164^19085	63654	Hans Havermann	03/2017
7040	(2^211430-5)/859	63644	Lelio R Paula	04/2012
7041	2^211401-91	63639	Lelio R Paula	08/2011
7042	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
7043	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
7044	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
7045	2^211333+15015	63618	Lelio R Paula	01/2013
7046	33^41889-32	63610	Norbert Schneider	03/2014
7047	13^57093+18	63599	Lelio R Paula	05/2013
7048	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
7049	(107*10^63576-17)/9	63578	Robert Price	02/2017
7050	23^46687-1020	63575	Enzo Doria	08/2012
7051	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
7052	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
7053	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
7054	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
7055	2*3^133227+5	63566	Lelio R Paula	04/2014
7056	2^211155+113	63564	Lelio R Paula	08/2011
7057	2^211134+345	63558	Lelio R Paula	09/2011
7058	2^211121+16385	63554	Lelio R Paula	09/2011
7059	16996^5483+5483^16996	63549	Hans Havermann	02/2017
7060	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
7061	3*10^63522+13	63523	Robert Price	08/2017
7062	15852^10157+10157^15852	63516	Hans Havermann	02/2017
7063	2^210948-15873	63502	Enzo Doria	04/2013
7064	7^75136+6	63498	Lelio R Paula	04/2013
7065	2^210928+12915	63496	Lelio R Paula	02/2013
7066	7*10^63493+39	63494	Robert Price	07/2016
7067	2^210909+135	63490	Lelio R Paula	08/2011
7069	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
7068	8*7^75098-3	63467	Lelio R Paula	09/2014
7070	17683^3882+3882^17683	63466	Hans Havermann	03/2017
7071	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
7072	2^210820-16905	63464	Enzo Doria	05/2013
7073	5^90795-36	63463	Lelio R Paula	04/2013
7074	2^210816-13197	63462	Enzo Doria	10/2012
7075	2^210750+133	63443	Lelio R Paula	08/2011
7076	291^25742+25742^291	63426	Norbert Schneider	09/2014
7077	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
7078	6^81480-139	63404	Lelio R Paula	04/2013
7079	2^210576-173	63390	Lelio R Paula	08/2011
7080	18^50497+55	63388	Lelio R Paula	05/2013
7081	2^210545+11	63381	Lelio R Paula	08/2011
7082	2^210543+63	63380	Lelio R Paula	08/2011
7083	83^33016+82	63361	Norbert Schneider	04/2015
7084	2^210464+98765331	63356	Jason Earls	12/2008
7085	7*10^63351+9	63352	Dmitry Domanov	11/2010
7086	p(13534)#/2+512	63348	Robert Price	05/2017
7087	1741^19546+19546^1741	63345	Serge Batalov	05/2014
7088	10^63336+19819	63337	Patrick De Geest	12/2013
7089	10^63336-122883	63336	Patrick De Geest	12/2013
7090	(19^49523-2^49523)/17	63327	Robert Price	09/2013
7091	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
7092	31191!2+256	63316	Robert Price	01/2015
7093	16458^7031+7031^16458	63315	Hans Havermann	01/2017
7094	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
7095	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
7096	2^210217+1299	63282	Lelio R Paula	09/2011
7097	(2^210221-3)/269	63281	Lelio R Paula	04/2012
7098	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
7099	96^31913-95	63261	Norbert Schneider	04/2016
7100	3^132572+280	63253	Lelio R Paula	04/2013
7101	3^132570-2^(132570-1)	63252	Robert Price	01/2016
7102	11^60734-4920	63248	Enzo Doria	01/2013
7104	2^210061+21	63235	Donovan Johnson	06/2006
7103	18^50375+95	63235	Lelio R Paula	05/2013
7105	85^32773-2	63233	Lelio R Paula	08/2013
7106	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
7107	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
7108	3*2^210022+5	63224	Lelio R Paula	04/2014
7109	15^53756+32	63222	Lelio R Paula	05/2013
7110	17^51380+22	63221	Lelio R Paula	05/2013
7111	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
7112	43^38700+42	63216	Norbert Schneider	06/2014
7113	5^90431-96	63209	Lelio R Paula	04/2013
7114	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
7115	(43*10^63200+83)/9	63201	Robert Price	08/2017
7116	2^209914-16005	63191	Enzo Doria	04/2013
7117	3*6^81190-5	63179	Lelio R Paula	09/2014
7118	2^209820+4257	63163	Lelio R Paula	10/2011
7120	99^31648+2	63158	Lelio R Paula	05/2013
7119	16976^5253+5253^16976	63158	Hans Havermann	01/2017
7121	2^209790+67	63154	Lelio R Paula	08/2011
7122	2^209759+90195	63144	Lelio R Paula	02/2013
7123	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
7124	2^209707+513	63129	Lelio R Paula	10/2011
7125	(3^132314-8)/17	63129	Lelio R Paula	04/2012
7126	(2*10^63117+7)/9	63117	Erik Branger	03/2011
7127	9*2^209654-7	63114	Lelio R Paula	04/2014
7128	11^60598-14	63107	Lelio R Paula	05/2013
7129	15103^15078+15078^15103	63106	Hans Havermann	01/2017
7130	15346^12941+12941^15346	63103	Hans Havermann	01/2017
7131	3^132253+76	63101	Lelio R Paula	04/2013
7132	17549^3936+3936^17549	63090	Hans Havermann	01/2017
7133	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
7134	(331^25033-1)/330	63077	Eric Chen	09/2017
7136	20^48480+31	63074	Lelio R Paula	06/2013
7135	(26*10^63073-23)/3	63074	Robert Price	08/2016
7137	2^209499+76253	63066	Enzo Doria	04/2016
7138	11^60546-11340	63053	Enzo Doria	12/2012
7139	2^209426+57889	63044	Yves Minet	02/2010
7140	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
7141	5^90189+54	63040	Lelio R Paula	04/2013
7142	(22*10^63034-73)/3	63035	Robert Price	09/2017
7143	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
7144	V(301486)	63007	Henri Lifchitz	05/2003
7145	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
7146	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
7147	6^80946-5^(80946-1)	62989	Robert Price	05/2016
7148	467^23596+23596^467	62986	Norbert Schneider	08/2016
7149	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
7150	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
7151	1456^19909+19909^1456	62976	Serge Batalov	05/2014
7153	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
7152	35^40772-1466	62955	Enzo Doria	03/2013
7154	5^90064-13706	62953	Enzo Doria	02/2013
7155	(13*10^62914+401)/9	62915	Robert Price	10/2017
7156	2^208993+107	62914	Lelio R Paula	08/2011
7157	2^208993+77	62914	Lelio R Paula	08/2011
7158	189^27636-2	62913	Lelio R Paula	10/2017
7159	(2^208948-7)/261	62898	Lelio R Paula	03/2012
7160	(151*10^62879-1)/3	62881	Robert Price	04/2017
7161	15^53464-82	62879	Lelio R Paula	05/2013
7162	2^208843-112921	62869	Enzo Doria	06/2014
7163	2^208779+81	62849	Henri Lifchitz	01/2007
7164	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
7165	(73*10^62824+17)/9	62825	Robert Price	10/2015
7166	3^131670-82	62823	Lelio R Paula	04/2013
7167	19^49128-90	62823	Lelio R Paula	05/2013
7168	11^60314-4410	62811	Enzo Doria	01/2013
7169	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
7170	2^208594+93	62794	Donovan Johnson	06/2008
7171	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
7172	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
7173	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
7174	10^62750+57	62751	Robert Price	01/2011
7175	10^62750-267429	62750	Patrick De Geest	01/2013
7176	2^208427-69	62743	Lelio R Paula	08/2011
7177	2^208421-111775	62741	Enzo Doria	05/2014
7178	2^208404-112079	62736	Enzo Doria	06/2014
7179	2^208343-2221	62718	Yves Minet	08/2013
7180	2^208335+513	62716	Lelio R Paula	10/2011
7182	(2^208328+47)/3	62713	Lelio R Paula	03/2012
7181	11^60220-2040	62713	Enzo Doria	12/2012
7183	2^208292+81	62703	Henri Lifchitz	10/2005
7184	15013^15012-15012	62698	Henri Lifchitz	10/2014
7185	2^208271-112747	62696	Enzo Doria	06/2014
7186	11^60202-4380	62694	Enzo Doria	01/2013
7187	(3^131403-4)/157	62693	Lelio R Paula	04/2012
7188	2^208127-126667	62653	Paul Bourdelais	01/2012
7189	71^33843+2	62653	Lelio R Paula	05/2013
7190	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
7191	2^208019+119	62620	Lelio R Paula	08/2011
7192	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
7193	11^60126-11370	62615	Enzo Doria	12/2012
7194	2^207976-2489	62608	Yves Minet	07/2014
7195	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7196	4*21^47335+205	62588	Curtis Bright	05/2015
7197	15^53210+8	62580	Lelio R Paula	05/2013
7198	2^207865+29	62574	Henri Lifchitz	08/2005
7199	15^53199-38	62567	Lelio R Paula	05/2013
7200	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
7201	2^207782+58905	62549	Lelio R Paula	10/2011
7202	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
7203	(2^207711+5)/13	62527	Lelio R Paula	03/2012
7204	(268*10^62523-1)/3	62525	Robert Price	10/2017
7205	10^62523+63	62524	Robert Price	01/2011
7206	10^62523-292373	62523	Patrick De Geest	01/2013
7207	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
7208	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
7209	2^207626-112157	62502	Enzo Doria	06/2014
7210	3^130987+52	62497	Lelio R Paula	04/2013
7211	8*6^80299-7	62486	Lelio R Paula	09/2014
7212	11^59997-2670	62481	Enzo Doria	12/2012
7213	93^31740+2	62480	Lelio R Paula	05/2013
7214	(10^62451+119)/3	62451	Serge Batalov	12/2014
7215	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
7216	2^207364+115	62423	Lelio R Paula	08/2011
7217	3^130815-46	62415	Lelio R Paula	04/2013
7218	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
7219	20^47968-9483	62408	Enzo Doria	03/2013
7220	(10^62402+101)/3	62402	Robert Price	04/2016
7221	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7222	(79*10^62387-61)/9	62388	Robert Price	10/2015
7223	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7224	6^80160-13	62377	Lelio R Paula	04/2013
7225	(7*10^62362+53)/3	62363	Robert Price	10/2017
7226	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7227	(17*10^62328-11)/3	62329	Robert Price	07/2015
7228	2^207023+11715	62321	Lelio R Paula	09/2011
7229	(265*10^62298+11)/3	62300	Robert Price	03/2017
7230	2^206947-69	62298	Lelio R Paula	08/2011
7231	2^206938+29835	62295	Lelio R Paula	02/2013
7232	2^206911-726877	62287	Paul Bourdelais	03/2013
7233	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7234	2^206892-112817	62281	Enzo Doria	06/2014
7235	(7*10^62278+113)/3	62279	Robert Price	10/2017
7236	3^130523+46	62276	Lelio R Paula	04/2013
7237	2^206872-113453	62275	Enzo Doria	07/2014
7238	2^206840-93	62266	Lelio R Paula	08/2011
7239	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7240	96^31406+95	62256	Norbert Schneider	03/2016
7241	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7242	2^206765-941683	62243	Paul Bourdelais	11/2012
7243	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7244	2^206755-1579	62240	Yves Minet	03/2013
7245	11^59764-5820	62238	Enzo Doria	01/2013
7246	5*10^62233+3	62234	Dmitry Domanov	11/2010
7247	8*3^130421+7	62228	Lelio R Paula	04/2014
7248	19^48661+10	62226	Lelio R Paula	05/2013
7250	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
7249	2^206705-112635	62225	Enzo Doria	06/2014

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Probable Primes Top 10000

(183432 PRPs in the top)