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 ?
6751	2^213314-455	64214	Yves Minet	02/2012
6752	39^40359-38	64214	Norbert Schneider	05/2014
6753	2^213292-16085	64208	Enzo Doria	04/2013
6754	2^213274-77	64202	Lelio R Paula	08/2011
6755	19^50203+78	64198	Lelio R Paula	08/2013
6756	2^213240-112865	64192	Enzo Doria	06/2014
6757	2^213190-112391	64177	Enzo Doria	06/2014
6758	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
6759	14^55991+27	64173	Lelio R Paula	07/2013
6760	2^213158-112581	64167	Enzo Doria	06/2014
6761	2^213148+91	64164	Lelio R Paula	08/2011
6762	6^82439+125	64151	Lelio R Paula	07/2013
6763	7*2^213102+9	64151	Lelio R Paula	04/2014
6764	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
6765	610^23017+23017^610	64110	Norbert Schneider	07/2016
6766	2^212950-64875	64105	Lelio R Paula	10/2011
6767	(266*10^64102-17)/3	64104	Robert Price	06/2016
6768	p(13679)#/2+64	64097	Robert Price	03/2017
6769	19^50119+94	64090	Lelio R Paula	08/2013
6770	2^212880-147	64084	Lelio R Paula	08/2011
6771	11^61523-4590	64070	Enzo Doria	01/2013
6772	5^91663+38	64070	Lelio R Paula	05/2013
6773	5^91650+52	64061	Lelio R Paula	05/2013
6774	2^212770+69	64051	Lelio R Paula	08/2011
6775	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
6776	(2*10^64041-17)/3	64041	Robert Price	08/2014
6777	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
6778	(29*10^64027+91)/3	64028	Robert Price	03/2016
6779	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
6780	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
6781	2^212663+53	64018	Lelio R Paula	08/2011
6782	(4*10^64014+197)/3	64015	Robert Price	03/2017
6783	10^63986+63	63987	Robert Price	01/2011
6784	10^63986-31557	63986	Patrick De Geest	05/2013
6785	31487!2-2^31487	63982	Robert Price	09/2015
6786	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
6787	5^91517+98	63968	Lelio R Paula	04/2013
6788	(62*10^63954-17)/9	63955	Robert Price	09/2015
6790	5^91493-4^91493	63951	Predrag Minovic	04/2004
6789	V(364793)	63951	Serge Batalov	03/2015
6792	19^50004+58	63943	Lelio R Paula	05/2013
6791	5*6^82172-7	63943	Lelio R Paula	09/2014
6793	(56*10^63942+223)/9	63943	Robert Price	07/2016
6794	19^50000-24	63938	Lelio R Paula	05/2013
6795	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
6796	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
6798	2^212344-183	63922	Lelio R Paula	08/2011
6797	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
6799	10^63916+79	63917	Robert Price	01/2011
6800	10^63916-76823	63916	Patrick De Geest	05/2013
6801	2^212295-25	63908	Lelio R Paula	08/2011
6802	2^212285-2383	63905	Yves Minet	10/2013
6803	267^26336+26336^267	63905	Norbert Schneider	09/2014
6804	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
6806	19^49962+60	63890	Lelio R Paula	05/2013
6805	3^133906-113056	63890	Enzo Doria	07/2014
6807	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
6808	3*6^82092+5	63881	Lelio R Paula	09/2014
6809	15441^13706+13706^15441	63879	Hans Havermann	02/2017
6810	2^212154-776351	63865	Paul Bourdelais	03/2013
6811	35^41359+2	63862	Lelio R Paula	05/2013
6812	(61*10^63857-43)/9	63858	Robert Price	09/2015
6813	(2^212131-3)/485	63856	Lelio R Paula	04/2012
6814	2^212112-459995	63853	Enzo Doria	06/2015
6815	15^54290+58	63850	Lelio R Paula	05/2013
6816	3*2^212097-7	63849	Lelio R Paula	04/2014
6817	55^36683-54	63842	Norbert Schneider	08/2014
6818	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
6819	(3^133805-7)/172	63839	Lelio R Paula	04/2012
6820	2^212049+149	63834	Lelio R Paula	08/2011
6821	5^91318-18	63829	Lelio R Paula	04/2013
6822	18468^2857+2857^18468	63824	Hans Havermann	03/2017
6823	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
6824	2^211961+12915	63807	Lelio R Paula	02/2013
6825	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
6826	747^22198+22198^747	63782	Norbert Schneider	07/2016
6827	2^211800-17169	63759	Enzo Doria	05/2013
6828	(85*10^63757-1)/3	63759	Robert Price	07/2017
6829	(14*10^63747-11)/3	63748	Erik Branger	09/2014
6830	91*19^49848+6	63746	Curtis Bright	05/2015
6831	18855^2402+2402^18855	63741	Hans Havermann	03/2017
6832	(142*10^63734-7)/9	63736	Robert Price	02/2017
6833	2^211699-111	63728	Lelio R Paula	08/2011
6834	11^61192-5550	63725	Enzo Doria	01/2013
6835	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
6836	6^81872-13	63709	Lelio R Paula	04/2013
6837	3^133522+98	63707	Lelio R Paula	05/2013
6839	2^211607-61	63701	Lelio R Paula	08/2011
6838	5^91135+8	63701	Lelio R Paula	04/2013
6840	11^61157-270	63689	Enzo Doria	07/2012
6841	10^63685+1145141919	63686	Marisa Kirisame	03/2015
6842	10^63685+103837	63686	Patrick De Geest	03/2016
6843	10^63685-130797	63685	Patrick De Geest	03/2016
6844	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
6845	2^211543+45	63681	Lelio R Paula	08/2011
6846	2^211534+43	63679	Lelio R Paula	08/2011
6847	11^61140-60	63671	Enzo Doria	07/2012
6848	2^211491-112321	63666	Enzo Doria	06/2014
6849	19085^2164+2164^19085	63654	Hans Havermann	03/2017
6850	(2^211430-5)/859	63644	Lelio R Paula	04/2012
6851	2^211401-91	63639	Lelio R Paula	08/2011
6852	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
6853	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
6854	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
6855	2^211333+15015	63618	Lelio R Paula	01/2013
6856	33^41889-32	63610	Norbert Schneider	03/2014
6857	13^57093+18	63599	Lelio R Paula	05/2013
6858	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
6859	(107*10^63576-17)/9	63578	Robert Price	02/2017
6860	23^46687-1020	63575	Enzo Doria	08/2012
6861	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
6862	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
6863	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
6865	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
6864	2*3^133227+5	63566	Lelio R Paula	04/2014
6866	2^211155+113	63564	Lelio R Paula	08/2011
6867	2^211134+345	63558	Lelio R Paula	09/2011
6868	2^211121+16385	63554	Lelio R Paula	09/2011
6869	16996^5483+5483^16996	63549	Hans Havermann	02/2017
6870	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
6871	15852^10157+10157^15852	63516	Hans Havermann	02/2017
6872	2^210948-15873	63502	Enzo Doria	04/2013
6873	7^75136+6	63498	Lelio R Paula	04/2013
6874	2^210928+12915	63496	Lelio R Paula	02/2013
6875	7*10^63493+39	63494	Robert Price	07/2016
6876	2^210909+135	63490	Lelio R Paula	08/2011
6877	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
6878	8*7^75098-3	63467	Lelio R Paula	09/2014
6879	17683^3882+3882^17683	63466	Hans Havermann	03/2017
6881	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
6880	2^210820-16905	63464	Enzo Doria	05/2013
6882	5^90795-36	63463	Lelio R Paula	04/2013
6883	2^210816-13197	63462	Enzo Doria	10/2012
6884	2^210750+133	63443	Lelio R Paula	08/2011
6885	291^25742+25742^291	63426	Norbert Schneider	09/2014
6886	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
6887	6^81480-139	63404	Lelio R Paula	04/2013
6888	2^210576-173	63390	Lelio R Paula	08/2011
6889	18^50497+55	63388	Lelio R Paula	05/2013
6890	2^210545+11	63381	Lelio R Paula	08/2011
6891	2^210543+63	63380	Lelio R Paula	08/2011
6892	83^33016+82	63361	Norbert Schneider	04/2015
6893	2^210464+98765331	63356	Jason Earls	12/2008
6894	7*10^63351+9	63352	Dmitry Domanov	11/2010
6895	p(13534)#/2+512	63348	Robert Price	05/2017
6896	1741^19546+19546^1741	63345	Serge Batalov	05/2014
6897	10^63336+19819	63337	Patrick De Geest	12/2013
6898	10^63336-122883	63336	Patrick De Geest	12/2013
6899	(19^49523-2^49523)/17	63327	Robert Price	09/2013
6900	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
6901	31191!2+256	63316	Robert Price	01/2015
6902	16458^7031+7031^16458	63315	Hans Havermann	01/2017
6903	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
6904	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
6905	2^210217+1299	63282	Lelio R Paula	09/2011
6906	(2^210221-3)/269	63281	Lelio R Paula	04/2012
6907	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
6908	96^31913-95	63261	Norbert Schneider	04/2016
6909	3^132572+280	63253	Lelio R Paula	04/2013
6910	3^132570-2^(132570-1)	63252	Robert Price	01/2016
6911	11^60734-4920	63248	Enzo Doria	01/2013
6913	2^210061+21	63235	Donovan Johnson	06/2006
6912	18^50375+95	63235	Lelio R Paula	05/2013
6914	85^32773-2	63233	Lelio R Paula	08/2013
6915	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
6916	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
6917	3*2^210022+5	63224	Lelio R Paula	04/2014
6918	15^53756+32	63222	Lelio R Paula	05/2013
6920	17^51380+22	63221	Lelio R Paula	05/2013
6919	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
6921	43^38700+42	63216	Norbert Schneider	06/2014
6922	5^90431-96	63209	Lelio R Paula	04/2013
6923	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
6924	2^209914-16005	63191	Enzo Doria	04/2013
6925	3*6^81190-5	63179	Lelio R Paula	09/2014
6926	2^209820+4257	63163	Lelio R Paula	10/2011
6928	99^31648+2	63158	Lelio R Paula	05/2013
6927	16976^5253+5253^16976	63158	Hans Havermann	01/2017
6929	2^209790+67	63154	Lelio R Paula	08/2011
6930	2^209759+90195	63144	Lelio R Paula	02/2013
6931	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
6932	2^209707+513	63129	Lelio R Paula	10/2011
6933	(3^132314-8)/17	63129	Lelio R Paula	04/2012
6934	(2*10^63117+7)/9	63117	Erik Branger	03/2011
6935	9*2^209654-7	63114	Lelio R Paula	04/2014
6936	11^60598-14	63107	Lelio R Paula	05/2013
6937	15103^15078+15078^15103	63106	Hans Havermann	01/2017
6938	15346^12941+12941^15346	63103	Hans Havermann	01/2017
6939	3^132253+76	63101	Lelio R Paula	04/2013
6940	17549^3936+3936^17549	63090	Hans Havermann	01/2017
6941	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
6943	20^48480+31	63074	Lelio R Paula	06/2013
6942	(26*10^63073-23)/3	63074	Robert Price	08/2016
6944	2^209499+76253	63066	Enzo Doria	04/2016
6945	11^60546-11340	63053	Enzo Doria	12/2012
6946	2^209426+57889	63044	Yves Minet	02/2010
6947	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
6948	5^90189+54	63040	Lelio R Paula	04/2013
6949	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
6950	V(301486)	63007	Henri Lifchitz	05/2003
6951	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
6952	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
6953	6^80946-5^(80946-1)	62989	Robert Price	05/2016
6954	467^23596+23596^467	62986	Norbert Schneider	08/2016
6955	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
6956	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
6957	1456^19909+19909^1456	62976	Serge Batalov	05/2014
6959	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
6958	35^40772-1466	62955	Enzo Doria	03/2013
6960	5^90064-13706	62953	Enzo Doria	02/2013
6961	2^208993+107	62914	Lelio R Paula	08/2011
6962	2^208993+77	62914	Lelio R Paula	08/2011
6963	(2^208948-7)/261	62898	Lelio R Paula	03/2012
6964	(151*10^62879-1)/3	62881	Robert Price	04/2017
6965	15^53464-82	62879	Lelio R Paula	05/2013
6966	2^208843-112921	62869	Enzo Doria	06/2014
6967	2^208779+81	62849	Henri Lifchitz	01/2007
6968	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
6969	(73*10^62824+17)/9	62825	Robert Price	10/2015
6970	3^131670-82	62823	Lelio R Paula	04/2013
6971	19^49128-90	62823	Lelio R Paula	05/2013
6972	11^60314-4410	62811	Enzo Doria	01/2013
6973	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
6974	2^208594+93	62794	Donovan Johnson	06/2008
6975	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
6976	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
6977	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
6978	10^62750+57	62751	Robert Price	01/2011
6979	10^62750-267429	62750	Patrick De Geest	01/2013
6980	2^208427-69	62743	Lelio R Paula	08/2011
6981	2^208421-111775	62741	Enzo Doria	05/2014
6982	2^208404-112079	62736	Enzo Doria	06/2014
6983	2^208343-2221	62718	Yves Minet	08/2013
6984	2^208335+513	62716	Lelio R Paula	10/2011
6986	(2^208328+47)/3	62713	Lelio R Paula	03/2012
6985	11^60220-2040	62713	Enzo Doria	12/2012
6987	2^208292+81	62703	Henri Lifchitz	10/2005
6988	15013^15012-15012	62698	Henri Lifchitz	10/2014
6989	2^208271-112747	62696	Enzo Doria	06/2014
6990	11^60202-4380	62694	Enzo Doria	01/2013
6991	(3^131403-4)/157	62693	Lelio R Paula	04/2012
6992	2^208127-126667	62653	Paul Bourdelais	01/2012
6993	71^33843+2	62653	Lelio R Paula	05/2013
6994	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
6996	2^208019+119	62620	Lelio R Paula	08/2011
6995	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
6997	11^60126-11370	62615	Enzo Doria	12/2012
6998	2^207976-2489	62608	Yves Minet	07/2014
6999	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7000	4*21^47335+205	62588	Curtis Bright	05/2015

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Probable Primes Top 10000

(177649 PRPs in the top)