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 ?
7751	15346^12941+12941^15346	63103	Hans Havermann	01/2017
7752	3^132253+76	63101	Lelio R Paula	04/2013
7753	(56*10^63100+403)/9	63101	Robert Price	10/2017
7754	17549^3936+3936^17549	63090	Hans Havermann	01/2017
7755	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
7756	(331^25033-1)/330	63077	Eric Chen	09/2017
7758	20^48480+31	63074	Lelio R Paula	06/2013
7757	(26*10^63073-23)/3	63074	Robert Price	08/2016
7759	2^209499+76253	63066	Enzo Doria	04/2016
7760	11^60546-11340	63053	Enzo Doria	12/2012
7761	2^209426+57889	63044	Yves Minet	02/2010
7762	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
7763	5^90189+54	63040	Lelio R Paula	04/2013
7764	(22*10^63034-73)/3	63035	Robert Price	09/2017
7765	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
7766	V(301486)	63007	Henri Lifchitz	05/2003
7767	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
7768	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
7769	6^80946-5^(80946-1)	62989	Robert Price	05/2016
7770	467^23596+23596^467	62986	Norbert Schneider	08/2016
7771	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
7772	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
7773	1456^19909+19909^1456	62976	Serge Batalov	05/2014
7775	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
7774	35^40772-1466	62955	Enzo Doria	03/2013
7776	5^90064-13706	62953	Enzo Doria	02/2013
7777	(22*10^62926+257)/9	62927	Robert Price	11/2017
7778	(13*10^62914+401)/9	62915	Robert Price	10/2017
7779	2^208993+107	62914	Lelio R Paula	08/2011
7780	2^208993+77	62914	Lelio R Paula	08/2011
7781	189^27636-2	62913	Lelio R Paula	10/2017
7782	(2^208948-7)/261	62898	Lelio R Paula	03/2012
7783	(151*10^62879-1)/3	62881	Robert Price	04/2017
7784	15^53464-82	62879	Lelio R Paula	05/2013
7785	2^208843-112921	62869	Enzo Doria	06/2014
7786	2^208779+81	62849	Henri Lifchitz	01/2007
7787	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
7788	(73*10^62824+17)/9	62825	Robert Price	10/2015
7789	3^131670-82	62823	Lelio R Paula	04/2013
7790	19^49128-90	62823	Lelio R Paula	05/2013
7791	11^60314-4410	62811	Enzo Doria	01/2013
7792	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
7793	2^208594+93	62794	Donovan Johnson	06/2008
7794	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
7795	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
7797	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
7796	10^62750+57	62751	Robert Price	01/2011
7798	10^62750-267429	62750	Patrick De Geest	01/2013
7799	2^208427-69	62743	Lelio R Paula	08/2011
7800	2^208421-111775	62741	Enzo Doria	05/2014
7801	2^208404-112079	62736	Enzo Doria	06/2014
7802	2^208343-2221	62718	Yves Minet	08/2013
7803	2^208335+513	62716	Lelio R Paula	10/2011
7805	(2^208328+47)/3	62713	Lelio R Paula	03/2012
7804	11^60220-2040	62713	Enzo Doria	12/2012
7806	2^208292+81	62703	Henri Lifchitz	10/2005
7807	15013^15012-15012	62698	Henri Lifchitz	10/2014
7808	2^208271-112747	62696	Enzo Doria	06/2014
7809	11^60202-4380	62694	Enzo Doria	01/2013
7810	(3^131403-4)/157	62693	Lelio R Paula	04/2012
7811	2^208127-126667	62653	Paul Bourdelais	01/2012
7812	71^33843+2	62653	Lelio R Paula	05/2013
7813	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
7814	2^208019+119	62620	Lelio R Paula	08/2011
7815	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
7816	11^60126-11370	62615	Enzo Doria	12/2012
7817	2^207976-2489	62608	Yves Minet	07/2014
7818	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7819	4*21^47335+205	62588	Curtis Bright	05/2015
7820	15^53210+8	62580	Lelio R Paula	05/2013
7821	2^207865+29	62574	Henri Lifchitz	08/2005
7822	15^53199-38	62567	Lelio R Paula	05/2013
7823	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
7824	2^207782+58905	62549	Lelio R Paula	10/2011
7825	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
7826	(2^207711+5)/13	62527	Lelio R Paula	03/2012
7827	(268*10^62523-1)/3	62525	Robert Price	10/2017
7828	10^62523+63	62524	Robert Price	01/2011
7829	10^62523-292373	62523	Patrick De Geest	01/2013
7831	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
7830	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
7832	2^207626-112157	62502	Enzo Doria	06/2014
7833	3^130987+52	62497	Lelio R Paula	04/2013
7834	8*6^80299-7	62486	Lelio R Paula	09/2014
7835	11^59997-2670	62481	Enzo Doria	12/2012
7836	93^31740+2	62480	Lelio R Paula	05/2013
7837	(10^62451+119)/3	62451	Serge Batalov	12/2014
7838	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
7839	2^207364+115	62423	Lelio R Paula	08/2011
7840	3^130815-46	62415	Lelio R Paula	04/2013
7841	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
7842	20^47968-9483	62408	Enzo Doria	03/2013
7843	(10^62402+101)/3	62402	Robert Price	04/2016
7844	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7845	(79*10^62387-61)/9	62388	Robert Price	10/2015
7846	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7847	6^80160-13	62377	Lelio R Paula	04/2013
7848	(7*10^62362+53)/3	62363	Robert Price	10/2017
7849	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7850	(17*10^62328-11)/3	62329	Robert Price	07/2015
7851	2^207023+11715	62321	Lelio R Paula	09/2011
7852	(265*10^62298+11)/3	62300	Robert Price	03/2017
7853	2^206947-69	62298	Lelio R Paula	08/2011
7854	2^206938+29835	62295	Lelio R Paula	02/2013
7855	2^206911-726877	62287	Paul Bourdelais	03/2013
7856	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7857	2^206892-112817	62281	Enzo Doria	06/2014
7858	(7*10^62278+113)/3	62279	Robert Price	10/2017
7859	3^130523+46	62276	Lelio R Paula	04/2013
7860	2^206872-113453	62275	Enzo Doria	07/2014
7861	2^206840-93	62266	Lelio R Paula	08/2011
7862	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7863	96^31406+95	62256	Norbert Schneider	03/2016
7864	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7865	2^206765-941683	62243	Paul Bourdelais	11/2012
7866	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7867	2^206755-1579	62240	Yves Minet	03/2013
7868	11^59764-5820	62238	Enzo Doria	01/2013
7869	5*10^62233+3	62234	Dmitry Domanov	11/2010
7870	8*3^130421+7	62228	Lelio R Paula	04/2014
7871	19^48661+10	62226	Lelio R Paula	05/2013
7872	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
7873	2^206705-112635	62225	Enzo Doria	06/2014
7874	3^130403+8680	62219	Lelio R Paula	04/2013
7875	11^59740-7110	62213	Enzo Doria	01/2013
7877	2^206596-167	62192	Lelio R Paula	08/2011
7876	2^206597+18915	62192	Lelio R Paula	02/2013
7878	6^79918+137	62189	Lelio R Paula	04/2013
7879	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
7880	2^206574+613	62185	Jason Earls	04/2008
7881	3^130328+80	62183	Lelio R Paula	04/2013
7882	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
7883	2^206550+76819	62178	Enzo Doria	05/2016
7884	11^59703-24	62175	Lelio R Paula	05/2013
7885	2^206524+75781	62170	Enzo Doria	04/2016
7886	2^206506+427	62165	Henri Lifchitz	01/2005
7887	2^206465+7695	62153	Lelio R Paula	02/2013
7888	2^206464-1649	62152	Yves Minet	03/2013
7889	5^88917+56	62151	Lelio R Paula	04/2013
7890	2^206444-111569	62146	Enzo Doria	05/2014
7891	5^88908-42	62145	Lelio R Paula	04/2013
7892	18^49495-29	62130	Lelio R Paula	05/2013
7893	3*6^79842-5	62130	Lelio R Paula	09/2014
7894	7*10^62127-17	62128	Robert Price	01/2017
7895	2^206373+8415	62125	Lelio R Paula	02/2013
7896	20^47745-9583	62118	Enzo Doria	03/2013
7897	41^38516-2	62118	Lelio R Paula	08/2013
7898	2^206332-58695	62113	Lelio R Paula	09/2011
7899	11^59639-1260	62108	Enzo Doria	11/2012
7900	2^206232-15893	62083	Enzo Doria	04/2013
7901	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
7902	2^206206+75799	62075	Enzo Doria	04/2016
7903	(74*10^62072+43)/9	62073	Robert Price	10/2015
7904	2^206194-185	62071	Lelio R Paula	08/2011
7905	6^79757-103	62064	Lelio R Paula	04/2013
7906	p(13285)#/2-64	62063	Robert Price	04/2017
7907	(29*10^62030-41)/3	62031	Robert Price	07/2016
7908	20^47675-81	62027	Lelio R Paula	06/2013
7909	3^129972+98	62013	Lelio R Paula	04/2013
7910	2^205962+3	62001	Donovan Johnson	02/2006
7911	2^205933-205933^2	61993	Henri Lifchitz	05/2005
7912	(68*10^61991+7)/3	61993	Robert Price	03/2016
7913	20^47641-663	61983	Enzo Doria	03/2013
7914	3^129861+2660	61960	Lelio R Paula	04/2013
7915	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
7916	18^49354-97	61953	Lelio R Paula	05/2013
7917	(209*10^61947-17)/3	61949	Robert Price	05/2017
7919	14*10^61937+1089	61939	Jens K. Andersen	11/2007
7918	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
7920	20^47600+63	61930	Lelio R Paula	06/2013
7921	(16384!+1185)/(3579*10705361)	61926	Makoto Morimoto	09/2017
7922	44117!3+243	61918	Robert Price	09/2014
7923	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
7924	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
7925	20^47575-81	61897	Lelio R Paula	06/2013
7926	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
7927	87^31909+86	61889	Norbert Schneider	10/2015
7928	2^205568+141	61883	Lelio R Paula	08/2011
7929	10^61868+58927	61869	Patrick De Geest	12/2012
7930	10^61868-39	61868	Robert Price	05/2011
7931	5^88505-88	61863	Lelio R Paula	04/2013
7932	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
7934	13^55528-98	61856	Lelio R Paula	05/2013
7933	(55^35543-1)/54	61856	Paul Bourdelais	08/2017
7935	30535!2-8	61844	Robert Price	06/2015
7936	11^59371-1200	61829	Enzo Doria	11/2012
7937	7*2^205370-5	61824	Lelio R Paula	04/2014
7938	(47*10^61821+403)/9	61822	Robert Price	04/2017
7939	2^205275+7695	61794	Lelio R Paula	02/2013
7940	2^205269+12915	61793	Lelio R Paula	02/2013
7941	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
7942	19^48309+40	61776	Lelio R Paula	05/2013
7943	(424*10^61770-1)/9	61772	Robert Price	11/2017
7944	2^205192-4079	61769	Yves Minet	06/2011
7945	2^205184+16095	61767	Lelio R Paula	09/2011
7946	20^47472-3423	61763	Enzo Doria	03/2013
7947	(17*10^61760-89)/9	61761	Robert Price	11/2017
7948	2^205149-1795	61757	Lelio R Paula	09/2011
7949	2^205110-17	61745	Lelio R Paula	08/2011
7950	(373^24007+1)/374	61737	Eric Chen	10/2017
7951	(2^205025-7)/25	61718	Lelio R Paula	03/2012
7952	27^43117-26^43117	61717	Robert Price	08/2012
7953	2^205016+37	61716	Lelio R Paula	08/2011
7954	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
7955	1263^19898+19898^1263	61712	Serge Batalov	05/2014
7956	135^28963-134	61701	Norbert Schneider	04/2015
7957	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
7958	(7*10^61696+167)/3	61696	Robert Kinser	10/2017
7959	(46*10^61693+17)/9	61694	Robert Price	06/2015
7960	((((((((((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
7961	1850^18879+18879^1850	61681	Serge Batalov	05/2014
7962	2^204891-1005	61679	Lelio R Paula	09/2011
7963	151^28306-2	61679	Lelio R Paula	10/2017
7964	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
7965	15937^7408+7408^15937	61672	Hans Havermann	02/2017
7966	5^88216-12	61661	Lelio R Paula	04/2013
7967	18185^2454+2454^18185	61645	Hans Havermann	01/2017
7969	2^204767-15865	61642	Enzo Doria	04/2013
7968	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
7970	7*2^204751-9	61638	Lelio R Paula	04/2014
7972	4*10^61625+21	61626	Robert Price	08/2016
7971	15369^10226+10226^15369	61626	Hans Havermann	02/2017
7973	2^204702-18125	61622	Enzo Doria	05/2013
7974	5*3^129146+8	61620	Lelio R Paula	04/2014
7975	2^204673+129	61613	Lelio R Paula	08/2011
7976	18^49079+97	61608	Lelio R Paula	05/2013
7977	106^30416+105	61602	Norbert Schneider	12/2016
7978	2^204590-33	61588	Lelio R Paula	08/2011
7979	2^204586-111975	61587	Enzo Doria	06/2014
7980	2^204580-16077	61585	Enzo Doria	04/2013
7981	2^204574-16041	61583	Enzo Doria	04/2013
7982	15^52358+56	61578	Lelio R Paula	05/2013
7983	(28*10^61574+11)/3	61575	Robert Price	11/2015
7984	2^204516-17493	61566	Enzo Doria	05/2013
7985	4*5^88076-3	61564	Lelio R Paula	09/2014
7986	11^59110-2520	61557	Enzo Doria	12/2012
7987	2^204477-58695	61554	Lelio R Paula	09/2011
7988	12^57026-73	61542	Lelio R Paula	05/2013
7989	(257^25537+1)/258	61541	Richard Fischer	04/2018
7990	17^50013+90	61539	Lelio R Paula	05/2013
7991	56^35201-55^35201	61538	Robert Price	10/2013
7992	8*7^72810+5	61533	Lelio R Paula	09/2014
7994	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
7993	43867!3-6561	61531	Robert Price	11/2015
7997	10^61525+9^(61525-1)	61526	Robert Price	03/2016
7995	10^61525+62257	61526	Patrick De Geest	12/2016
7996	14821^14166+14166^14821	61526	Hans Havermann	01/2017
7999	12^57010-85	61525	Lelio R Paula	05/2013
7998	10^61525-213579	61525	Patrick De Geest	12/2016
8000	2^204332-99	61511	Lelio R Paula	08/2011

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Probable Primes Top 10000

(224660 PRPs in the top)