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 (> 50000)	Who ?	When ?
7751	65^37636+16	68231	Lelio R Paula	01/2016
7752	5^97615-4^(97615+1)	68230	Robert Price	04/2016
7753	12^63200-43	68205	Lelio R Paula	07/2013
7754	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
7755	3^142925+8680	68193	Lelio R Paula	06/2013
7756	3*2^226512-7	68188	Lelio R Paula	04/2014
7757	14^59484+57	68177	Lelio R Paula	08/2013
7758	11^65438-2190	68147	Enzo Doria	12/2012
7759	91^34784-2	68144	Lelio R Paula	09/2013
7760	16589^12810+12810^16589	68141	Hans Havermann	10/2019
7761	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
7762	(22*10^68133-37)/3	68134	Robert Price	05/2017
7763	5^97476+36	68133	Lelio R Paula	06/2013
7764	3*5^97474-2	68132	Lelio R Paula	09/2014
7765	12^63130+49	68129	Lelio R Paula	07/2013
7766	2^226281+5385	68118	Lelio R Paula	04/2012
7767	2^226257-3049	68111	Yves Minet	10/2014
7768	(28*10^68107-43)/3	68108	Robert Price	04/2016
7769	2^226243-2587	68106	Yves Minet	07/2014
7770	20^52346-11	68104	Lelio R Paula	09/2013
7771	2^226205-99	68095	Lelio R Paula	02/2012
7772	2^226187-49	68090	Lelio R Paula	02/2012
7773	3^142708+76	68090	Lelio R Paula	06/2013
7774	7*10^68088-89	68089	Robert Price	01/2017
7775	18562^4653+4653^18562	68081	Hans Havermann	09/2019
7776	2^226154+71839	68080	Enzo Doria	04/2016
7777	(10^68078+59)/3	68078	Serge Batalov	12/2014
7779	14^59387+69	68066	Lelio R Paula	08/2013
7778	2^226108-113429	68066	Enzo Doria	07/2014
7780	(62*10^68059-197)/9	68060	Robert Price	10/2017
7781	(24^49307-1)/23	68053	Robert Price	04/2012
7782	15^57859-28	68048	Lelio R Paula	08/2013
7783	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
7784	2^226015-111361	68038	Enzo Doria	05/2014
7785	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
7786	4*10^68020+91	68021	Robert Price	11/2017
7787	16181^15948+15948^16181	68004	Hans Havermann	09/2019
7788	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
7789	2^225878-1017	67997	Lelio R Paula	04/2012
7790	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
7791	3*2^225865+5	67993	Lelio R Paula	04/2014
7792	11^65284-5820	67987	Enzo Doria	01/2013
7793	19^53166+70	67987	Lelio R Paula	08/2013
7794	2^225837+75407	67984	Enzo Doria	04/2016
7795	3^142464-112654	67973	Enzo Doria	06/2014
7796	16851^10802+10802^16851	67969	Hans Havermann	09/2019
7797	2^225777+95	67966	Lelio R Paula	02/2012
7798	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
7799	2^225609-18445	67916	Enzo Doria	05/2013
7800	2^225542-177	67895	Lelio R Paula	02/2012
7801	2^225536-29	67894	Henri Lifchitz	05/2005
7802	11^65190-3390	67889	Enzo Doria	12/2012
7803	16971^9986+9986^16971	67874	Hans Havermann	09/2019
7804	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7805	11^65168-4830	67866	Enzo Doria	01/2013
7806	10^67863+58627	67864	Patrick De Geest	01/2016
7807	16258^14933+14933^16258	67864	Hans Havermann	09/2019
7808	10^67863-11	67863	Robert Price	05/2011
7809	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7810	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7811	9*6^87164-7	67828	Lelio R Paula	09/2014
7812	131^32034+130	67825	Norbert Schneider	03/2015
7813	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7814	17761^6586+6586^17761	67823	Hans Havermann	09/2019
7815	(134*10^67816+7)/3	67818	Robert Price	02/2017
7816	2^225261+855	67811	Lelio R Paula	04/2012
7817	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7818	(4*10^67796+23)/9	67796	Robert Price	11/2014
7819	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7820	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7821	(4*10^67784+149)/9	67784	Robert Price	03/2017
7822	8177^17322+17322^8177	67774	Norbert Schneider	03/2019
7823	2^225120+151	67768	Lelio R Paula	02/2012
7824	(44^41233+1)/45	67763	Robert Price	11/2013
7825	89933!6-16	67747	Robert Price	08/2018
7826	8*10^67742+9	67743	Dmitry Domanov	11/2010
7827	2^224977+1089	67725	Lelio R Paula	04/2012
7828	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7829	11^65011-5970	67702	Enzo Doria	01/2013
7830	88*10^67691+7	67693	Robert Price	11/2016
7831	11^65000-7140	67691	Enzo Doria	01/2013
7832	2^224841+59	67684	Lelio R Paula	02/2012
7833	33129!2+2^33129	67684	Robert Price	09/2015
7834	2^224827+8415	67680	Lelio R Paula	02/2013
7835	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7836	2^224815-49789	67677	Henri Lifchitz	04/2005
7837	7257^17528+17528^7257	67672	Norbert Schneider	08/2019
7838	(43*10^67664+11)/9	67665	Robert Price	06/2015
7839	(292*10^67659-1)/3	67661	Robert Price	01/2017
7840	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7841	2^224744+577294575	67655	Lelio R Paula	02/2016
7842	((1+sqrt(7)+sqrt(6))^45863-1)((1+sqrt(7)-sqrt(6))^45863-1)((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(7	67653	Mike Oakes	05/2009
7843	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7844	2^224700+1915	67642	Lelio R Paula	04/2012
7845	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7846	2^224658-93	67629	Lelio R Paula	02/2012
7847	2^224624-13077	67619	Enzo Doria	10/2012
7848	18^53860-3319	67609	Enzo Doria	03/2013
7849	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7850	89762!6-3	67606	Robert Price	08/2018
7851	2^224578-111041	67605	Enzo Doria	05/2014
7852	2^224569-113233	67603	Enzo Doria	07/2014
7853	2^224562-113171	67600	Enzo Doria	07/2014
7854	2^224556-113129	67599	Enzo Doria	07/2014
7855	6*7^79980-5	67592	Lelio R Paula	09/2014
7856	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7857	10^67579+164779	67580	Patrick De Geest	07/2017
7859	(52*10^67578-61)/9	67579	Robert Price	09/2015
7858	10^67579-401	67579	Robert Price	06/2017
7860	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7861	22115^1134+1134^22115	67553	Hans Havermann	08/2019
7862	((10^33771-1)10000/9+6389)10^33771+(10^33771-1)/9	67546	Hans Havermann	05/2019
7863	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7864	(709*10^67517-7)/9	67519	Robert Price	09/2017
7865	47719!3-59049	67516	Robert Price	12/2015
7866	16356^13411+13411^16356	67509	Hans Havermann	09/2019
7867	(22^50287+1)/23	67506	Robert Price	06/2013
7868	16671^11198+11198^16671	67504	Hans Havermann	09/2019
7869	3*10^67499+67	67500	Robert Price	11/2017
7870	11^64811-5820	67494	Enzo Doria	01/2013
7871	131^31870+31870^131	67478	Serge Batalov	05/2014
7872	9*10^67468+7	67469	Dmitry Domanov	11/2010
7873	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7874	128^32001+32001^128	67433	Serge Batalov	05/2014
7875	(89*10^67431-17)/9	67432	Robert Price	11/2015
7876	2^223912-111059	67405	Enzo Doria	05/2014
7878	2^223913+73697	67405	Enzo Doria	04/2016
7877	(2*10^67405-23)/3	67405	Robert Price	09/2017
7879	(10^67404+179)/9	67404	Serge Batalov	12/2014
7880	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7881	9*7^79728-2	67379	Lelio R Paula	09/2014
7882	(28*10^67378-43)/3	67379	Robert Price	04/2016
7883	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7884	211^28988-2	67377	Lelio R Paula	09/2013
7885	4*10^67375+91	67376	Robert Price	11/2017
7886	2^223793-18069	67369	Enzo Doria	05/2013
7887	2^223777-2521	67364	Yves Minet	07/2014
7888	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
7889	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
7890	V(340138)	67336	Serge Batalov	03/2015
7891	43125^14528-106	67334	Enzo Doria	07/2012
7892	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
7893	8*10^67302-51	67303	Robert Price	10/2017
7894	17458^7153+7153^17458	67292	Hans Havermann	08/2016
7895	16366^12925+12925^16366	67288	Hans Havermann	08/2016
7896	37^42906-2	67286	Lelio R Paula	08/2013
7897	18^53592-13	67273	Lelio R Paula	08/2013
7898	V(396221)	67256	Serge Batalov	03/2015
7900	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
7899	(14*10^67235-101)/3	67236	Robert Price	04/2017
7901	53^38993-52^38993	67235	Robert Price	01/2013
7902	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
7903	2^223333+315	67230	Lelio R Paula	04/2012
7904	2^223278-111041	67214	Enzo Doria	05/2014
7905	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
7906	2^223256-45	67207	Lelio R Paula	02/2012
7907	2^223253-112111	67206	Enzo Doria	06/2014
7908	18407^4474+4474^18407	67199	Hans Havermann	08/2016
7909	47^40182+40182^47	67189	Norbert Schneider	11/2014
7910	13^60309+94	67181	Lelio R Paula	07/2013
7911	11^64503-84	67173	Lelio R Paula	07/2013
7912	3^140781+236	67170	Lelio R Paula	06/2013
7913	2^223107-865057	67162	Paul Bourdelais	03/2013
7914	2^223100-59	67160	Lelio R Paula	02/2012
7915	2^223087+71963	67156	Enzo Doria	04/2016
7917	18^53481-3779	67134	Enzo Doria	03/2013
7916	(326^26713-1)/325	67134	Eric Chen	09/2017
7918	4^111473-62573	67114	Mike Oakes	02/2011
7919	2^222943+29	67113	Henri Lifchitz	08/2005
7920	(2^222939-9)/103	67110	Lelio R Paula	04/2012
7921	2^222862-459161	67089	Enzo Doria	05/2015
7922	2^222828+8193	67078	Lelio R Paula	04/2012
7923	3^140570+2660	67069	Lelio R Paula	06/2013
7924	20731^1716+1716^20731	67055	Hans Havermann	08/2019
7925	2^222744+855	67053	Lelio R Paula	04/2012
7926	13^60189+84	67048	Lelio R Paula	07/2013
7927	2*10^67043-51	67044	Robert Price	11/2017
7928	22588^929+929^22588	67042	Hans Havermann	08/2019
7929	2^222701+577294575	67040	Lelio R Paula	02/2016
7930	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7931	(151*10^67027-7)/9	67029	Robert Price	07/2017
7932	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7933	2^222614-111041	67014	Enzo Doria	05/2014
7934	16255^13242+13242^16255	67003	Hans Havermann	08/2019
7935	16477^11650+11650^16477	67001	Hans Havermann	08/2019
7936	118^32333-117	66991	Norbert Schneider	08/2018
7937	2^222520-1907	66986	Yves Minet	03/2013
7938	(4^111231+23)/3	66968	Robert Price	02/2017
7939	16206^13549+13549^16206	66962	Hans Havermann	08/2019
7940	2^222408-111275	66952	Enzo Doria	05/2014
7941	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7942	2^222378-1005	66943	Lelio R Paula	04/2012
7943	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7944	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7945	2^222325-112255	66927	Enzo Doria	06/2014
7946	21789^1178+1178^21789	66918	Hans Havermann	08/2019
7947	20^51428+33	66910	Lelio R Paula	08/2013
7948	2^222224-18509	66897	Enzo Doria	05/2013
7949	(38*10^66896+187)/9	66897	Robert Price	11/2017
7950	2^222192-869688105	66887	Lelio R Paula	02/2016
7951	(19*10^66878-43)/3	66879	Robert Price	10/2017
7952	11^64219-64	66878	Lelio R Paula	07/2013
7953	2^222151-17295	66875	Lelio R Paula	04/2012
7954	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7955	2^222085-111031	66855	Enzo Doria	05/2014
7956	8*10^66848-13	66849	Robert Price	05/2017
7957	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7958	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7959	19^52265+52	66835	Lelio R Paula	08/2013
7960	2*10^66826-27	66827	Robert Price	02/2017
7961	4*6^85867+5	66819	Lelio R Paula	09/2014
7962	11955^16384+2	66807	Matt Stath	12/2018
7963	15^56800+8	66802	Lelio R Paula	08/2013
7964	(2^221891-2^110946+1)/5	66796		11/2006
7965	10^66793+69441	66794	Patrick De Geest	05/2013
7966	10^66793-63	66793	Robert Price	05/2011
7967	35^43256-1704	66791	Enzo Doria	03/2013
7969	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7968	88769!6-48	66786	Robert Price	08/2018
7970	7^79023-54	66783	Lelio R Paula	06/2013
7971	104^33109-103	66782	Norbert Schneider	11/2016
7972	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7973	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7975	2^221768+183	66759	Lelio R Paula	02/2012
7974	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7976	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7977	11^64097+48	66751	Lelio R Paula	07/2013
7978	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7979	(19*10^66748+413)/9	66749	Robert Price	10/2017
7980	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7981	8*6^85758-7	66734	Lelio R Paula	09/2014
7982	135^31325+2	66733	Lelio R Paula	05/2013
7983	(49*10^66729+41)/9	66730	Robert Price	07/2015
7984	(349*10^66720-7)/9	66722	Robert Price	03/2017
7985	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7986	(25*10^66714+71)/3	66715	Robert Price	01/2017
7987	11^64061-780	66713	Enzo Doria	11/2012
7988	7^78929+4	66703	Lelio R Paula	06/2013
7989	11^64048-930	66700	Enzo Doria	11/2012
7990	120^32079-119	66699	Norbert Schneider	09/2018
7991	2*7^78921+5	66697	Lelio R Paula	09/2014
7992	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7993	16330^12117+12117^16330	66682	Hans Havermann	08/2019
7994	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7995	2^221479+72953	66672	Enzo Doria	04/2016
7997	10^66666+275403	66667	Patrick De Geest	03/2010
7996	16317^12182+12182^16317	66667	Hans Havermann	08/2019
7998	10^66666-115521	66666	Patrick De Geest	03/2010
7999	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
8000	4*10^66653+21	66654	Robert Price	08/2016

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Probable Primes Top 10000

(255169 PRPs in the top)