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	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
6752	11^65011-5970	67702	Enzo Doria	01/2013
6753	88*10^67691+7	67693	Robert Price	11/2016
6754	11^65000-7140	67691	Enzo Doria	01/2013
6755	2^224841+59	67684	Lelio R Paula	02/2012
6756	33129!2+2^33129	67684	Robert Price	09/2015
6757	2^224827+8415	67680	Lelio R Paula	02/2013
6758	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
6759	2^224815-49789	67677	Henri Lifchitz	04/2005
6760	(43*10^67664+11)/9	67665	Robert Price	06/2015
6761	(292*10^67659-1)/3	67661	Robert Price	01/2017
6762	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
6763	2^224744+577294575	67655	Lelio R Paula	02/2016
6764	((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
6765	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
6766	2^224700+1915	67642	Lelio R Paula	04/2012
6767	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
6768	2^224658-93	67629	Lelio R Paula	02/2012
6769	2^224624-13077	67619	Enzo Doria	10/2012
6770	18^53860-3319	67609	Enzo Doria	03/2013
6771	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
6772	2^224578-111041	67605	Enzo Doria	05/2014
6773	2^224569-113233	67603	Enzo Doria	07/2014
6774	2^224562-113171	67600	Enzo Doria	07/2014
6775	2^224556-113129	67599	Enzo Doria	07/2014
6776	6*7^79980-5	67592	Lelio R Paula	09/2014
6777	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
6778	10^67579+164779	67580	Patrick De Geest	07/2017
6780	(52*10^67578-61)/9	67579	Robert Price	09/2015
6779	10^67579-401	67579	Robert Price	06/2017
6781	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
6782	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
6783	(709*10^67517-7)/9	67519	Robert Price	09/2017
6784	47719!3-59049	67516	Robert Price	12/2015
6785	(22^50287+1)/23	67506	Robert Price	06/2013
6786	3*10^67499+67	67500	Robert Price	11/2017
6787	11^64811-5820	67494	Enzo Doria	01/2013
6788	131^31870+31870^131	67478	Serge Batalov	05/2014
6789	9*10^67468+7	67469	Dmitry Domanov	11/2010
6790	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
6791	128^32001+32001^128	67433	Serge Batalov	05/2014
6792	(89*10^67431-17)/9	67432	Robert Price	11/2015
6793	2^223912-111059	67405	Enzo Doria	05/2014
6795	2^223913+73697	67405	Enzo Doria	04/2016
6794	(2*10^67405-23)/3	67405	Robert Price	09/2017
6796	(10^67404+179)/9	67404	Serge Batalov	12/2014
6797	18738^3955+3955^18738	67404	Hans Havermann	09/2016
6798	9*7^79728-2	67379	Lelio R Paula	09/2014
6799	(28*10^67378-43)/3	67379	Robert Price	04/2016
6800	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
6801	211^28988-2	67377	Lelio R Paula	09/2013
6802	4*10^67375+91	67376	Robert Price	11/2017
6803	2^223793-18069	67369	Enzo Doria	05/2013
6804	2^223777-2521	67364	Yves Minet	07/2014
6805	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
6806	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
6807	V(340138)	67336	Serge Batalov	03/2015
6808	43125^14528-106	67334	Enzo Doria	07/2012
6809	8*10^67302-51	67303	Robert Price	10/2017
6810	17458^7153+7153^17458	67292	Hans Havermann	08/2016
6811	16366^12925+12925^16366	67288	Hans Havermann	08/2016
6812	37^42906-2	67286	Lelio R Paula	08/2013
6813	18^53592-13	67273	Lelio R Paula	08/2013
6814	V(396221)	67256	Serge Batalov	03/2015
6816	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
6815	(14*10^67235-101)/3	67236	Robert Price	04/2017
6817	53^38993-52^38993	67235	Robert Price	01/2013
6818	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
6819	2^223333+315	67230	Lelio R Paula	04/2012
6820	2^223278-111041	67214	Enzo Doria	05/2014
6821	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
6822	2^223256-45	67207	Lelio R Paula	02/2012
6823	2^223253-112111	67206	Enzo Doria	06/2014
6824	18407^4474+4474^18407	67199	Hans Havermann	08/2016
6825	47^40182+40182^47	67189	Norbert Schneider	11/2014
6826	13^60309+94	67181	Lelio R Paula	07/2013
6827	11^64503-84	67173	Lelio R Paula	07/2013
6828	3^140781+236	67170	Lelio R Paula	06/2013
6829	2^223107-865057	67162	Paul Bourdelais	03/2013
6830	2^223100-59	67160	Lelio R Paula	02/2012
6831	2^223087+71963	67156	Enzo Doria	04/2016
6832	18^53481-3779	67134	Enzo Doria	03/2013
6833	(326^26713-1)/325	67134	Eric Chen	09/2017
6834	4^111473-62573	67114	Mike Oakes	02/2011
6835	2^222943+29	67113	Henri Lifchitz	08/2005
6836	(2^222939-9)/103	67110	Lelio R Paula	04/2012
6837	2^222862-459161	67089	Enzo Doria	05/2015
6838	2^222828+8193	67078	Lelio R Paula	04/2012
6839	3^140570+2660	67069	Lelio R Paula	06/2013
6840	2^222744+855	67053	Lelio R Paula	04/2012
6841	13^60189+84	67048	Lelio R Paula	07/2013
6842	2*10^67043-51	67044	Robert Price	11/2017
6843	2^222701+577294575	67040	Lelio R Paula	02/2016
6844	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
6845	(151*10^67027-7)/9	67029	Robert Price	07/2017
6846	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
6847	2^222614-111041	67014	Enzo Doria	05/2014
6848	2^222520-1907	66986	Yves Minet	03/2013
6849	(4^111231+23)/3	66968	Robert Price	02/2017
6850	2^222408-111275	66952	Enzo Doria	05/2014
6851	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
6852	2^222378-1005	66943	Lelio R Paula	04/2012
6853	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
6854	7^79202-6^(79202+1)	66934	Robert Price	06/2016
6855	2^222325-112255	66927	Enzo Doria	06/2014
6856	20^51428+33	66910	Lelio R Paula	08/2013
6858	2^222224-18509	66897	Enzo Doria	05/2013
6857	(38*10^66896+187)/9	66897	Robert Price	11/2017
6859	2^222192-869688105	66887	Lelio R Paula	02/2016
6860	(19*10^66878-43)/3	66879	Robert Price	10/2017
6861	11^64219-64	66878	Lelio R Paula	07/2013
6862	2^222151-17295	66875	Lelio R Paula	04/2012
6863	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
6864	2^222085-111031	66855	Enzo Doria	05/2014
6865	8*10^66848-13	66849	Robert Price	05/2017
6866	(3^140087+4)/13	66838	Lelio R Paula	04/2012
6867	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
6868	19^52265+52	66835	Lelio R Paula	08/2013
6869	2*10^66826-27	66827	Robert Price	02/2017
6870	4*6^85867+5	66819	Lelio R Paula	09/2014
6871	15^56800+8	66802	Lelio R Paula	08/2013
6872	(2^221891-2^110946+1)/5	66796		11/2006
6873	10^66793+69441	66794	Patrick De Geest	05/2013
6874	10^66793-63	66793	Robert Price	05/2011
6875	35^43256-1704	66791	Enzo Doria	03/2013
6876	3^139976+2^(139976-1)	66786	Robert Price	05/2016
6877	7^79023-54	66783	Lelio R Paula	06/2013
6878	104^33109-103	66782	Norbert Schneider	11/2016
6879	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
6880	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
6882	2^221768+183	66759	Lelio R Paula	02/2012
6881	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
6883	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
6884	11^64097+48	66751	Lelio R Paula	07/2013
6885	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
6886	(19*10^66748+413)/9	66749	Robert Price	10/2017
6887	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
6888	8*6^85758-7	66734	Lelio R Paula	09/2014
6889	135^31325+2	66733	Lelio R Paula	05/2013
6890	(49*10^66729+41)/9	66730	Robert Price	07/2015
6891	(349*10^66720-7)/9	66722	Robert Price	03/2017
6892	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
6893	(25*10^66714+71)/3	66715	Robert Price	01/2017
6894	11^64061-780	66713	Enzo Doria	11/2012
6895	7^78929+4	66703	Lelio R Paula	06/2013
6896	11^64048-930	66700	Enzo Doria	11/2012
6897	2*7^78921+5	66697	Lelio R Paula	09/2014
6898	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
6899	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
6900	2^221479+72953	66672	Enzo Doria	04/2016
6901	10^66666+275403	66667	Patrick De Geest	03/2010
6902	10^66666-115521	66666	Patrick De Geest	03/2010
6903	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
6904	4*10^66653+21	66654	Robert Price	08/2016
6905	(10^66650+149)/3	66650	Serge Batalov	12/2014
6906	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
6907	2^221391-2145	66646	Lelio R Paula	04/2012
6908	(5*10^66613-119)/3	66614	Robert Price	04/2016
6909	2^221273-113233	66610	Enzo Doria	07/2014
6910	3^139571-46	66593	Lelio R Paula	06/2013
6911	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
6912	2^221181-869688105	66583	Lelio R Paula	02/2016
6913	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
6914	2^221126+133	66566	Lelio R Paula	02/2012
6915	12^61680+91	66564	Lelio R Paula	07/2013
6916	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
6917	(13*10^66551-73)/3	66552	Robert Price	12/2016
6918	11^63901-1590	66547	Enzo Doria	12/2012
6919	11^63901-1500	66547	Enzo Doria	12/2012
6920	6^85517+23	66546	Lelio R Paula	07/2013
6921	17^54069-40	66530	Lelio R Paula	08/2013
6922	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
6923	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
6925	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
6924	3^139432+26	66526	Lelio R Paula	06/2013
6926	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
6927	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
6928	6^85481+85481	66518	Henri Lifchitz	08/2014
6929	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
6930	13^59687+66	66488	Lelio R Paula	07/2013
6931	(49*10^66485-31)/9	66486	Robert Price	07/2015
6932	(46*10^66469+17)/9	66470	Robert Price	06/2015
6933	2^220790+97	66465	Lelio R Paula	02/2012
6934	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
6935	40009^14441-102	66460	Enzo Doria	07/2012
6936	2^220736-143	66449	Lelio R Paula	02/2012
6937	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
6938	2^220675+69	66430	Lelio R Paula	02/2012
6939	2^220633-111381	66418	Enzo Doria	05/2014
6940	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
6941	2^220596-15813	66407	Enzo Doria	04/2013
6942	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
6943	2^220549-1859173	66392	Enzo Doria	04/2016
6944	2^220478-161	66371	Lelio R Paula	02/2012
6945	5^94938-14636	66359	Enzo Doria	02/2013
6946	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
6947	2^220253-114871	66303	Enzo Doria	05/2015
6948	12^61432+95	66297	Lelio R Paula	07/2013
6949	2^220192-111563	66285	Enzo Doria	05/2014
6950	2^220188-111449	66284	Enzo Doria	05/2014
6951	(4*10^66284+23)/9	66284	Robert Price	11/2014
6952	32501!2+2	66266	Robert Price	01/2015
6953	(8*10^66261-101)/3	66262	Robert Price	10/2017
6954	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
6955	(47^39623-1)/46	66252	Robert Price	06/2014
6956	2^220044-97305	66240	Lelio R Paula	04/2012
6957	(77*10^66237-257)/9	66238	Robert Price	10/2017
6958	29^45285+2	66225	Ray Chandler	08/2011
6959	15^56289+38	66202	Lelio R Paula	08/2013
6960	3^138749+98	66201	Lelio R Paula	06/2013
6961	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
6962	2^219904-16995	66198	Lelio R Paula	10/2011
6963	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
6964	Phi(198552,10)	66177	Ray Chandler	07/2010
6965	4*6^85041+7	66176	Lelio R Paula	09/2014
6966	2^219812-3149	66171	Yves Minet	10/2009
6967	2^219795-611167	66165	Paul Bourdelais	03/2013
6968	32455!2+512	66162	Robert Price	02/2015
6969	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
6971	(11^63521-4^63521)/7	66150	Robert Price	03/2013
6970	5*7^78274-6	66150	Lelio R Paula	09/2014
6972	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
6973	2^219679-112015	66130	Enzo Doria	05/2014
6974	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
6975	2^219600+76561	66107	Enzo Doria	05/2016
6976	2^219594+255255	66105	Lelio R Paula	10/2011
6977	4*7^78210-3	66096	Lelio R Paula	09/2014
6978	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
6979	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
6980	2^219496+66615	66075	Lelio R Paula	10/2011
6981	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
6982	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
6983	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
6984	10^66033+19	66034	Robert Price	01/2011
6985	10^66033-78309	66033	Patrick De Geest	05/2013
6986	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
6987	2^219304+454245	66018	Henri Lifchitz	03/2007
6988	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
6989	2^219273-112635	66008	Enzo Doria	06/2014
6990	2^219250+25	66001	Lelio R Paula	08/2011
6991	132^31123+131	65999	Norbert Schneider	03/2015
6992	V(319871)	65987	Serge Batalov	03/2015
6993	2^219189-195	65983	Lelio R Paula	08/2011
6994	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
6995	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
6996	2^219112-17009	65960	Enzo Doria	05/2013
6997	2^219093-111201	65954	Enzo Doria	05/2014
6998	2^219089-112099	65953	Enzo Doria	06/2014
6999	46714!3+81	65950	Robert Price	09/2014
7000	(11*10^65944-131)/3	65945	Robert Price	02/2017

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)