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 ?
2751	262147#+316847	113552	Makoto Morimoto	02/2016
2752	2^377026-458903	113497	Enzo Doria	04/2015
2753	(29*10^113468-17)/3	113469	Robert Price	09/2019
2754	35^73477-34^73477	113454	Robert Price	05/2012
2755	2^376790+27	113426	Lelio R Paula	03/2013
2756	2^376786-112701	113424	Enzo Doria	06/2014
2757	2^376731+21	113408	Lelio R Paula	03/2013
2759	2^376634+1871245	113379	Enzo Doria	05/2016
2758	(4^188318+17)/3	113379	Robert Price	02/2017
2760	2^376576-344369	113361	Enzo Doria	07/2015
2761	2^376549-4543	113353	Yves Minet	03/2019
2762	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2763	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2764	2^376128-21237	113226	Enzo Doria	06/2013
2765	5*10^113224-81	113225	Robert Price	01/2019
2766	(46*10^113162+521)/9	113163	Robert Price	02/2019
2767	2^375638-1787171	113079	Enzo Doria	03/2016
2768	2^375537+4847	113048	Yves Minet	02/2011
2769	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2770	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2771	2^375350-3221	112992	Yves Minet	07/2011
2772	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2773	2^375305+76757	112979	Enzo Doria	05/2016
2774	2^375258+1874989	112964	Enzo Doria	07/2016
2775	(29^77237-1)/28	112950	Robert Price	04/2012
2776	2^375154+74959	112933	Enzo Doria	04/2016
2777	2^374993-2787163	112885	Enzo Doria	11/2015
2778	123^53970+2	112793	Lelio R Paula	06/2013
2779	2^374640-4685	112778	Yves Minet	05/2019
2780	p(22852)#/2+512	112745	Robert Price	05/2017
2781	(11*10^112742-131)/3	112743	Robert Price	09/2018
2782	2^374441-21049	112718	Enzo Doria	06/2013
2783	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2784	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2785	3^236011-8828	112606	Enzo Doria	05/2014
2786	39^70666+2	112435	Lelio R Paula	11/2013
2787	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2788	2^373306-1840931	112377	Enzo Doria	06/2015
2789	2^373117+1872107	112320	Enzo Doria	05/2016
2790	2^373040+2792761	112297	Enzo Doria	03/2016
2791	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2792	2^372950+7	112270	Lelio R Paula	03/2013
2793	2^372945+1872167	112268	Enzo Doria	05/2016
2794	2^372695+72113	112193	Enzo Doria	04/2016
2795	2^372689-2563	112191	Yves Minet	07/2014
2796	2^372638-1859441	112176	Enzo Doria	03/2016
2797	3^235074-113056	112159	Enzo Doria	07/2014
2798	131^52949-130	112108	Norbert Schneider	02/2019
2799	(91*10^112098-1)/9	112100	Robert Price	04/2015
2800	2^372310-85061	112077	Paul Bourdelais	02/2012
2801	(10^112067+53)/9	112067	Serge Batalov	07/2015
2802	75^59760+2	112054	Lelio R Paula	08/2013
2803	8*10^112018-49	112019	Robert Price	08/2019
2804	2^372108+74221	112016	Enzo Doria	04/2016
2805	5*10^112003+81	112004	Robert Price	03/2019
2806	215^48018+48018^215	112000	Norbert Schneider	10/2018
2807	2^371970-459491	111975	Enzo Doria	05/2015
2808	41^69427-40^69427	111971	Robert Price	07/2012
2809	(10^111902+71)/9	111902	Serge Batalov	07/2015
2810	2^371440-112865	111815	Enzo Doria	06/2014
2811	2^371426-459161	111811	Enzo Doria	05/2015
2812	2^371276-461267	111766	Enzo Doria	07/2015
2813	98079!4-1024	111747	Robert Price	11/2019
2814	2^371098-113261	111712	Enzo Doria	07/2014
2815	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2816	2^371044+1869391	111696	Enzo Doria	05/2016
2817	88^57416+87	111645	Norbert Schneider	11/2015
2818	2^370829-109693	111631	Enzo Doria	04/2014
2819	15^94906-2	111619	Lelio R Paula	11/2013
2820	2^370695-4627	111591	Yves Minet	05/2019
2822	2^370643-37	111575	Yves Minet	01/2012
2821	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2823	2^370610-3911	111565	Yves Minet	04/2017
2824	286^45405+45405^286	111532	Norbert Schneider	04/2015
2825	4*5^159563-9	111531	Lelio R Paula	11/2014
2826	(4^185225+23)/3	111517	Robert Price	10/2018
2827	2^370393-2797093	111500	Enzo Doria	03/2016
2828	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2829	2^370292-2791979	111469	Enzo Doria	03/2016
2830	2^370177-461551	111435	Enzo Doria	07/2015
2831	109^54683-108	111413	Norbert Schneider	02/2017
2832	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2833	2^369974+733	111374	Lelio R Paula	05/2013
2834	121^53470+120	111367	Norbert Schneider	10/2018
2835	2^369915-286267	111356	Enzo Doria	07/2015
2836	2^369855-1615	111338	Lelio R Paula	05/2017
2837	7*10^111325+3	111326	Robert Price	08/2015
2838	51^65176+2	111293	Lelio R Paula	08/2013
2839	2^369643-1865767	111274	Enzo Doria	03/2016
2840	2^369603+885	111262	Lelio R Paula	05/2017
2841	L(532277)	111240	Renaud Lifchitz	03/2004
2842	105^55033-2	111233	Lelio R Paula	10/2017
2843	(35*10^111232-737)/9	111233	Robert Price	07/2018
2844	9*10^111201-29	111202	Robert Price	09/2019
2845	2^369392+29835	111199	Lelio R Paula	05/2017
2846	2^369354-3413	111187	Yves Minet	12/2016
2847	2^369296-27	111170	Lelio R Paula	02/2013
2848	2^369239-109837	111153	Enzo Doria	05/2014
2849	2^369224-291839	111148	Enzo Doria	07/2015
2850	2^369216+2798881	111146	Enzo Doria	04/2016
2851	10^111111+163849	111112	Patrick De Geest	03/2017
2852	10^111111-312911	111111	Patrick De Geest	03/2017
2853	2^369092-216923	111108	Enzo Doria	05/2014
2854	2^369081-55	111105	Lelio R Paula	02/2013
2855	88^57124-87	111077	Norbert Schneider	11/2015
2856	2^368980+753	111075	Lelio R Paula	05/2013
2857	2^368946-3623	111064	Yves Minet	03/2017
2858	2^368929+29835	111059	Lelio R Paula	05/2017
2859	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2860	111^54298+110	111057	Norbert Schneider	04/2017
2861	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2862	2^368641-460303	110972	Enzo Doria	06/2015
2863	2^368619-109087	110966	Enzo Doria	04/2014
2864	(74*10^110961+313)/9	110962	Robert Price	06/2019
2865	3*2^368489+7	110927	Lelio R Paula	09/2014
2866	(14*10^110922+61)/3	110923	Robert Price	12/2018
2867	97411!4-2	110913	Robert Price	07/2017
2868	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2869	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2870	2^368050-64875	110795	Lelio R Paula	05/2017
2871	2^368048+25	110794	Lelio R Paula	02/2013
2872	69^60239-2	110771	Lelio R Paula	10/2013
2873	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2874	2^367924-69	110757	Lelio R Paula	02/2013
2875	2^367709-109723	110692	Enzo Doria	04/2014
2876	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2877	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2878	140^51515-139	110558	Norbert Schneider	04/2019
2879	2^367215+1879223	110543	Enzo Doria	09/2016
2880	2^367141+41	110521	Lelio R Paula	02/2013
2881	2^367126+29835	110516	Lelio R Paula	05/2017
2882	(11*10^110496+49)/3	110497	Robert Price	07/2018
2883	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2884	7*10^110468-23	110469	Robert Price	07/2019
2885	2^366853+5711	110434	Lelio R Paula	05/2017
2886	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2887	2^366816+315	110423	Lelio R Paula	05/2017
2888	2^366775-2787037	110411	Enzo Doria	03/2016
2889	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2890	2^366751+2797553	110404	Enzo Doria	03/2016
2891	2^366748+255	110403	Lelio R Paula	05/2017
2892	2^366738-2985	110400	Yves Minet	09/2014
2893	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2894	2^366716+1871791	110393	Enzo Doria	05/2016
2895	2^366649+1871687	110373	Enzo Doria	05/2016
2896	2^366629-351205	110367	Enzo Doria	06/2015
2897	2^366558+1874479	110345	Enzo Doria	06/2016
2898	(23*10^110290+19)/3	110291	Robert Price	07/2019
2899	18^87853-4409	110280	Enzo Doria	03/2013
2900	2^366218-23	110243	Lelio R Paula	02/2013
2901	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2902	2^366178-343991	110231	Enzo Doria	07/2015
2903	2^365944+1871341	110161	Enzo Doria	05/2016
2904	2^365838-461267	110129	Enzo Doria	07/2015
2905	2^365763-6555	110106	Lelio R Paula	04/2017
2906	(2^365689+2^182845+1)/5	110083		11/2006
2907	2^365666-459161	110077	Enzo Doria	05/2015
2908	3*10^110076-7	110077	Robert Price	08/2015
2909	13^98785-72	110041	Lelio R Paula	03/2017
2910	(25^78707+1)/26	110027	Robert Price	06/2013
2911	(7*10^110006-151)/9	110006	Robert Price	02/2018
2912	6^141361-7	110001	Lelio R Paula	11/2014
2913	20^84536+81	109984	Lelio R Paula	03/2017
2914	5*2^365347-9	109982	Lelio R Paula	09/2014
2915	9*6^141303+7	109957	Lelio R Paula	11/2014
2916	78^58099+77	109929	Norbert Schneider	02/2015
2917	2*10^109928-7	109929	Robert Price	10/2015
2918	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2919	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2920	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2921	18^87533-11	109878	Lelio R Paula	04/2017
2922	2^364982-5	109871	Henri Lifchitz	04/2006
2923	3*10^109861+59	109862	Robert Price	08/2018
2924	2^364936-1867979	109857	Enzo Doria	04/2016
2925	2^364867-112087	109836	Enzo Doria	06/2014
2926	4^182415-85061	109825	Mike Oakes	06/2011
2927	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2928	2^364687-187	109782	Lelio R Paula	01/2012
2929	2^364644+67	109769	Lelio R Paula	01/2012
2930	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2931	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2932	(55*10^109759+89)/9	109760	Robert Price	03/2019
2933	12^101694+73	109747	Lelio R Paula	03/2017
2934	13^98518-66	109744	Lelio R Paula	03/2017
2936	2^364478-113261	109719	Enzo Doria	07/2014
2935	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
2937	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2938	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2939	3^229824+340	109654	Lelio R Paula	03/2017
2940	(2*10^109645-71)/3	109645	Robert Price	12/2017
2941	2^364169-112813	109626	Enzo Doria	06/2014
2942	10^109615+21	109616	Lelio R Paula	03/2017
2943	10^109615-456267	109615	Patrick De Geest	03/2017
2944	2^364094-113	109604	Lelio R Paula	01/2012
2945	(4^182026+11)/3	109591	Robert Price	02/2017
2946	2^364041-6883	109588	Lelio R Paula	09/2011
2947	12^101545+11	109586	Lelio R Paula	03/2017
2948	2^363842-2787101	109528	Enzo Doria	03/2016
2949	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2950	2^363769+5711	109506	Lelio R Paula	04/2017
2951	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2952	p(22245)#/2-8	109462	Robert Price	01/2017
2953	2^363556+55	109442	Lelio R Paula	01/2012
2954	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2955	2^363406+1871569	109397	Enzo Doria	05/2016
2956	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2957	3^229236+100	109374	Lelio R Paula	03/2017
2958	2^363268-58695	109355	Lelio R Paula	04/2017
2959	2^363191-112321	109332	Enzo Doria	06/2014
2960	4*10^109316-63	109317	Robert Price	10/2018
2961	2^363120+3	109311	Donovan Johnson	04/2006
2962	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2963	2^363042-114641	109287	Enzo Doria	04/2015
2964	2^363020-112793	109280	Enzo Doria	06/2014
2965	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2966	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2967	5^156181+38	109166	Lelio R Paula	02/2017
2968	4*10^109142+91	109143	Robert Price	08/2018
2969	3^228750+68	109142	Lelio R Paula	03/2017
2970	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2971	65^60167-64^60167	109078	Robert Price	08/2013
2972	7*3^228589-2	109066	Lelio R Paula	09/2014
2973	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2974	2*7^129008+9	109025	Lelio R Paula	11/2014
2975	(5*10^108960+91)/3	108961	Robert Price	04/2018
2976	2^361957+76367	108960	Enzo Doria	05/2016
2977	2^361873-1411	108935	Yves Minet	01/2013
2978	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2979	115^52842-114	108892	Norbert Schneider	07/2018
2980	13^97745-24	108883	Lelio R Paula	03/2017
2981	17^88475+8	108864	Lelio R Paula	04/2017
2982	2^361567+51	108843	Lelio R Paula	01/2012
2983	2^361563-109501	108842	Enzo Doria	04/2014
2984	12^100852+83	108838	Lelio R Paula	03/2017
2985	2^361497+767	108822	Lelio R Paula	01/2012
2986	2^361280-112349	108757	Enzo Doria	06/2014
2987	2^361271-5955	108754	Lelio R Paula	04/2017
2988	12^100757+19	108736	Lelio R Paula	03/2017
2989	14^94849-61	108710	Lelio R Paula	05/2017
2990	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2991	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2992	2^360973+1299	108664	Lelio R Paula	04/2017
2993	2^360959-109101	108660	Enzo Doria	04/2014
2994	6*5^155454+7	108659	Lelio R Paula	11/2014
2995	10^108656+79	108657	Lelio R Paula	02/2017
2996	10^108656-50001	108656	Patrick De Geest	03/2017
2997	2^360918-35	108648	Lelio R Paula	01/2012
2998	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2999	3*10^108624-49	108625	Robert Price	07/2018
3000	2^360706-458903	108584	Enzo Doria	04/2015

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Probable Primes Top 10000

(255244 PRPs in the top)