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	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2752	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
2753	2*10^115784-27	115785	Robert Price	05/2018
2754	10^115773+126739	115774	Patrick De Geest	04/2018
2756	10^115773-1000000001	115773	Robert Price	03/2018
2755	10^115773-396221	115773	Patrick De Geest	04/2018
2757	2^384530+1874305	115756	Enzo Doria	06/2016
2758	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
2759	(44*10^115697-413)/9	115698	Robert Price	03/2019
2760	2^384312+81091	115690	Yves Minet	02/2010
2761	(4*10^115668-79)/3	115669	Robert Price	02/2018
2762	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
2763	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
2764	18^92125-92125^18	115642	Dylan Delgado	08/2019
2765	3^242337-4042	115625	Enzo Doria	05/2014
2766	7*10^115561+79	115562	Robert Price	07/2019
2767	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
2768	2^383780-3149	115530	Yves Minet	10/2014
2769	(41*10^115523-383)/9	115524	Robert Price	11/2018
2770	2^383560-455	115464	Yves Minet	03/2012
2771	(2^383544+5)/3	115458	Lelio R Paula	03/2014
2772	89^59221-88^59221	115445	Robert Price	06/2015
2773	2^383347+1869413	115399	Enzo Doria	05/2016
2774	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
2775	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
2776	2^383039+1869509	115307	Enzo Doria	05/2016
2777	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
2778	2^382633+73697	115185	Enzo Doria	04/2016
2779	2^382509-113593	115147	Enzo Doria	08/2014
2780	2^382502-2791721	115145	Enzo Doria	03/2016
2781	9^120590-120590	115073	Robert Price	03/2014
2782	2^382198+9	115054	Lelio R Paula	03/2013
2783	(89*10^115030-179)/9	115031	Robert Price	12/2019
2784	2^381883-59197	114959	Enzo Doria	10/2015
2786	2^381806-4481	114936	Yves Minet	07/2011
2785	2^381808-1851507	114936	Enzo Doria	08/2015
2787	2^381774-112373	114926	Enzo Doria	06/2014
2788	2^381555-109051	114860	Enzo Doria	04/2014
2789	2^381546-113501	114857	Enzo Doria	08/2014
2790	2^381360-110429	114801	Enzo Doria	05/2014
2791	(17*10^114795+79)/3	114796	Robert Price	04/2019
2792	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
2793	2^381252-115079	114769	Enzo Doria	06/2015
2794	2^381209-29323	114756	Enzo Doria	07/2015
2795	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
2796	2^381201+1873205	114753	Enzo Doria	06/2016
2797	(85*10^114737+293)/9	114738	Robert Price	12/2019
2798	(265*10^114736+17)/3	114738	Robert Price	03/2020
2799	2^380974-112991	114685	Enzo Doria	07/2014
2800	88^58949-87	114626	Norbert Schneider	11/2015
2801	2^380700+91	114603	Lelio R Paula	03/2013
2802	10^114575+3^114576	114576	Mike Oakes	09/2010
2803	10^114575+66561	114576	Patrick De Geest	02/2017
2804	10^114575-581081	114575	Patrick De Geest	02/2017
2805	2^380587-115315	114569	Enzo Doria	06/2015
2806	2^380513-216925	114546	Enzo Doria	05/2014
2807	2^380451-1840087	114528	Enzo Doria	06/2015
2808	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
2809	2^380279-461347	114476	Enzo Doria	07/2015
2810	2^380021+1871147	114398	Enzo Doria	05/2016
2811	2^380005+1869707	114393	Enzo Doria	05/2016
2812	2^379958-113297	114379	Enzo Doria	07/2014
2813	2^379881-109105	114356	Enzo Doria	04/2014
2814	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
2815	(4*10^114340+83)/3	114341	Robert Price	02/2018
2816	(26*10^114317-77)/3	114318	Robert Price	11/2019
2817	(4*10^114296+149)/9	114296	Robert Price	04/2018
2818	88^58773-87	114284	Norbert Schneider	11/2015
2819	2^379529-2790283	114250	Enzo Doria	03/2016
2820	2^379522+1869115	114248	Enzo Doria	05/2016
2821	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
2822	2^379317-115033	114186	Enzo Doria	06/2015
2823	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
2824	(4*10^114076+143)/3	114077	Robert Price	03/2018
2825	(46*10^113969+683)/9	113970	Robert Price	03/2019
2826	2*10^113941+9	113942	Dmitry Domanov	11/2010
2827	4*10^113905+91	113906	Robert Price	08/2018
2828	4*10^113874-21	113875	Robert Price	09/2018
2829	2^378272-16565	113872	Enzo Doria	04/2013
2830	2^378217-109075	113855	Enzo Doria	04/2014
2831	2^378198+67	113849	Lelio R Paula	03/2013
2832	2^378173-3249	113842	Yves Minet	12/2014
2833	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
2834	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
2835	2^378128-262977	113828	Enzo Doria	05/2014
2836	2^378123-113215	113827	Enzo Doria	07/2014
2837	6^146274-18893	113824	Enzo Doria	03/2013
2838	2^378078+75	113813	Lelio R Paula	03/2013
2839	2^377940+63	113772	Lelio R Paula	03/2013
2840	2^377941-2785843	113772	Enzo Doria	04/2016
2841	2^377810+1875109	113733	Enzo Doria	09/2016
2842	2^377803-1838635	113731	Enzo Doria	05/2015
2843	2^377799+52223	113729	Yves Minet	08/2010
2844	11^109190-270	113710	Enzo Doria	12/2012
2845	7*10^113693+9	113694	Robert Price	09/2015
2846	(82*10^113681+161)/9	113682	Robert Price	10/2019
2847	4*10^113658+49	113659	Robert Price	01/2019
2848	(2*10^113631+529)/9	113631	Robert Price	01/2018
2849	2^377408-2798279	113612	Enzo Doria	04/2016
2850	5*10^113586+57	113587	Robert Price	12/2018
2851	2^377222+93679	113556	Yves Minet	02/2011
2852	262147#+316847	113552	Makoto Morimoto	02/2016
2853	2^377026-458903	113497	Enzo Doria	04/2015
2854	(29*10^113468-17)/3	113469	Robert Price	09/2019
2855	35^73477-34^73477	113454	Robert Price	05/2012
2856	2^376790+27	113426	Lelio R Paula	03/2013
2857	2^376786-112701	113424	Enzo Doria	06/2014
2858	2^376731+21	113408	Lelio R Paula	03/2013
2859	2^376634+1871245	113379	Enzo Doria	05/2016
2860	(4^188318+17)/3	113379	Robert Price	02/2017
2861	2^376576-344369	113361	Enzo Doria	07/2015
2862	2^376549-4543	113353	Yves Minet	03/2019
2863	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2864	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2865	2^376128-21237	113226	Enzo Doria	06/2013
2866	5*10^113224-81	113225	Robert Price	01/2019
2867	(46*10^113162+521)/9	113163	Robert Price	02/2019
2868	2^375638-1787171	113079	Enzo Doria	03/2016
2869	2^375537+4847	113048	Yves Minet	02/2011
2870	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2871	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2872	2^375350-3221	112992	Yves Minet	07/2011
2873	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2874	2^375305+76757	112979	Enzo Doria	05/2016
2875	2^375258+1874989	112964	Enzo Doria	07/2016
2876	(29^77237-1)/28	112950	Robert Price	04/2012
2877	2^375154+74959	112933	Enzo Doria	04/2016
2878	(85*10^112919+293)/9	112920	Robert Price	12/2019
2879	2^374993-2787163	112885	Enzo Doria	11/2015
2880	123^53970+2	112793	Lelio R Paula	06/2013
2881	2^374640-4685	112778	Yves Minet	05/2019
2882	p(22852)#/2+512	112745	Robert Price	05/2017
2883	(11*10^112742-131)/3	112743	Robert Price	09/2018
2884	2^374441-21049	112718	Enzo Doria	06/2013
2885	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2886	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2887	3^236011-8828	112606	Enzo Doria	05/2014
2888	39^70666+2	112435	Lelio R Paula	11/2013
2889	(134*10^112400+7)/3	112402	Robert Price	02/2020
2890	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2891	2^373306-1840931	112377	Enzo Doria	06/2015
2892	(142*10^112352-7)/9	112354	Robert Price	12/2019
2893	2^373117+1872107	112320	Enzo Doria	05/2016
2894	2^373040+2792761	112297	Enzo Doria	03/2016
2895	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2896	2^372950+7	112270	Lelio R Paula	03/2013
2897	2^372945+1872167	112268	Enzo Doria	05/2016
2898	2^372695+72113	112193	Enzo Doria	04/2016
2899	2^372689-2563	112191	Yves Minet	07/2014
2900	2^372638-1859441	112176	Enzo Doria	03/2016
2901	3^235074-113056	112159	Enzo Doria	07/2014
2902	131^52949-130	112108	Norbert Schneider	02/2019
2903	(91*10^112098-1)/9	112100	Robert Price	04/2015
2904	2^372310-85061	112077	Paul Bourdelais	02/2012
2905	(10^112067+53)/9	112067	Serge Batalov	07/2015
2906	75^59760+2	112054	Lelio R Paula	08/2013
2907	8*10^112018-49	112019	Robert Price	08/2019
2908	2^372108+74221	112016	Enzo Doria	04/2016
2909	(184*10^112007-1)/3	112009	Robert Price	02/2020
2910	5*10^112003+81	112004	Robert Price	03/2019
2911	215^48018+48018^215	112000	Norbert Schneider	10/2018
2912	2^371970-459491	111975	Enzo Doria	05/2015
2913	41^69427-40^69427	111971	Robert Price	07/2012
2914	(10^111902+71)/9	111902	Serge Batalov	07/2015
2915	2^371440-112865	111815	Enzo Doria	06/2014
2916	2^371426-459161	111811	Enzo Doria	05/2015
2917	2^371276-461267	111766	Enzo Doria	07/2015
2918	98079!4-1024	111747	Robert Price	11/2019
2919	2^371098-113261	111712	Enzo Doria	07/2014
2920	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2921	2^371044+1869391	111696	Enzo Doria	05/2016
2922	88^57416+87	111645	Norbert Schneider	11/2015
2923	2^370829-109693	111631	Enzo Doria	04/2014
2924	15^94906-2	111619	Lelio R Paula	11/2013
2925	2^370695-4627	111591	Yves Minet	05/2019
2927	2^370643-37	111575	Yves Minet	01/2012
2926	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2928	2^370610-3911	111565	Yves Minet	04/2017
2929	286^45405+45405^286	111532	Norbert Schneider	04/2015
2930	4*5^159563-9	111531	Lelio R Paula	11/2014
2931	(4^185225+23)/3	111517	Robert Price	10/2018
2932	2^370393-2797093	111500	Enzo Doria	03/2016
2933	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2934	2^370292-2791979	111469	Enzo Doria	03/2016
2935	2^370177-461551	111435	Enzo Doria	07/2015
2936	109^54683-108	111413	Norbert Schneider	02/2017
2937	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2938	2^369974+733	111374	Lelio R Paula	05/2013
2939	121^53470+120	111367	Norbert Schneider	10/2018
2940	2^369915-286267	111356	Enzo Doria	07/2015
2941	2^369855-1615	111338	Lelio R Paula	05/2017
2942	7*10^111325+3	111326	Robert Price	08/2015
2943	51^65176+2	111293	Lelio R Paula	08/2013
2944	2^369643-1865767	111274	Enzo Doria	03/2016
2945	2^369603+885	111262	Lelio R Paula	05/2017
2946	L(532277)	111240	Renaud Lifchitz	03/2004
2947	105^55033-2	111233	Lelio R Paula	10/2017
2948	(35*10^111232-737)/9	111233	Robert Price	07/2018
2949	9*10^111201-29	111202	Robert Price	09/2019
2950	2^369392+29835	111199	Lelio R Paula	05/2017
2951	2^369354-3413	111187	Yves Minet	12/2016
2952	2^369296-27	111170	Lelio R Paula	02/2013
2953	2^369239-109837	111153	Enzo Doria	05/2014
2954	2^369224-291839	111148	Enzo Doria	07/2015
2955	2^369216+2798881	111146	Enzo Doria	04/2016
2956	10^111111+163849	111112	Patrick De Geest	03/2017
2957	10^111111-312911	111111	Patrick De Geest	03/2017
2958	2^369092-216923	111108	Enzo Doria	05/2014
2959	2^369081-55	111105	Lelio R Paula	02/2013
2960	88^57124-87	111077	Norbert Schneider	11/2015
2961	2^368980+753	111075	Lelio R Paula	05/2013
2962	2^368946-3623	111064	Yves Minet	03/2017
2963	2^368929+29835	111059	Lelio R Paula	05/2017
2964	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2965	111^54298+110	111057	Norbert Schneider	04/2017
2966	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2967	2^368641-460303	110972	Enzo Doria	06/2015
2968	2^368619-109087	110966	Enzo Doria	04/2014
2969	(74*10^110961+313)/9	110962	Robert Price	06/2019
2970	3*2^368489+7	110927	Lelio R Paula	09/2014
2971	(14*10^110922+61)/3	110923	Robert Price	12/2018
2972	97411!4-2	110913	Robert Price	07/2017
2973	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2974	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2975	2^368050-64875	110795	Lelio R Paula	05/2017
2976	2^368048+25	110794	Lelio R Paula	02/2013
2977	69^60239-2	110771	Lelio R Paula	10/2013
2978	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2979	2^367924-69	110757	Lelio R Paula	02/2013
2980	2^367709-109723	110692	Enzo Doria	04/2014
2981	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2982	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2983	140^51515-139	110558	Norbert Schneider	04/2019
2984	2^367215+1879223	110543	Enzo Doria	09/2016
2985	2^367141+41	110521	Lelio R Paula	02/2013
2986	2^367126+29835	110516	Lelio R Paula	05/2017
2987	(11*10^110496+49)/3	110497	Robert Price	07/2018
2988	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2989	7*10^110468-23	110469	Robert Price	07/2019
2990	2^366853+5711	110434	Lelio R Paula	05/2017
2991	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2992	2^366816+315	110423	Lelio R Paula	05/2017
2993	2^366775-2787037	110411	Enzo Doria	03/2016
2994	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2995	2^366751+2797553	110404	Enzo Doria	03/2016
2996	2^366748+255	110403	Lelio R Paula	05/2017
2997	2^366738-2985	110400	Yves Minet	09/2014
2998	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2999	2^366716+1871791	110393	Enzo Doria	05/2016
3000	2^366649+1871687	110373	Enzo Doria	05/2016

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PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)