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	2^370610-3911	111565	Yves Minet	04/2017
2752	286^45405+45405^286	111532	Norbert Schneider	04/2015
2753	4*5^159563-9	111531	Lelio R Paula	11/2014
2754	(4^185225+23)/3	111517	Robert Price	10/2018
2755	2^370393-2797093	111500	Enzo Doria	03/2016
2756	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2757	2^370292-2791979	111469	Enzo Doria	03/2016
2758	2^370177-461551	111435	Enzo Doria	07/2015
2759	109^54683-108	111413	Norbert Schneider	02/2017
2760	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2761	2^369974+733	111374	Lelio R Paula	05/2013
2762	121^53470+120	111367	Norbert Schneider	10/2018
2763	2^369915-286267	111356	Enzo Doria	07/2015
2764	2^369855-1615	111338	Lelio R Paula	05/2017
2765	7*10^111325+3	111326	Robert Price	08/2015
2766	51^65176+2	111293	Lelio R Paula	08/2013
2767	2^369643-1865767	111274	Enzo Doria	03/2016
2768	2^369603+885	111262	Lelio R Paula	05/2017
2769	L(532277)	111240	Renaud Lifchitz	03/2004
2770	105^55033-2	111233	Lelio R Paula	10/2017
2771	(35*10^111232-737)/9	111233	Robert Price	07/2018
2772	2^369392+29835	111199	Lelio R Paula	05/2017
2773	2^369354-3413	111187	Yves Minet	12/2016
2774	2^369296-27	111170	Lelio R Paula	02/2013
2775	2^369239-109837	111153	Enzo Doria	05/2014
2776	2^369224-291839	111148	Enzo Doria	07/2015
2777	2^369216+2798881	111146	Enzo Doria	04/2016
2778	10^111111+163849	111112	Patrick De Geest	03/2017
2779	10^111111-312911	111111	Patrick De Geest	03/2017
2780	2^369092-216923	111108	Enzo Doria	05/2014
2781	2^369081-55	111105	Lelio R Paula	02/2013
2782	88^57124-87	111077	Norbert Schneider	11/2015
2783	2^368980+753	111075	Lelio R Paula	05/2013
2784	2^368946-3623	111064	Yves Minet	03/2017
2785	2^368929+29835	111059	Lelio R Paula	05/2017
2786	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2787	111^54298+110	111057	Norbert Schneider	04/2017
2788	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2789	2^368641-460303	110972	Enzo Doria	06/2015
2790	2^368619-109087	110966	Enzo Doria	04/2014
2791	(74*10^110961+313)/9	110962	Robert Price	06/2019
2792	3*2^368489+7	110927	Lelio R Paula	09/2014
2793	(14*10^110922+61)/3	110923	Robert Price	12/2018
2794	97411!4-2	110913	Robert Price	07/2017
2795	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2796	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2797	2^368050-64875	110795	Lelio R Paula	05/2017
2798	2^368048+25	110794	Lelio R Paula	02/2013
2799	69^60239-2	110771	Lelio R Paula	10/2013
2800	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2801	2^367924-69	110757	Lelio R Paula	02/2013
2802	2^367709-109723	110692	Enzo Doria	04/2014
2803	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2804	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2805	140^51515-139	110558	Norbert Schneider	04/2019
2806	2^367215+1879223	110543	Enzo Doria	09/2016
2807	2^367141+41	110521	Lelio R Paula	02/2013
2808	2^367126+29835	110516	Lelio R Paula	05/2017
2809	(11*10^110496+49)/3	110497	Robert Price	07/2018
2810	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2811	7*10^110468-23	110469	Robert Price	07/2019
2812	2^366853+5711	110434	Lelio R Paula	05/2017
2813	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2814	2^366816+315	110423	Lelio R Paula	05/2017
2815	2^366775-2787037	110411	Enzo Doria	03/2016
2816	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2817	2^366751+2797553	110404	Enzo Doria	03/2016
2818	2^366748+255	110403	Lelio R Paula	05/2017
2819	2^366738-2985	110400	Yves Minet	09/2014
2820	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2821	2^366716+1871791	110393	Enzo Doria	05/2016
2822	2^366649+1871687	110373	Enzo Doria	05/2016
2823	2^366629-351205	110367	Enzo Doria	06/2015
2824	2^366558+1874479	110345	Enzo Doria	06/2016
2825	(23*10^110290+19)/3	110291	Robert Price	07/2019
2826	18^87853-4409	110280	Enzo Doria	03/2013
2827	2^366218-23	110243	Lelio R Paula	02/2013
2828	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2829	2^366178-343991	110231	Enzo Doria	07/2015
2830	2^365944+1871341	110161	Enzo Doria	05/2016
2831	2^365838-461267	110129	Enzo Doria	07/2015
2832	2^365763-6555	110106	Lelio R Paula	04/2017
2833	(2^365689+2^182845+1)/5	110083		11/2006
2834	2^365666-459161	110077	Enzo Doria	05/2015
2835	3*10^110076-7	110077	Robert Price	08/2015
2836	13^98785-72	110041	Lelio R Paula	03/2017
2837	(25^78707+1)/26	110027	Robert Price	06/2013
2838	(7*10^110006-151)/9	110006	Robert Price	02/2018
2839	6^141361-7	110001	Lelio R Paula	11/2014
2840	20^84536+81	109984	Lelio R Paula	03/2017
2841	5*2^365347-9	109982	Lelio R Paula	09/2014
2842	9*6^141303+7	109957	Lelio R Paula	11/2014
2843	78^58099+77	109929	Norbert Schneider	02/2015
2844	2*10^109928-7	109929	Robert Price	10/2015
2845	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2846	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2847	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2848	18^87533-11	109878	Lelio R Paula	04/2017
2849	2^364982-5	109871	Henri Lifchitz	04/2006
2850	3*10^109861+59	109862	Robert Price	08/2018
2851	2^364936-1867979	109857	Enzo Doria	04/2016
2852	2^364867-112087	109836	Enzo Doria	06/2014
2853	4^182415-85061	109825	Mike Oakes	06/2011
2854	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2855	2^364687-187	109782	Lelio R Paula	01/2012
2856	2^364644+67	109769	Lelio R Paula	01/2012
2857	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2858	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2859	(55*10^109759+89)/9	109760	Robert Price	03/2019
2860	12^101694+73	109747	Lelio R Paula	03/2017
2861	13^98518-66	109744	Lelio R Paula	03/2017
2862	2^364478-113261	109719	Enzo Doria	07/2014
2863	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
2864	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2865	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2866	3^229824+340	109654	Lelio R Paula	03/2017
2867	(2*10^109645-71)/3	109645	Robert Price	12/2017
2868	2^364169-112813	109626	Enzo Doria	06/2014
2869	10^109615+21	109616	Lelio R Paula	03/2017
2870	10^109615-456267	109615	Patrick De Geest	03/2017
2871	2^364094-113	109604	Lelio R Paula	01/2012
2872	(4^182026+11)/3	109591	Robert Price	02/2017
2873	2^364041-6883	109588	Lelio R Paula	09/2011
2874	12^101545+11	109586	Lelio R Paula	03/2017
2875	2^363842-2787101	109528	Enzo Doria	03/2016
2876	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2877	2^363769+5711	109506	Lelio R Paula	04/2017
2878	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2879	p(22245)#/2-8	109462	Robert Price	01/2017
2880	2^363556+55	109442	Lelio R Paula	01/2012
2881	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2882	2^363406+1871569	109397	Enzo Doria	05/2016
2883	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2884	3^229236+100	109374	Lelio R Paula	03/2017
2885	2^363268-58695	109355	Lelio R Paula	04/2017
2886	2^363191-112321	109332	Enzo Doria	06/2014
2887	4*10^109316-63	109317	Robert Price	10/2018
2888	2^363120+3	109311	Donovan Johnson	04/2006
2889	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2890	2^363042-114641	109287	Enzo Doria	04/2015
2891	2^363020-112793	109280	Enzo Doria	06/2014
2892	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2893	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2894	5^156181+38	109166	Lelio R Paula	02/2017
2895	4*10^109142+91	109143	Robert Price	08/2018
2896	3^228750+68	109142	Lelio R Paula	03/2017
2897	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2898	65^60167-64^60167	109078	Robert Price	08/2013
2899	7*3^228589-2	109066	Lelio R Paula	09/2014
2900	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2901	2*7^129008+9	109025	Lelio R Paula	11/2014
2902	(5*10^108960+91)/3	108961	Robert Price	04/2018
2903	2^361957+76367	108960	Enzo Doria	05/2016
2904	2^361873-1411	108935	Yves Minet	01/2013
2905	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2906	115^52842-114	108892	Norbert Schneider	07/2018
2907	13^97745-24	108883	Lelio R Paula	03/2017
2908	17^88475+8	108864	Lelio R Paula	04/2017
2909	2^361567+51	108843	Lelio R Paula	01/2012
2910	2^361563-109501	108842	Enzo Doria	04/2014
2911	12^100852+83	108838	Lelio R Paula	03/2017
2912	2^361497+767	108822	Lelio R Paula	01/2012
2913	2^361280-112349	108757	Enzo Doria	06/2014
2914	2^361271-5955	108754	Lelio R Paula	04/2017
2915	12^100757+19	108736	Lelio R Paula	03/2017
2916	14^94849-61	108710	Lelio R Paula	05/2017
2917	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2918	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2919	2^360973+1299	108664	Lelio R Paula	04/2017
2920	2^360959-109101	108660	Enzo Doria	04/2014
2921	6*5^155454+7	108659	Lelio R Paula	11/2014
2922	10^108656+79	108657	Lelio R Paula	02/2017
2923	10^108656-50001	108656	Patrick De Geest	03/2017
2924	2^360918-35	108648	Lelio R Paula	01/2012
2925	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2926	3*10^108624-49	108625	Robert Price	07/2018
2927	2^360706-458903	108584	Enzo Doria	04/2015
2928	2^360641-113185	108564	Enzo Doria	07/2014
2929	2^360618+75019	108557	Enzo Doria	04/2016
2930	(14*10^108545-221)/9	108546	Robert Price	04/2018
2931	(44*10^108544-233)/9	108545	Robert Price	01/2019
2932	3*5^155286+2	108541	Lelio R Paula	11/2014
2933	7^128422+4	108530	Lelio R Paula	11/2014
2934	7^128421-80	108529	Lelio R Paula	03/2017
2935	2^360497+53807	108521	Yves Minet	07/2010
2936	2^360468-4559	108512	Yves Minet	03/2019
2938	2^360366+1459	108481	Lelio R Paula	09/2011
2937	2^360364-1499	108481	Yves Minet	05/2013
2939	14^94642-23	108472	Lelio R Paula	05/2017
2940	4*10^108412+9	108413	Robert Price	05/2015
2941	133^51042-132	108406	Norbert Schneider	02/2019
2942	2^360093-351103	108399	Enzo Doria	06/2015
2943	2^360042+723	108384	Lelio R Paula	01/2012
2944	85^56164-2	108364	Lelio R Paula	10/2013
2945	2^359937-29323	108352	Enzo Doria	07/2015
2946	2^359898-19997	108341	Enzo Doria	06/2013
2947	2*5^154948-7	108305	Lelio R Paula	11/2014
2948	10^108303+13	108304	Lelio R Paula	02/2017
2949	10^108303-207959	108303	Patrick De Geest	03/2017
2950	7*10^108300+69	108301	Robert Price	07/2019
2951	2^359730+753	108290	Lelio R Paula	12/2011
2952	(8*10^108273+13)/3	108274	Robert Price	06/2018
2953	2^359650-19797	108266	Enzo Doria	06/2013
2954	91^55259-90^55259	108255	Robert Price	07/2015
2955	4*10^108238-71	108239	Robert Price	12/2018
2956	3^226845+68	108233	Lelio R Paula	03/2017
2957	5^154822-12866	108216	Enzo Doria	05/2014
2958	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2959	2^359454-177	108207	Lelio R Paula	12/2011
2960	(19*10^108184+191)/3	108185	Robert Price	05/2019
2961	6^139022-59	108181	Lelio R Paula	02/2017
2962	(19*10^108176-43)/3	108177	Robert Price	05/2019
2963	2^359352-179	108176	Lelio R Paula	12/2011
2964	2^359338-1858781	108172	Enzo Doria	04/2016
2965	12^100230-97	108167	Lelio R Paula	03/2017
2966	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2967	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2968	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2969	6^138956-59	108129	Lelio R Paula	02/2017
2970	2^359184+30285	108126	Lelio R Paula	04/2017
2971	13^97059+10	108119	Lelio R Paula	03/2017
2972	2^359137-81	108112	Lelio R Paula	12/2011
2974	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2973	2^359110-11655	108103	Lelio R Paula	04/2017
2975	8*6^138875+5	108067	Lelio R Paula	11/2014
2976	2^358987-216919	108066	Enzo Doria	05/2014
2977	39^67918-67918^39	108062	Norbert Schneider	02/2017
2978	2^358785-16933	108006	Enzo Doria	05/2013
2979	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2980	6^138770-77	107985	Lelio R Paula	02/2017
2981	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2982	10^107976+19	107977	Lelio R Paula	02/2017
2983	10^107976-202103	107976	Patrick De Geest	03/2017
2984	2^358684+75781	107975	Enzo Doria	04/2016
2985	99^54094+2	107952	Lelio R Paula	06/2013
2986	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2987	2^358538+55	107931	Lelio R Paula	12/2011
2988	2^358517-109009	107925	Enzo Doria	03/2014
2989	3^226159+104	107906	Lelio R Paula	03/2017
2990	2^358310-11655	107863	Lelio R Paula	03/2017
2991	2^358275-112987	107852	Enzo Doria	07/2014
2992	2^358233-20005	107839	Enzo Doria	06/2013
2993	2^358194+175	107828	Lelio R Paula	12/2011
2994	107^53125-106	107812	Norbert Schneider	12/2016
2995	3^225922-2	107793	Lelio R Paula	10/2013
2996	12^99874-95	107783	Lelio R Paula	03/2017
2997	2^358030-171	107778	Lelio R Paula	12/2011
2998	11^103488-4170	107772	Enzo Doria	12/2012
2999	2^357930-4547	107748	Yves Minet	03/2019
3000	2^357911-20089	107742	Enzo Doria	06/2013

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)