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	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2752	2^366716+1871791	110393	Enzo Doria	05/2016
2753	2^366649+1871687	110373	Enzo Doria	05/2016
2754	2^366629-351205	110367	Enzo Doria	06/2015
2755	2^366558+1874479	110345	Enzo Doria	06/2016
2756	18^87853-4409	110280	Enzo Doria	03/2013
2757	2^366218-23	110243	Lelio R Paula	02/2013
2758	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2759	2^366178-343991	110231	Enzo Doria	07/2015
2760	2^365944+1871341	110161	Enzo Doria	05/2016
2761	2^365838-461267	110129	Enzo Doria	07/2015
2762	2^365763-6555	110106	Lelio R Paula	04/2017
2763	(2^365689+2^182845+1)/5	110083		11/2006
2764	2^365666-459161	110077	Enzo Doria	05/2015
2765	3*10^110076-7	110077	Robert Price	08/2015
2766	13^98785-72	110041	Lelio R Paula	03/2017
2767	(25^78707+1)/26	110027	Robert Price	06/2013
2768	(7*10^110006-151)/9	110006	Robert Price	02/2018
2769	6^141361-7	110001	Lelio R Paula	11/2014
2770	20^84536+81	109984	Lelio R Paula	03/2017
2771	5*2^365347-9	109982	Lelio R Paula	09/2014
2772	9*6^141303+7	109957	Lelio R Paula	11/2014
2773	78^58099+77	109929	Norbert Schneider	02/2015
2774	2*10^109928-7	109929	Robert Price	10/2015
2775	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2776	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2777	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2778	18^87533-11	109878	Lelio R Paula	04/2017
2779	2^364982-5	109871	Henri Lifchitz	04/2006
2780	3*10^109861+59	109862	Robert Price	08/2018
2781	2^364936-1867979	109857	Enzo Doria	04/2016
2782	2^364867-112087	109836	Enzo Doria	06/2014
2783	4^182415-85061	109825	Mike Oakes	06/2011
2784	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2785	2^364687-187	109782	Lelio R Paula	01/2012
2786	2^364644+67	109769	Lelio R Paula	01/2012
2787	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2788	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2789	(55*10^109759+89)/9	109760	Robert Price	03/2019
2790	12^101694+73	109747	Lelio R Paula	03/2017
2791	13^98518-66	109744	Lelio R Paula	03/2017
2792	2^364478-113261	109719	Enzo Doria	07/2014
2793	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
2794	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2795	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2796	3^229824+340	109654	Lelio R Paula	03/2017
2797	(2*10^109645-71)/3	109645	Robert Price	12/2017
2798	2^364169-112813	109626	Enzo Doria	06/2014
2799	10^109615+21	109616	Lelio R Paula	03/2017
2800	10^109615-456267	109615	Patrick De Geest	03/2017
2801	2^364094-113	109604	Lelio R Paula	01/2012
2802	(4^182026+11)/3	109591	Robert Price	02/2017
2803	2^364041-6883	109588	Lelio R Paula	09/2011
2804	12^101545+11	109586	Lelio R Paula	03/2017
2805	2^363842-2787101	109528	Enzo Doria	03/2016
2806	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2807	2^363769+5711	109506	Lelio R Paula	04/2017
2808	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2809	p(22245)#/2-8	109462	Robert Price	01/2017
2810	2^363556+55	109442	Lelio R Paula	01/2012
2811	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2812	2^363406+1871569	109397	Enzo Doria	05/2016
2813	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2814	3^229236+100	109374	Lelio R Paula	03/2017
2815	2^363268-58695	109355	Lelio R Paula	04/2017
2816	2^363191-112321	109332	Enzo Doria	06/2014
2817	4*10^109316-63	109317	Robert Price	10/2018
2818	2^363120+3	109311	Donovan Johnson	04/2006
2819	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2820	2^363042-114641	109287	Enzo Doria	04/2015
2821	2^363020-112793	109280	Enzo Doria	06/2014
2822	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2823	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2824	5^156181+38	109166	Lelio R Paula	02/2017
2825	4*10^109142+91	109143	Robert Price	08/2018
2826	3^228750+68	109142	Lelio R Paula	03/2017
2827	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2828	65^60167-64^60167	109078	Robert Price	08/2013
2829	7*3^228589-2	109066	Lelio R Paula	09/2014
2830	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2831	2*7^129008+9	109025	Lelio R Paula	11/2014
2832	(5*10^108960+91)/3	108961	Robert Price	04/2018
2833	2^361957+76367	108960	Enzo Doria	05/2016
2834	2^361873-1411	108935	Yves Minet	01/2013
2835	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2836	115^52842-114	108892	Norbert Schneider	07/2018
2837	13^97745-24	108883	Lelio R Paula	03/2017
2838	17^88475+8	108864	Lelio R Paula	04/2017
2839	2^361567+51	108843	Lelio R Paula	01/2012
2840	2^361563-109501	108842	Enzo Doria	04/2014
2841	12^100852+83	108838	Lelio R Paula	03/2017
2842	2^361497+767	108822	Lelio R Paula	01/2012
2843	2^361280-112349	108757	Enzo Doria	06/2014
2844	2^361271-5955	108754	Lelio R Paula	04/2017
2845	12^100757+19	108736	Lelio R Paula	03/2017
2846	14^94849-61	108710	Lelio R Paula	05/2017
2847	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2848	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2849	2^360973+1299	108664	Lelio R Paula	04/2017
2850	2^360959-109101	108660	Enzo Doria	04/2014
2851	6*5^155454+7	108659	Lelio R Paula	11/2014
2852	10^108656+79	108657	Lelio R Paula	02/2017
2853	10^108656-50001	108656	Patrick De Geest	03/2017
2854	2^360918-35	108648	Lelio R Paula	01/2012
2855	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2856	3*10^108624-49	108625	Robert Price	07/2018
2857	2^360706-458903	108584	Enzo Doria	04/2015
2858	2^360641-113185	108564	Enzo Doria	07/2014
2859	2^360618+75019	108557	Enzo Doria	04/2016
2860	(14*10^108545-221)/9	108546	Robert Price	04/2018
2861	(44*10^108544-233)/9	108545	Robert Price	01/2019
2862	3*5^155286+2	108541	Lelio R Paula	11/2014
2863	7^128422+4	108530	Lelio R Paula	11/2014
2864	7^128421-80	108529	Lelio R Paula	03/2017
2865	2^360497+53807	108521	Yves Minet	07/2010
2866	2^360468-4559	108512	Yves Minet	03/2019
2867	2^360366+1459	108481	Lelio R Paula	09/2011
2868	2^360364-1499	108481	Yves Minet	05/2013
2869	14^94642-23	108472	Lelio R Paula	05/2017
2870	4*10^108412+9	108413	Robert Price	05/2015
2871	133^51042-132	108406	Norbert Schneider	02/2019
2872	2^360093-351103	108399	Enzo Doria	06/2015
2873	2^360042+723	108384	Lelio R Paula	01/2012
2874	85^56164-2	108364	Lelio R Paula	10/2013
2875	2^359937-29323	108352	Enzo Doria	07/2015
2876	2^359898-19997	108341	Enzo Doria	06/2013
2877	2*5^154948-7	108305	Lelio R Paula	11/2014
2878	10^108303+13	108304	Lelio R Paula	02/2017
2879	10^108303-207959	108303	Patrick De Geest	03/2017
2880	2^359730+753	108290	Lelio R Paula	12/2011
2881	(8*10^108273+13)/3	108274	Robert Price	06/2018
2882	2^359650-19797	108266	Enzo Doria	06/2013
2883	91^55259-90^55259	108255	Robert Price	07/2015
2884	4*10^108238-71	108239	Robert Price	12/2018
2885	3^226845+68	108233	Lelio R Paula	03/2017
2886	5^154822-12866	108216	Enzo Doria	05/2014
2887	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2888	2^359454-177	108207	Lelio R Paula	12/2011
2889	(19*10^108184+191)/3	108185	Robert Price	05/2019
2890	6^139022-59	108181	Lelio R Paula	02/2017
2891	(19*10^108176-43)/3	108177	Robert Price	05/2019
2892	2^359352-179	108176	Lelio R Paula	12/2011
2893	2^359338-1858781	108172	Enzo Doria	04/2016
2894	12^100230-97	108167	Lelio R Paula	03/2017
2895	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2896	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2897	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2898	6^138956-59	108129	Lelio R Paula	02/2017
2899	2^359184+30285	108126	Lelio R Paula	04/2017
2900	13^97059+10	108119	Lelio R Paula	03/2017
2901	2^359137-81	108112	Lelio R Paula	12/2011
2903	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2902	2^359110-11655	108103	Lelio R Paula	04/2017
2904	8*6^138875+5	108067	Lelio R Paula	11/2014
2905	2^358987-216919	108066	Enzo Doria	05/2014
2906	39^67918-67918^39	108062	Norbert Schneider	02/2017
2907	2^358785-16933	108006	Enzo Doria	05/2013
2908	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2909	6^138770-77	107985	Lelio R Paula	02/2017
2910	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2911	10^107976+19	107977	Lelio R Paula	02/2017
2912	10^107976-202103	107976	Patrick De Geest	03/2017
2913	2^358684+75781	107975	Enzo Doria	04/2016
2914	99^54094+2	107952	Lelio R Paula	06/2013
2915	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2916	2^358538+55	107931	Lelio R Paula	12/2011
2917	2^358517-109009	107925	Enzo Doria	03/2014
2918	3^226159+104	107906	Lelio R Paula	03/2017
2919	2^358310-11655	107863	Lelio R Paula	03/2017
2920	2^358275-112987	107852	Enzo Doria	07/2014
2921	2^358233-20005	107839	Enzo Doria	06/2013
2922	2^358194+175	107828	Lelio R Paula	12/2011
2923	107^53125-106	107812	Norbert Schneider	12/2016
2924	3^225922-2	107793	Lelio R Paula	10/2013
2925	12^99874-95	107783	Lelio R Paula	03/2017
2926	2^358030-171	107778	Lelio R Paula	12/2011
2927	11^103488-4170	107772	Enzo Doria	12/2012
2928	2^357930-4547	107748	Yves Minet	03/2019
2929	2^357911-20089	107742	Enzo Doria	06/2013
2930	2^357885+12857	107735	Yves Minet	07/2010
2931	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
2932	7^127473+40	107728	Lelio R Paula	03/2017
2933	5*2^357850+9	107725	Lelio R Paula	09/2014
2934	2^357786-291191	107705	Enzo Doria	06/2015
2935	18^85798-23	107700	Lelio R Paula	04/2017
2936	(14*10^107694-83)/3	107695	Robert Price	12/2018
2937	2^357688-1854269	107675	Enzo Doria	09/2015
2938	2^357671-112225	107670	Enzo Doria	06/2014
2939	2^357618-21005	107654	Enzo Doria	06/2013
2940	2^357615-17505	107653	Enzo Doria	05/2013
2941	(30^72871-1)/29	107638	Robert Price	12/2011
2942	2^357521+1870217	107625	Enzo Doria	05/2016
2943	2^357477-1203	107612	Lelio R Paula	03/2017
2944	5^153894-18	107568	Lelio R Paula	02/2017
2945	2^357324-69059	107566	Enzo Doria	11/2015
2946	467^40296+40296^467	107563	Norbert Schneider	03/2019
2947	2^357283-869688105	107553	Lelio R Paula	01/2017
2948	2^357280-16805	107552	Enzo Doria	05/2013
2949	10^107547+481719	107548	Patrick De Geest	03/2017
2950	10^107547-47	107547	Lelio R Paula	02/2017
2951	17^87396-32	107537	Lelio R Paula	04/2017
2952	2^357081+107	107493	Lelio R Paula	12/2011
2953	2^357058-3911	107486	Yves Minet	04/2017
2954	3^225274+64	107484	Lelio R Paula	03/2017
2955	18^85619-95	107476	Lelio R Paula	04/2017
2956	3^225248-130	107471	Lelio R Paula	03/2017
2957	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
2958	2^356935-18085	107449	Enzo Doria	05/2013
2959	10^107409+37	107410	Lelio R Paula	02/2017
2960	10^107409-329633	107409	Patrick De Geest	03/2017
2961	2^356787-109027	107404	Enzo Doria	04/2014
2962	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
2963	3*10^107389+77	107390	Robert Price	09/2018
2964	5^153622-42	107378	Lelio R Paula	02/2017
2965	2^356699-97305	107378	Lelio R Paula	03/2017
2966	2^356654+85	107364	Lelio R Paula	11/2011
2967	2^356641-19921	107360	Enzo Doria	06/2013
2968	2^356623-465	107355	Lelio R Paula	03/2017
2969	19^83945-92	107345	Lelio R Paula	02/2017
2970	10^107334+28149	107335	Patrick De Geest	03/2017
2971	10^107334-83	107334	Lelio R Paula	02/2017
2972	2^356518+885	107323	Lelio R Paula	03/2017
2973	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
2974	2^356442-114713	107300	Enzo Doria	04/2015
2975	2^356425+72257	107295	Enzo Doria	04/2016
2976	2^356351-112237	107273	Enzo Doria	06/2014
2977	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
2978	2^356322+74539	107264	Enzo Doria	04/2016
2979	2^356274+1874479	107250	Enzo Doria	06/2016
2980	20^82422-93	107234	Lelio R Paula	02/2017
2981	2^356157-20365	107214	Enzo Doria	06/2013
2982	2^356129-18949	107206	Enzo Doria	05/2013
2983	2^356100-109587	107197	Enzo Doria	04/2014
2984	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
2985	2^355968-64875	107158	Lelio R Paula	01/2017
2986	2^355952+1870321	107153	Enzo Doria	05/2016
2987	2^355915-117	107142	Lelio R Paula	11/2011
2988	(16*10^107140+77)/3	107141	Robert Price	03/2019
2989	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
2990	3^224495-8	107112	Lelio R Paula	12/2013
2991	7^126691-44	107067	Lelio R Paula	03/2017
2992	4^177830-8243	107065	Mike Oakes	02/2011
2993	2^355524-21237	107024	Enzo Doria	06/2013
2994	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
2995	2^355494-19901	107015	Enzo Doria	06/2013
2996	2^355454-869688105	107003	Lelio R Paula	01/2017
2997	2^355366+54615	106976	Lelio R Paula	01/2017
2998	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
2999	2^355275-19861	106949	Enzo Doria	06/2013
3000	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)