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	2^364094-113	109604	Lelio R Paula	01/2012
2752	(4^182026+11)/3	109591	Robert Price	02/2017
2753	2^364041-6883	109588	Lelio R Paula	09/2011
2754	12^101545+11	109586	Lelio R Paula	03/2017
2755	2^363842-2787101	109528	Enzo Doria	03/2016
2756	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2757	2^363769+5711	109506	Lelio R Paula	04/2017
2758	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2759	p(22245)#/2-8	109462	Robert Price	01/2017
2760	2^363556+55	109442	Lelio R Paula	01/2012
2761	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2762	2^363406+1871569	109397	Enzo Doria	05/2016
2763	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2764	3^229236+100	109374	Lelio R Paula	03/2017
2765	2^363268-58695	109355	Lelio R Paula	04/2017
2766	2^363191-112321	109332	Enzo Doria	06/2014
2767	4*10^109316-63	109317	Robert Price	10/2018
2768	2^363120+3	109311	Donovan Johnson	04/2006
2769	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2770	2^363042-114641	109287	Enzo Doria	04/2015
2771	2^363020-112793	109280	Enzo Doria	06/2014
2772	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2773	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2774	5^156181+38	109166	Lelio R Paula	02/2017
2775	4*10^109142+91	109143	Robert Price	08/2018
2776	3^228750+68	109142	Lelio R Paula	03/2017
2777	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2778	65^60167-64^60167	109078	Robert Price	08/2013
2779	7*3^228589-2	109066	Lelio R Paula	09/2014
2780	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2781	2*7^129008+9	109025	Lelio R Paula	11/2014
2782	(5*10^108960+91)/3	108961	Robert Price	04/2018
2783	2^361957+76367	108960	Enzo Doria	05/2016
2784	2^361873-1411	108935	Yves Minet	01/2013
2785	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2786	115^52842-114	108892	Norbert Schneider	07/2018
2787	13^97745-24	108883	Lelio R Paula	03/2017
2788	17^88475+8	108864	Lelio R Paula	04/2017
2789	2^361567+51	108843	Lelio R Paula	01/2012
2790	2^361563-109501	108842	Enzo Doria	04/2014
2791	12^100852+83	108838	Lelio R Paula	03/2017
2792	2^361497+767	108822	Lelio R Paula	01/2012
2793	2^361280-112349	108757	Enzo Doria	06/2014
2794	2^361271-5955	108754	Lelio R Paula	04/2017
2795	12^100757+19	108736	Lelio R Paula	03/2017
2796	14^94849-61	108710	Lelio R Paula	05/2017
2797	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2798	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2799	2^360973+1299	108664	Lelio R Paula	04/2017
2800	2^360959-109101	108660	Enzo Doria	04/2014
2801	6*5^155454+7	108659	Lelio R Paula	11/2014
2802	10^108656+79	108657	Lelio R Paula	02/2017
2803	10^108656-50001	108656	Patrick De Geest	03/2017
2804	2^360918-35	108648	Lelio R Paula	01/2012
2805	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2806	3*10^108624-49	108625	Robert Price	07/2018
2807	2^360706-458903	108584	Enzo Doria	04/2015
2808	2^360641-113185	108564	Enzo Doria	07/2014
2809	2^360618+75019	108557	Enzo Doria	04/2016
2810	(14*10^108545-221)/9	108546	Robert Price	04/2018
2811	(44*10^108544-233)/9	108545	Robert Price	01/2019
2812	3*5^155286+2	108541	Lelio R Paula	11/2014
2813	7^128422+4	108530	Lelio R Paula	11/2014
2814	7^128421-80	108529	Lelio R Paula	03/2017
2815	2^360497+53807	108521	Yves Minet	07/2010
2816	2^360468-4559	108512	Yves Minet	03/2019
2818	2^360366+1459	108481	Lelio R Paula	09/2011
2817	2^360364-1499	108481	Yves Minet	05/2013
2819	14^94642-23	108472	Lelio R Paula	05/2017
2820	4*10^108412+9	108413	Robert Price	05/2015
2821	133^51042-132	108406	Norbert Schneider	02/2019
2822	2^360093-351103	108399	Enzo Doria	06/2015
2823	2^360042+723	108384	Lelio R Paula	01/2012
2824	85^56164-2	108364	Lelio R Paula	10/2013
2825	2^359937-29323	108352	Enzo Doria	07/2015
2826	2^359898-19997	108341	Enzo Doria	06/2013
2827	2*5^154948-7	108305	Lelio R Paula	11/2014
2828	10^108303+13	108304	Lelio R Paula	02/2017
2829	10^108303-207959	108303	Patrick De Geest	03/2017
2830	2^359730+753	108290	Lelio R Paula	12/2011
2831	(8*10^108273+13)/3	108274	Robert Price	06/2018
2832	2^359650-19797	108266	Enzo Doria	06/2013
2833	91^55259-90^55259	108255	Robert Price	07/2015
2834	4*10^108238-71	108239	Robert Price	12/2018
2835	3^226845+68	108233	Lelio R Paula	03/2017
2836	5^154822-12866	108216	Enzo Doria	05/2014
2837	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2838	2^359454-177	108207	Lelio R Paula	12/2011
2839	6^139022-59	108181	Lelio R Paula	02/2017
2840	2^359352-179	108176	Lelio R Paula	12/2011
2841	2^359338-1858781	108172	Enzo Doria	04/2016
2842	12^100230-97	108167	Lelio R Paula	03/2017
2843	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2844	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2845	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2846	6^138956-59	108129	Lelio R Paula	02/2017
2847	2^359184+30285	108126	Lelio R Paula	04/2017
2848	13^97059+10	108119	Lelio R Paula	03/2017
2849	2^359137-81	108112	Lelio R Paula	12/2011
2851	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2850	2^359110-11655	108103	Lelio R Paula	04/2017
2852	8*6^138875+5	108067	Lelio R Paula	11/2014
2853	2^358987-216919	108066	Enzo Doria	05/2014
2854	39^67918-67918^39	108062	Norbert Schneider	02/2017
2855	2^358785-16933	108006	Enzo Doria	05/2013
2856	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2857	6^138770-77	107985	Lelio R Paula	02/2017
2858	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2859	10^107976+19	107977	Lelio R Paula	02/2017
2860	10^107976-202103	107976	Patrick De Geest	03/2017
2861	2^358684+75781	107975	Enzo Doria	04/2016
2862	99^54094+2	107952	Lelio R Paula	06/2013
2863	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2864	2^358538+55	107931	Lelio R Paula	12/2011
2865	2^358517-109009	107925	Enzo Doria	03/2014
2866	3^226159+104	107906	Lelio R Paula	03/2017
2867	2^358310-11655	107863	Lelio R Paula	03/2017
2868	2^358275-112987	107852	Enzo Doria	07/2014
2869	2^358233-20005	107839	Enzo Doria	06/2013
2870	2^358194+175	107828	Lelio R Paula	12/2011
2871	107^53125-106	107812	Norbert Schneider	12/2016
2872	3^225922-2	107793	Lelio R Paula	10/2013
2873	12^99874-95	107783	Lelio R Paula	03/2017
2874	2^358030-171	107778	Lelio R Paula	12/2011
2875	11^103488-4170	107772	Enzo Doria	12/2012
2876	2^357930-4547	107748	Yves Minet	03/2019
2877	2^357911-20089	107742	Enzo Doria	06/2013
2878	2^357885+12857	107735	Yves Minet	07/2010
2879	7^127473+40	107728	Lelio R Paula	03/2017
2880	5*2^357850+9	107725	Lelio R Paula	09/2014
2881	2^357786-291191	107705	Enzo Doria	06/2015
2882	18^85798-23	107700	Lelio R Paula	04/2017
2883	(14*10^107694-83)/3	107695	Robert Price	12/2018
2884	2^357688-1854269	107675	Enzo Doria	09/2015
2885	2^357671-112225	107670	Enzo Doria	06/2014
2886	2^357618-21005	107654	Enzo Doria	06/2013
2887	2^357615-17505	107653	Enzo Doria	05/2013
2888	(30^72871-1)/29	107638	Robert Price	12/2011
2889	2^357521+1870217	107625	Enzo Doria	05/2016
2890	2^357477-1203	107612	Lelio R Paula	03/2017
2891	5^153894-18	107568	Lelio R Paula	02/2017
2892	2^357324-69059	107566	Enzo Doria	11/2015
2893	467^40296+40296^467	107563	Norbert Schneider	03/2019
2894	2^357283-869688105	107553	Lelio R Paula	01/2017
2895	2^357280-16805	107552	Enzo Doria	05/2013
2896	10^107547+481719	107548	Patrick De Geest	03/2017
2897	10^107547-47	107547	Lelio R Paula	02/2017
2898	17^87396-32	107537	Lelio R Paula	04/2017
2899	2^357081+107	107493	Lelio R Paula	12/2011
2900	2^357058-3911	107486	Yves Minet	04/2017
2901	3^225274+64	107484	Lelio R Paula	03/2017
2902	18^85619-95	107476	Lelio R Paula	04/2017
2903	3^225248-130	107471	Lelio R Paula	03/2017
2904	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
2905	2^356935-18085	107449	Enzo Doria	05/2013
2906	10^107409+37	107410	Lelio R Paula	02/2017
2907	10^107409-329633	107409	Patrick De Geest	03/2017
2908	2^356787-109027	107404	Enzo Doria	04/2014
2909	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
2910	3*10^107389+77	107390	Robert Price	09/2018
2911	5^153622-42	107378	Lelio R Paula	02/2017
2912	2^356699-97305	107378	Lelio R Paula	03/2017
2913	2^356654+85	107364	Lelio R Paula	11/2011
2914	2^356641-19921	107360	Enzo Doria	06/2013
2915	2^356623-465	107355	Lelio R Paula	03/2017
2916	19^83945-92	107345	Lelio R Paula	02/2017
2917	10^107334+28149	107335	Patrick De Geest	03/2017
2918	10^107334-83	107334	Lelio R Paula	02/2017
2919	2^356518+885	107323	Lelio R Paula	03/2017
2920	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
2921	2^356442-114713	107300	Enzo Doria	04/2015
2922	2^356425+72257	107295	Enzo Doria	04/2016
2923	2^356351-112237	107273	Enzo Doria	06/2014
2924	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
2925	2^356322+74539	107264	Enzo Doria	04/2016
2926	2^356274+1874479	107250	Enzo Doria	06/2016
2927	20^82422-93	107234	Lelio R Paula	02/2017
2928	2^356157-20365	107214	Enzo Doria	06/2013
2929	2^356129-18949	107206	Enzo Doria	05/2013
2930	2^356100-109587	107197	Enzo Doria	04/2014
2931	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
2932	2^355968-64875	107158	Lelio R Paula	01/2017
2933	2^355952+1870321	107153	Enzo Doria	05/2016
2934	2^355915-117	107142	Lelio R Paula	11/2011
2935	(16*10^107140+77)/3	107141	Robert Price	03/2019
2936	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
2937	3^224495-8	107112	Lelio R Paula	12/2013
2938	7^126691-44	107067	Lelio R Paula	03/2017
2939	4^177830-8243	107065	Mike Oakes	02/2011
2940	2^355524-21237	107024	Enzo Doria	06/2013
2941	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
2942	2^355494-19901	107015	Enzo Doria	06/2013
2943	2^355454-869688105	107003	Lelio R Paula	01/2017
2944	2^355366+54615	106976	Lelio R Paula	01/2017
2945	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
2946	2^355275-19861	106949	Enzo Doria	06/2013
2947	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
2948	4*10^106892-3	106893	Robert Price	10/2015
2949	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
2950	2^354946-3	106850	M. Frind & P. Underwood	08/2002
2951	2^354873-18693	106828	Enzo Doria	05/2013
2952	2^354828+4257	106814	Lelio R Paula	01/2017
2953	436^40459+40459^436	106791	Norbert Schneider	03/2019
2954	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
2955	2^354640-354640+1	106758	Robert Price	10/2014
2956	2^354585+95	106741	Lelio R Paula	10/2011
2957	2^354553+189	106732	Lelio R Paula	10/2011
2958	2^354514-109031	106720	Enzo Doria	04/2014
2959	2^354509-109465	106718	Enzo Doria	04/2014
2960	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
2961	15^90710+28	106684	Lelio R Paula	04/2017
2962	7^126237+34	106683	Lelio R Paula	03/2017
2963	2^354385-115315	106681	Enzo Doria	06/2015
2964	2^354327-19305	106664	Enzo Doria	06/2013
2965	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
2966	10^106636+97	106637	Lelio R Paula	02/2017
2967	10^106636-22923	106636	Patrick De Geest	03/2017
2968	2^354220-57	106631	Lelio R Paula	10/2011
2969	2^354157-17041	106612	Enzo Doria	05/2013
2970	12^98778+73	106600	Lelio R Paula	02/2017
2971	2^354064+1870651	106584	Enzo Doria	05/2016
2972	2^353992-57	106563	Lelio R Paula	10/2011
2973	NSW(139160)	106535	Robert Price	12/2018
2974	(7*10^106516+113)/3	106517	Robert Price	02/2018
2975	2^353832-1853849	106515	Enzo Doria	09/2015
2976	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
2977	2^353794-18453	106503	Enzo Doria	05/2013
2978	2^353728+7695	106483	Lelio R Paula	01/2017
2979	2^353672-303	106466	Yves Minet	02/2012
2980	6^136811+101	106460	Lelio R Paula	02/2017
2981	2^353641+1871981	106457	Enzo Doria	05/2016
2982	(8*10^106454-29)/3	106455	Robert Price	07/2018
2983	2^353553+54615	106431	Lelio R Paula	01/2017
2984	2^353544-18897	106428	Enzo Doria	05/2013
2985	6^136729-133	106396	Lelio R Paula	02/2017
2986	2^353418+1605	106390	Lelio R Paula	01/2017
2987	2^353387+65	106381	Lelio R Paula	10/2011
2988	2^353372+74311	106376	Enzo Doria	04/2016
2989	2^353344-3693	106368	Yves Minet	03/2017
2990	2^353277-20089	106347	Enzo Doria	06/2013
2991	2^353275+72173	106347	Enzo Doria	04/2016
2992	2^353268-17705	106345	Enzo Doria	05/2013
2993	2^353267-19857	106344	Enzo Doria	06/2013
2994	(46*10^106343+143)/9	106344	Robert Price	01/2019
2995	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
2996	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
2997	2^353025+72257	106272	Enzo Doria	04/2016
2999	2^352932-20345	106244	Enzo Doria	06/2013
2998	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
3000	2^352883-187	106229	Lelio R Paula	10/2011

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)