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 (> 30000)	Who ?	When ?
2751	2^358275-112987	107852	Enzo Doria	07/2014
2752	2^358233-20005	107839	Enzo Doria	06/2013
2753	2^358194+175	107828	Lelio R Paula	12/2011
2754	107^53125-106	107812	Norbert Schneider	12/2016
2755	3^225922-2	107793	Lelio R Paula	10/2013
2756	12^99874-95	107783	Lelio R Paula	03/2017
2757	2^358030-171	107778	Lelio R Paula	12/2011
2758	11^103488-4170	107772	Enzo Doria	12/2012
2759	2^357911-20089	107742	Enzo Doria	06/2013
2760	2^357885+12857	107735	Yves Minet	07/2010
2761	7^127473+40	107728	Lelio R Paula	03/2017
2762	5*2^357850+9	107725	Lelio R Paula	09/2014
2763	2^357786-291191	107705	Enzo Doria	06/2015
2764	18^85798-23	107700	Lelio R Paula	04/2017
2765	2^357688-1854269	107675	Enzo Doria	09/2015
2766	2^357671-112225	107670	Enzo Doria	06/2014
2767	2^357618-21005	107654	Enzo Doria	06/2013
2768	2^357615-17505	107653	Enzo Doria	05/2013
2769	(30^72871-1)/29	107638	Robert Price	12/2011
2770	2^357521+1870217	107625	Enzo Doria	05/2016
2771	2^357477-1203	107612	Lelio R Paula	03/2017
2772	5^153894-18	107568	Lelio R Paula	02/2017
2773	2^357324-69059	107566	Enzo Doria	11/2015
2774	2^357283-869688105	107553	Lelio R Paula	01/2017
2775	2^357280-16805	107552	Enzo Doria	05/2013
2776	10^107547+481719	107548	Patrick De Geest	03/2017
2777	10^107547-47	107547	Lelio R Paula	02/2017
2778	17^87396-32	107537	Lelio R Paula	04/2017
2779	2^357081+107	107493	Lelio R Paula	12/2011
2780	2^357058-3911	107486	Yves Minet	04/2017
2781	3^225274+64	107484	Lelio R Paula	03/2017
2782	18^85619-95	107476	Lelio R Paula	04/2017
2783	3^225248-130	107471	Lelio R Paula	03/2017
2784	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
2785	2^356935-18085	107449	Enzo Doria	05/2013
2786	10^107409+37	107410	Lelio R Paula	02/2017
2787	10^107409-329633	107409	Patrick De Geest	03/2017
2788	2^356787-109027	107404	Enzo Doria	04/2014
2789	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
2790	3*10^107389+77	107390	Robert Price	09/2018
2791	5^153622-42	107378	Lelio R Paula	02/2017
2792	2^356699-97305	107378	Lelio R Paula	03/2017
2793	2^356654+85	107364	Lelio R Paula	11/2011
2794	2^356641-19921	107360	Enzo Doria	06/2013
2795	2^356623-465	107355	Lelio R Paula	03/2017
2796	19^83945-92	107345	Lelio R Paula	02/2017
2797	10^107334+28149	107335	Patrick De Geest	03/2017
2798	10^107334-83	107334	Lelio R Paula	02/2017
2799	2^356518+885	107323	Lelio R Paula	03/2017
2800	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
2801	2^356442-114713	107300	Enzo Doria	04/2015
2802	2^356425+72257	107295	Enzo Doria	04/2016
2803	2^356351-112237	107273	Enzo Doria	06/2014
2805	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
2804	2^356322+74539	107264	Enzo Doria	04/2016
2806	2^356274+1874479	107250	Enzo Doria	06/2016
2807	20^82422-93	107234	Lelio R Paula	02/2017
2808	2^356157-20365	107214	Enzo Doria	06/2013
2809	2^356129-18949	107206	Enzo Doria	05/2013
2810	2^356100-109587	107197	Enzo Doria	04/2014
2811	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
2812	2^355968-64875	107158	Lelio R Paula	01/2017
2813	2^355952+1870321	107153	Enzo Doria	05/2016
2814	2^355915-117	107142	Lelio R Paula	11/2011
2815	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
2816	3^224495-8	107112	Lelio R Paula	12/2013
2817	7^126691-44	107067	Lelio R Paula	03/2017
2818	4^177830-8243	107065	Mike Oakes	02/2011
2819	2^355524-21237	107024	Enzo Doria	06/2013
2820	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
2821	2^355494-19901	107015	Enzo Doria	06/2013
2822	2^355454-869688105	107003	Lelio R Paula	01/2017
2823	2^355366+54615	106976	Lelio R Paula	01/2017
2824	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
2825	2^355275-19861	106949	Enzo Doria	06/2013
2826	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
2827	4*10^106892-3	106893	Robert Price	10/2015
2828	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
2829	2^354946-3	106850	M. Frind & P. Underwood	08/2002
2830	2^354873-18693	106828	Enzo Doria	05/2013
2831	2^354828+4257	106814	Lelio R Paula	01/2017
2832	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
2833	2^354640-354640+1	106758	Robert Price	10/2014
2834	2^354585+95	106741	Lelio R Paula	10/2011
2835	2^354553+189	106732	Lelio R Paula	10/2011
2836	2^354514-109031	106720	Enzo Doria	04/2014
2837	2^354509-109465	106718	Enzo Doria	04/2014
2838	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
2839	15^90710+28	106684	Lelio R Paula	04/2017
2840	7^126237+34	106683	Lelio R Paula	03/2017
2841	2^354385-115315	106681	Enzo Doria	06/2015
2842	2^354327-19305	106664	Enzo Doria	06/2013
2843	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
2844	10^106636+97	106637	Lelio R Paula	02/2017
2845	10^106636-22923	106636	Patrick De Geest	03/2017
2846	2^354220-57	106631	Lelio R Paula	10/2011
2847	2^354157-17041	106612	Enzo Doria	05/2013
2848	12^98778+73	106600	Lelio R Paula	02/2017
2849	2^354064+1870651	106584	Enzo Doria	05/2016
2850	2^353992-57	106563	Lelio R Paula	10/2011
2851	NSW(139160)	106535	Robert Price	12/2018
2852	(7*10^106516+113)/3	106517	Robert Price	02/2018
2853	2^353832-1853849	106515	Enzo Doria	09/2015
2854	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
2855	2^353794-18453	106503	Enzo Doria	05/2013
2856	2^353728+7695	106483	Lelio R Paula	01/2017
2857	2^353672-303	106466	Yves Minet	02/2012
2858	6^136811+101	106460	Lelio R Paula	02/2017
2859	2^353641+1871981	106457	Enzo Doria	05/2016
2860	(8*10^106454-29)/3	106455	Robert Price	07/2018
2861	2^353553+54615	106431	Lelio R Paula	01/2017
2862	2^353544-18897	106428	Enzo Doria	05/2013
2863	6^136729-133	106396	Lelio R Paula	02/2017
2864	2^353418+1605	106390	Lelio R Paula	01/2017
2865	2^353387+65	106381	Lelio R Paula	10/2011
2866	2^353372+74311	106376	Enzo Doria	04/2016
2867	2^353344-3693	106368	Yves Minet	03/2017
2869	2^353277-20089	106347	Enzo Doria	06/2013
2868	2^353275+72173	106347	Enzo Doria	04/2016
2870	2^353268-17705	106345	Enzo Doria	05/2013
2871	2^353267-19857	106344	Enzo Doria	06/2013
2872	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
2873	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
2874	2^353025+72257	106272	Enzo Doria	04/2016
2876	2^352932-20345	106244	Enzo Doria	06/2013
2875	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
2877	2^352883-187	106229	Lelio R Paula	10/2011
2878	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
2879	2^352814-131	106208	Lelio R Paula	10/2011
2880	2^352752+73951	106189	Enzo Doria	04/2016
2881	6^136434+5	106167	Lelio R Paula	11/2014
2882	7*5^151872-8	106155	Lelio R Paula	11/2014
2883	105^52520-2	106153	Lelio R Paula	10/2017
2884	2^352601-1604809	106144	Enzo Doria	05/2015
2885	12^98353-43	106141	Lelio R Paula	02/2017
2886	2^352585-18901	106139	Enzo Doria	05/2013
2887	(2^352554-3)/193	106128	Lelio R Paula	12/2013
2888	2^352540+15015	106126	Lelio R Paula	01/2017
2889	2^352524-3149	106121	Yves Minet	10/2014
2890	2^352486-1858781	106109	Enzo Doria	04/2016
2891	2^352444+12705	106097	Lelio R Paula	01/2017
2892	2^352228-18953	106032	Enzo Doria	05/2013
2893	2^352107+1872533	105995	Enzo Doria	05/2016
2894	2^352066-2591	105983	Yves Minet	07/2014
2895	2^352030+715	105972	Lelio R Paula	10/2011
2896	9*6^136176-5	105967	Lelio R Paula	11/2014
2897	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
2898	155^48377+2	105962	Lelio R Paula	08/2013
2899	2^351865+1869707	105922	Enzo Doria	05/2016
2900	2^351831+23	105912	Lelio R Paula	10/2011
2901	9*2^351784-5	105899	Lelio R Paula	09/2014
2902	2^351671-112387	105864	Enzo Doria	06/2014
2903	2^351669-109501	105863	Enzo Doria	04/2014
2904	2^351644+74731	105856	Enzo Doria	04/2016
2905	13^95025-42	105853	Lelio R Paula	12/2016
2906	2^351599+15015	105842	Lelio R Paula	01/2017
2907	19^82763+90	105834	Lelio R Paula	01/2017
2908	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
2909	20^81329-51	105812	Lelio R Paula	01/2017
2910	(5*10^105811+211)/9	105811	Robert Price	02/2018
2911	2^351483+28425	105807	Lelio R Paula	01/2017
2912	15^89960+86	105802	Lelio R Paula	02/2017
2913	2^351460-17289	105801	Enzo Doria	05/2013
2914	19^82735+22	105798	Lelio R Paula	01/2017
2915	2^351435-109077	105793	Enzo Doria	04/2014
2916	2^351393+1089	105780	Lelio R Paula	01/2017
2917	2^351364+72631	105772	Enzo Doria	04/2016
2918	2^351305+1872467	105754	Enzo Doria	05/2016
2919	3^221649+16	105754	Lelio R Paula	11/2016
2920	8*3^221637-5	105749	Lelio R Paula	09/2014
2921	2^351279-2780449	105746	Enzo Doria	03/2016
2922	15^89903-26	105735	Lelio R Paula	02/2017
2923	2^351213-73	105726	Lelio R Paula	10/2011
2924	2^351192-4589	105720	Yves Minet	07/2011
2925	20^81250-33	105709	Lelio R Paula	12/2016
2926	2^351076-113159	105685	Enzo Doria	07/2014
2927	93^53688-2	105684	Lelio R Paula	09/2013
2928	2^351060-4559	105680	Yves Minet	07/2011
2929	11^101473-750	105674	Enzo Doria	11/2012
2930	3*5^151181-8	105672	Lelio R Paula	11/2014
2931	15^89831-34	105650	Lelio R Paula	02/2017
2933	11^101448-360	105648	Enzo Doria	08/2012
2932	3*7^125011+4	105648	Lelio R Paula	11/2014
2934	2^350943-113269	105645	Enzo Doria	07/2014
2935	2^350868-19725	105622	Enzo Doria	06/2013
2936	2^350858-59291	105619	Enzo Doria	10/2015
2937	2^350851+135	105617	Lelio R Paula	10/2011
2938	2^350841-741	105614	Lelio R Paula	01/2017
2939	3*10^105582+77	105583	Robert Price	09/2018
2940	8*10^105571+3	105572	Robert Price	08/2015
2941	2^350674-78557	105564	Jorge Menendez	03/2018
2942	2*5^151026-3	105563	Lelio R Paula	11/2014
2943	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
2944	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
2945	3^221211+236	105545	Lelio R Paula	11/2016
2946	(32*10^105530-77)/9	105531	Robert Price	06/2018
2947	10^105515+33	105516	Lelio R Paula	11/2016
2948	10^105515-41033	105515	Patrick De Geest	12/2016
2949	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
2950	17^85732-72	105489	Lelio R Paula	01/2017
2951	2^350307-110329	105453	Enzo Doria	05/2014
2952	2^350253-20365	105437	Enzo Doria	06/2013
2953	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
2954	2^350139-109009	105403	Enzo Doria	04/2014
2955	3*5^150763+4	105380	Lelio R Paula	11/2014
2956	12^97643+91	105375	Lelio R Paula	02/2017
2957	6*5^150744-7	105367	Lelio R Paula	11/2014
2958	2^349996-112169	105360	Enzo Doria	06/2014
2959	11^101142-1080	105329	Enzo Doria	12/2012
2960	(68*10^105320-41)/9	105321	Robert Price	10/2013
2961	3^220712-9934	105307	Enzo Doria	05/2014
2962	7*10^105296+9	105297	Robert Price	09/2015
2963	2^349739+1873373	105282	Enzo Doria	06/2016
2964	7^124574+24	105278	Lelio R Paula	11/2016
2965	2^349708-20957	105273	Enzo Doria	06/2013
2966	2^349649-20469	105255	Enzo Doria	06/2013
2967	2^349607-20109	105243	Enzo Doria	06/2013
2968	2^349594-19085	105239	Enzo Doria	05/2013
2969	2^349530+1874479	105220	Enzo Doria	06/2016
2970	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
2971	3^220464-112852	105189	Enzo Doria	07/2014
2972	2^349419-17349	105186	Enzo Doria	05/2013
2973	2^349400-2579	105180	Yves Minet	07/2014
2974	8*5^150471+3	105176	Lelio R Paula	11/2014
2975	655^37342+37342^655	105165	Norbert Schneider	08/2018
2976	13^94403+94	105160	Lelio R Paula	12/2016
2977	2^349301-112309	105151	Enzo Doria	06/2014
2978	9*2^349220+5	105127	Lelio R Paula	09/2014
2979	7*3^220317+8	105119	Lelio R Paula	09/2014
2980	7^124386+88	105119	Lelio R Paula	11/2016
2981	2^349171-19657	105111	Enzo Doria	06/2013
2982	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
2983	(2^349111-5)/3	105093	Lelio R Paula	12/2013
2984	675^37142+37142^675	105087	Norbert Schneider	08/2018
2985	2^348981-2797573	105054	Enzo Doria	04/2016
2986	2^348869-6555	105021	Lelio R Paula	01/2017
2987	5^150217+78	104998	Lelio R Paula	11/2016
2988	2^348703-113005	104971	Enzo Doria	06/2014
2990	2^348612-809	104943	Yves Minet	05/2013
2989	(73*10^104942-1)/9	104943	Robert Price	01/2015
2991	2^348583-350407	104934	Enzo Doria	06/2015
2992	2^348531-949	104919	Yves Minet	05/2012
2993	20^80636-59	104910	Lelio R Paula	12/2016
2994	2^348437+35	104890	Lelio R Paula	09/2011
2995	2^348348+135	104864	Lelio R Paula	09/2011
2997	(2^348284+9)/25	104843	Lelio R Paula	12/2013
2996	75^55914-74	104843	Norbert Schneider	01/2015
2998	2^348268+255255	104840	Lelio R Paula	01/2017
2999	5^149985-52	104836	Lelio R Paula	11/2016
3000	2^348224-20249	104826	Enzo Doria	06/2013

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PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)