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	2^360706-458903	108584	Enzo Doria	04/2015
2752	2^360641-113185	108564	Enzo Doria	07/2014
2753	2^360618+75019	108557	Enzo Doria	04/2016
2754	(14*10^108545-221)/9	108546	Robert Price	04/2018
2755	(44*10^108544-233)/9	108545	Robert Price	01/2019
2756	3*5^155286+2	108541	Lelio R Paula	11/2014
2757	7^128422+4	108530	Lelio R Paula	11/2014
2758	7^128421-80	108529	Lelio R Paula	03/2017
2759	2^360497+53807	108521	Yves Minet	07/2010
2760	2^360366+1459	108481	Lelio R Paula	09/2011
2761	2^360364-1499	108481	Yves Minet	05/2013
2762	14^94642-23	108472	Lelio R Paula	05/2017
2763	4*10^108412+9	108413	Robert Price	05/2015
2764	2^360093-351103	108399	Enzo Doria	06/2015
2765	2^360042+723	108384	Lelio R Paula	01/2012
2766	85^56164-2	108364	Lelio R Paula	10/2013
2767	2^359937-29323	108352	Enzo Doria	07/2015
2768	2^359898-19997	108341	Enzo Doria	06/2013
2769	2*5^154948-7	108305	Lelio R Paula	11/2014
2770	10^108303+13	108304	Lelio R Paula	02/2017
2771	10^108303-207959	108303	Patrick De Geest	03/2017
2772	2^359730+753	108290	Lelio R Paula	12/2011
2773	(8*10^108273+13)/3	108274	Robert Price	06/2018
2774	2^359650-19797	108266	Enzo Doria	06/2013
2775	91^55259-90^55259	108255	Robert Price	07/2015
2776	4*10^108238-71	108239	Robert Price	12/2018
2777	3^226845+68	108233	Lelio R Paula	03/2017
2778	5^154822-12866	108216	Enzo Doria	05/2014
2779	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
2780	2^359454-177	108207	Lelio R Paula	12/2011
2781	6^139022-59	108181	Lelio R Paula	02/2017
2782	2^359352-179	108176	Lelio R Paula	12/2011
2783	2^359338-1858781	108172	Enzo Doria	04/2016
2784	12^100230-97	108167	Lelio R Paula	03/2017
2785	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
2786	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
2787	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
2788	6^138956-59	108129	Lelio R Paula	02/2017
2789	2^359184+30285	108126	Lelio R Paula	04/2017
2790	13^97059+10	108119	Lelio R Paula	03/2017
2791	2^359137-81	108112	Lelio R Paula	12/2011
2793	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
2792	2^359110-11655	108103	Lelio R Paula	04/2017
2794	8*6^138875+5	108067	Lelio R Paula	11/2014
2795	2^358987-216919	108066	Enzo Doria	05/2014
2796	39^67918-67918^39	108062	Norbert Schneider	02/2017
2797	2^358785-16933	108006	Enzo Doria	05/2013
2798	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
2799	6^138770-77	107985	Lelio R Paula	02/2017
2800	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
2801	10^107976+19	107977	Lelio R Paula	02/2017
2802	10^107976-202103	107976	Patrick De Geest	03/2017
2803	2^358684+75781	107975	Enzo Doria	04/2016
2804	99^54094+2	107952	Lelio R Paula	06/2013
2805	(2^358583-9)/391	107942	Lelio R Paula	12/2013
2806	2^358538+55	107931	Lelio R Paula	12/2011
2807	2^358517-109009	107925	Enzo Doria	03/2014
2808	3^226159+104	107906	Lelio R Paula	03/2017
2809	2^358310-11655	107863	Lelio R Paula	03/2017
2810	2^358275-112987	107852	Enzo Doria	07/2014
2811	2^358233-20005	107839	Enzo Doria	06/2013
2812	2^358194+175	107828	Lelio R Paula	12/2011
2813	107^53125-106	107812	Norbert Schneider	12/2016
2814	3^225922-2	107793	Lelio R Paula	10/2013
2815	12^99874-95	107783	Lelio R Paula	03/2017
2816	2^358030-171	107778	Lelio R Paula	12/2011
2817	11^103488-4170	107772	Enzo Doria	12/2012
2818	2^357911-20089	107742	Enzo Doria	06/2013
2819	2^357885+12857	107735	Yves Minet	07/2010
2820	7^127473+40	107728	Lelio R Paula	03/2017
2821	5*2^357850+9	107725	Lelio R Paula	09/2014
2822	2^357786-291191	107705	Enzo Doria	06/2015
2823	18^85798-23	107700	Lelio R Paula	04/2017
2824	(14*10^107694-83)/3	107695	Robert Price	12/2018
2825	2^357688-1854269	107675	Enzo Doria	09/2015
2826	2^357671-112225	107670	Enzo Doria	06/2014
2827	2^357618-21005	107654	Enzo Doria	06/2013
2828	2^357615-17505	107653	Enzo Doria	05/2013
2829	(30^72871-1)/29	107638	Robert Price	12/2011
2830	2^357521+1870217	107625	Enzo Doria	05/2016
2831	2^357477-1203	107612	Lelio R Paula	03/2017
2832	5^153894-18	107568	Lelio R Paula	02/2017
2833	2^357324-69059	107566	Enzo Doria	11/2015
2834	2^357283-869688105	107553	Lelio R Paula	01/2017
2835	2^357280-16805	107552	Enzo Doria	05/2013
2836	10^107547+481719	107548	Patrick De Geest	03/2017
2837	10^107547-47	107547	Lelio R Paula	02/2017
2838	17^87396-32	107537	Lelio R Paula	04/2017
2839	2^357081+107	107493	Lelio R Paula	12/2011
2840	2^357058-3911	107486	Yves Minet	04/2017
2841	3^225274+64	107484	Lelio R Paula	03/2017
2842	18^85619-95	107476	Lelio R Paula	04/2017
2843	3^225248-130	107471	Lelio R Paula	03/2017
2844	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
2845	2^356935-18085	107449	Enzo Doria	05/2013
2846	10^107409+37	107410	Lelio R Paula	02/2017
2847	10^107409-329633	107409	Patrick De Geest	03/2017
2848	2^356787-109027	107404	Enzo Doria	04/2014
2849	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
2850	3*10^107389+77	107390	Robert Price	09/2018
2851	5^153622-42	107378	Lelio R Paula	02/2017
2852	2^356699-97305	107378	Lelio R Paula	03/2017
2853	2^356654+85	107364	Lelio R Paula	11/2011
2854	2^356641-19921	107360	Enzo Doria	06/2013
2855	2^356623-465	107355	Lelio R Paula	03/2017
2856	19^83945-92	107345	Lelio R Paula	02/2017
2857	10^107334+28149	107335	Patrick De Geest	03/2017
2858	10^107334-83	107334	Lelio R Paula	02/2017
2859	2^356518+885	107323	Lelio R Paula	03/2017
2860	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
2861	2^356442-114713	107300	Enzo Doria	04/2015
2862	2^356425+72257	107295	Enzo Doria	04/2016
2863	2^356351-112237	107273	Enzo Doria	06/2014
2865	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
2864	2^356322+74539	107264	Enzo Doria	04/2016
2866	2^356274+1874479	107250	Enzo Doria	06/2016
2867	20^82422-93	107234	Lelio R Paula	02/2017
2868	2^356157-20365	107214	Enzo Doria	06/2013
2869	2^356129-18949	107206	Enzo Doria	05/2013
2870	2^356100-109587	107197	Enzo Doria	04/2014
2871	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
2872	2^355968-64875	107158	Lelio R Paula	01/2017
2873	2^355952+1870321	107153	Enzo Doria	05/2016
2874	2^355915-117	107142	Lelio R Paula	11/2011
2875	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
2876	3^224495-8	107112	Lelio R Paula	12/2013
2877	7^126691-44	107067	Lelio R Paula	03/2017
2878	4^177830-8243	107065	Mike Oakes	02/2011
2879	2^355524-21237	107024	Enzo Doria	06/2013
2880	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
2881	2^355494-19901	107015	Enzo Doria	06/2013
2882	2^355454-869688105	107003	Lelio R Paula	01/2017
2883	2^355366+54615	106976	Lelio R Paula	01/2017
2884	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
2885	2^355275-19861	106949	Enzo Doria	06/2013
2886	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
2887	4*10^106892-3	106893	Robert Price	10/2015
2888	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
2889	2^354946-3	106850	M. Frind & P. Underwood	08/2002
2890	2^354873-18693	106828	Enzo Doria	05/2013
2891	2^354828+4257	106814	Lelio R Paula	01/2017
2892	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
2893	2^354640-354640+1	106758	Robert Price	10/2014
2894	2^354585+95	106741	Lelio R Paula	10/2011
2895	2^354553+189	106732	Lelio R Paula	10/2011
2896	2^354514-109031	106720	Enzo Doria	04/2014
2897	2^354509-109465	106718	Enzo Doria	04/2014
2898	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
2899	15^90710+28	106684	Lelio R Paula	04/2017
2900	7^126237+34	106683	Lelio R Paula	03/2017
2901	2^354385-115315	106681	Enzo Doria	06/2015
2902	2^354327-19305	106664	Enzo Doria	06/2013
2903	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
2904	10^106636+97	106637	Lelio R Paula	02/2017
2905	10^106636-22923	106636	Patrick De Geest	03/2017
2906	2^354220-57	106631	Lelio R Paula	10/2011
2907	2^354157-17041	106612	Enzo Doria	05/2013
2908	12^98778+73	106600	Lelio R Paula	02/2017
2909	2^354064+1870651	106584	Enzo Doria	05/2016
2910	2^353992-57	106563	Lelio R Paula	10/2011
2911	NSW(139160)	106535	Robert Price	12/2018
2912	(7*10^106516+113)/3	106517	Robert Price	02/2018
2913	2^353832-1853849	106515	Enzo Doria	09/2015
2914	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
2915	2^353794-18453	106503	Enzo Doria	05/2013
2916	2^353728+7695	106483	Lelio R Paula	01/2017
2917	2^353672-303	106466	Yves Minet	02/2012
2918	6^136811+101	106460	Lelio R Paula	02/2017
2919	2^353641+1871981	106457	Enzo Doria	05/2016
2920	(8*10^106454-29)/3	106455	Robert Price	07/2018
2921	2^353553+54615	106431	Lelio R Paula	01/2017
2922	2^353544-18897	106428	Enzo Doria	05/2013
2923	6^136729-133	106396	Lelio R Paula	02/2017
2924	2^353418+1605	106390	Lelio R Paula	01/2017
2925	2^353387+65	106381	Lelio R Paula	10/2011
2926	2^353372+74311	106376	Enzo Doria	04/2016
2927	2^353344-3693	106368	Yves Minet	03/2017
2928	2^353277-20089	106347	Enzo Doria	06/2013
2929	2^353275+72173	106347	Enzo Doria	04/2016
2930	2^353268-17705	106345	Enzo Doria	05/2013
2931	2^353267-19857	106344	Enzo Doria	06/2013
2932	(46*10^106343+143)/9	106344	Robert Price	01/2019
2933	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
2934	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
2935	2^353025+72257	106272	Enzo Doria	04/2016
2937	2^352932-20345	106244	Enzo Doria	06/2013
2936	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
2938	2^352883-187	106229	Lelio R Paula	10/2011
2939	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
2940	2^352814-131	106208	Lelio R Paula	10/2011
2941	2^352752+73951	106189	Enzo Doria	04/2016
2942	6^136434+5	106167	Lelio R Paula	11/2014
2943	7*5^151872-8	106155	Lelio R Paula	11/2014
2944	105^52520-2	106153	Lelio R Paula	10/2017
2945	2^352601-1604809	106144	Enzo Doria	05/2015
2946	12^98353-43	106141	Lelio R Paula	02/2017
2947	2^352585-18901	106139	Enzo Doria	05/2013
2948	(2^352554-3)/193	106128	Lelio R Paula	12/2013
2949	2^352540+15015	106126	Lelio R Paula	01/2017
2950	2^352524-3149	106121	Yves Minet	10/2014
2951	2^352486-1858781	106109	Enzo Doria	04/2016
2952	2^352444+12705	106097	Lelio R Paula	01/2017
2953	2^352228-18953	106032	Enzo Doria	05/2013
2954	2^352107+1872533	105995	Enzo Doria	05/2016
2955	2^352066-2591	105983	Yves Minet	07/2014
2956	2^352030+715	105972	Lelio R Paula	10/2011
2957	9*6^136176-5	105967	Lelio R Paula	11/2014
2958	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
2959	155^48377+2	105962	Lelio R Paula	08/2013
2960	2^351865+1869707	105922	Enzo Doria	05/2016
2961	2^351831+23	105912	Lelio R Paula	10/2011
2962	9*2^351784-5	105899	Lelio R Paula	09/2014
2963	2^351671-112387	105864	Enzo Doria	06/2014
2964	2^351669-109501	105863	Enzo Doria	04/2014
2965	2^351644+74731	105856	Enzo Doria	04/2016
2966	13^95025-42	105853	Lelio R Paula	12/2016
2967	2^351599+15015	105842	Lelio R Paula	01/2017
2968	19^82763+90	105834	Lelio R Paula	01/2017
2969	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
2970	20^81329-51	105812	Lelio R Paula	01/2017
2971	(5*10^105811+211)/9	105811	Robert Price	02/2018
2972	2^351483+28425	105807	Lelio R Paula	01/2017
2973	15^89960+86	105802	Lelio R Paula	02/2017
2974	2^351460-17289	105801	Enzo Doria	05/2013
2975	19^82735+22	105798	Lelio R Paula	01/2017
2976	2^351435-109077	105793	Enzo Doria	04/2014
2977	2^351393+1089	105780	Lelio R Paula	01/2017
2978	2^351364+72631	105772	Enzo Doria	04/2016
2979	2^351305+1872467	105754	Enzo Doria	05/2016
2980	3^221649+16	105754	Lelio R Paula	11/2016
2981	8*3^221637-5	105749	Lelio R Paula	09/2014
2982	2^351279-2780449	105746	Enzo Doria	03/2016
2983	15^89903-26	105735	Lelio R Paula	02/2017
2984	2^351213-73	105726	Lelio R Paula	10/2011
2985	2^351192-4589	105720	Yves Minet	07/2011
2986	20^81250-33	105709	Lelio R Paula	12/2016
2987	2^351076-113159	105685	Enzo Doria	07/2014
2988	93^53688-2	105684	Lelio R Paula	09/2013
2989	2^351060-4559	105680	Yves Minet	07/2011
2990	11^101473-750	105674	Enzo Doria	11/2012
2991	3*5^151181-8	105672	Lelio R Paula	11/2014
2992	15^89831-34	105650	Lelio R Paula	02/2017
2994	11^101448-360	105648	Enzo Doria	08/2012
2993	3*7^125011+4	105648	Lelio R Paula	11/2014
2995	2^350943-113269	105645	Enzo Doria	07/2014
2996	2^350868-19725	105622	Enzo Doria	06/2013
2997	2^350858-59291	105619	Enzo Doria	10/2015
2998	2^350851+135	105617	Lelio R Paula	10/2011
2999	2^350841-741	105614	Lelio R Paula	01/2017
3000	3*10^105582+77	105583	Robert Price	09/2018

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)