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	2^349607-20109	105243	Enzo Doria	06/2013
2752	2^349594-19085	105239	Enzo Doria	05/2013
2753	2^349530+1874479	105220	Enzo Doria	06/2016
2754	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
2755	3^220464-112852	105189	Enzo Doria	07/2014
2756	2^349419-17349	105186	Enzo Doria	05/2013
2757	2^349400-2579	105180	Yves Minet	07/2014
2758	8*5^150471+3	105176	Lelio R Paula	11/2014
2759	13^94403+94	105160	Lelio R Paula	12/2016
2760	2^349301-112309	105151	Enzo Doria	06/2014
2761	9*2^349220+5	105127	Lelio R Paula	09/2014
2762	7*3^220317+8	105119	Lelio R Paula	09/2014
2763	7^124386+88	105119	Lelio R Paula	11/2016
2764	2^349171-19657	105111	Enzo Doria	06/2013
2765	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
2766	(2^349111-5)/3	105093	Lelio R Paula	12/2013
2767	2^348981-2797573	105054	Enzo Doria	04/2016
2768	2^348869-6555	105021	Lelio R Paula	01/2017
2769	5^150217+78	104998	Lelio R Paula	11/2016
2770	2^348703-113005	104971	Enzo Doria	06/2014
2772	2^348612-809	104943	Yves Minet	05/2013
2771	(73*10^104942-1)/9	104943	Robert Price	01/2015
2773	2^348583-350407	104934	Enzo Doria	06/2015
2774	2^348531-949	104919	Yves Minet	05/2012
2775	20^80636-59	104910	Lelio R Paula	12/2016
2776	2^348437+35	104890	Lelio R Paula	09/2011
2777	2^348348+135	104864	Lelio R Paula	09/2011
2778	(2^348284+9)/25	104843	Lelio R Paula	12/2013
2779	75^55914-74	104843	Norbert Schneider	01/2015
2780	2^348268+255255	104840	Lelio R Paula	01/2017
2781	5^149985-52	104836	Lelio R Paula	11/2016
2782	2^348224-20249	104826	Enzo Doria	06/2013
2783	2^348212-20105	104823	Enzo Doria	06/2013
2784	20^80562+19	104814	Lelio R Paula	12/2016
2785	2*10^104811-87	104812	Robert Price	04/2018
2786	2^348149-20053	104804	Enzo Doria	06/2013
2787	2^348095-171	104788	Lelio R Paula	09/2011
2788	2^348003-20377	104760	Enzo Doria	06/2013
2789	2^347994-741	104757	Lelio R Paula	12/2016
2790	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
2791	2^347910-109937	104732	Enzo Doria	04/2014
2792	5^149794+28	104702	Lelio R Paula	11/2016
2793	105^51800-2	104698	Lelio R Paula	10/2017
2794	(16^86939+3^86939)/19	104684	Robert Price	06/2013
2795	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
2796	2^347731-18609	104678	Enzo Doria	05/2013
2797	4*6^134519+7	104677	Lelio R Paula	11/2014
2798	2^347612-18545	104642	Enzo Doria	05/2013
2799	6^134465+95	104635	Lelio R Paula	11/2016
2800	2^347517-17301	104614	Enzo Doria	05/2013
2801	3^219222-310	104596	Lelio R Paula	11/2016
2802	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
2803	2^347372-17853	104570	Enzo Doria	05/2013
2804	2^347314+99	104552	Lelio R Paula	09/2011
2805	2^347300-22233	104548	Enzo Doria	06/2013
2806	2^347287-19845	104544	Enzo Doria	06/2013
2807	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
2808	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
2809	7*2^347239-3	104531	Lelio R Paula	09/2014
2810	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
2811	5*3^219047+8	104513	Lelio R Paula	09/2014
2812	2^347148-109073	104502	Enzo Doria	04/2014
2813	2^347129-20145	104497	Enzo Doria	06/2013
2814	2^346923-19585	104435	Enzo Doria	05/2013
2815	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
2816	2^346854+346854^2+1	104414	Robert Price	06/2014
2817	2^346834+11715	104408	Lelio R Paula	04/2015
2818	79^55009+78	104387	Norbert Schneider	02/2015
2819	3^218744+58	104368	Lelio R Paula	11/2016
2820	2^346649+65	104352	Lelio R Paula	09/2011
2821	2^346638-17265	104349	Enzo Doria	05/2013
2823	2^346527-111817	104316	Enzo Doria	05/2014
2822	6^134055+101	104316	Lelio R Paula	11/2016
2824	6^134013+163	104283	Lelio R Paula	11/2016
2825	18^83049-89	104250	Lelio R Paula	01/2017
2826	2^346213+484049	104221	Enzo Doria	04/2017
2827	18^83021-91	104214	Lelio R Paula	01/2017
2828	10^104212+128779	104213	Patrick De Geest	05/2016
2829	10^104212+237447	104213	Patrick De Geest	05/2016
2830	10^104212+242139	104213	Patrick De Geest	05/2016
2831	10^104212+269199	104213	Patrick De Geest	05/2016
2832	(10^104212-71)/1	104212	Serge Batalov	12/2014
2833	2^346078+7695	104180	Lelio R Paula	12/2016
2834	2^346055-19537	104173	Enzo Doria	05/2013
2835	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
2836	2^346037-20125	104168	Enzo Doria	06/2013
2837	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
2838	6^133854-17993	104159	Enzo Doria	03/2013
2839	2^345990+1874239	104154	Enzo Doria	06/2016
2840	2^345988-20373	104153	Enzo Doria	06/2013
2841	3*5^148968+8	104125	Lelio R Paula	11/2014
2842	p(21253)#/2+8	104113	Robert Price	01/2017
2843	322^41507+41507^322	104094	Norbert Schneider	12/2014
2844	6^133768-17423	104092	Enzo Doria	03/2013
2845	2^345786-19557	104092	Enzo Doria	05/2013
2846	171^46606-2	104072	Lelio R Paula	10/2017
2847	2^345704-149	104068	Lelio R Paula	09/2011
2848	6^133704-17273	104042	Enzo Doria	02/2013
2849	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
2850	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
2851	2^345547+11	104021	Lelio R Paula	09/2011
2852	2^345504+723	104008	Lelio R Paula	09/2011
2853	2^345498-20037	104006	Enzo Doria	06/2013
2854	18^82854-37	104005	Lelio R Paula	01/2017
2855	2^345486-109065	104002	Enzo Doria	04/2014
2856	2^345487-1851507	104002	Enzo Doria	08/2015
2857	2^345476+777	103999	Lelio R Paula	09/2011
2858	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
2859	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
2860	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
2861	2^345106-112181	103888	Enzo Doria	06/2014
2862	2^345079+99	103880	Lelio R Paula	09/2011
2863	11^99736-1500	103865	Enzo Doria	12/2012
2864	2^344842-20157	103808	Enzo Doria	06/2013
2865	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
2866	2^344802-20765	103796	Enzo Doria	06/2013
2867	2^344794-3821	103794	Yves Minet	05/2011
2868	2^344782-109103	103790	Enzo Doria	04/2014
2869	3^217521-112292	103784	Enzo Doria	06/2014
2870	2^344759-3505	103783	Lelio R Paula	11/2016
2871	2^344735-147	103776	Lelio R Paula	09/2011
2872	L(496533)-p(496533)	103770	Robert Price	02/2018
2873	2*10^103749-69	103750	Robert Price	03/2018
2874	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
2875	2^344607-108891	103738	Enzo Doria	03/2014
2876	2^344541-19561	103718	Enzo Doria	05/2013
2877	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
2878	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
2879	2^344444-455	103688	Yves Minet	03/2012
2880	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
2881	2^344317-109933	103650	Enzo Doria	04/2014
2882	2^344309-1852033	103648	Enzo Doria	08/2015
2883	2^344213-21253	103619	Enzo Doria	06/2013
2884	2^344196-465	103614	Lelio R Paula	11/2016
2885	2^344187-20001	103611	Enzo Doria	06/2013
2886	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
2887	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
2888	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
2889	2^344085-20365	103580	Enzo Doria	06/2013
2890	5^148169+54	103566	Lelio R Paula	11/2016
2891	2^344017-108795	103560	Enzo Doria	03/2014
2892	2^343971-5077	103546	Lelio R Paula	09/2011
2893	2^343899+141	103524	Lelio R Paula	08/2011
2894	6^133029-67	103517	Lelio R Paula	11/2016
2895	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
2896	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
2897	5^148014-24	103458	Lelio R Paula	11/2016
2898	2^343604+9931	103436	Yves Minet	01/2011
2899	2^343601-21189	103435	Enzo Doria	06/2013
2900	2^343508-115229	103407	Enzo Doria	06/2015
2901	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
2902	3^216685-113056	103386	Enzo Doria	07/2014
2903	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
2904	11^99262-20	103371	Lelio R Paula	12/2016
2905	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
2906	2^343356-2791889	103361	Enzo Doria	03/2016
2907	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
2908	2^343182-171	103309	Lelio R Paula	08/2011
2909	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
2910	2^343079-1835611	103278	Enzo Doria	05/2015
2911	2^343063-1147	103273	Yves Minet	06/2013
2912	9*6^132689+7	103254	Lelio R Paula	11/2014
2913	2^342979-18085	103247	Enzo Doria	05/2013
2914	2^342966-16995	103244	Lelio R Paula	11/2016
2915	5^147650+16	103203	Lelio R Paula	11/2016
2916	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
2917	2^342817+2707067	103199	Enzo Doria	03/2016
2918	43^63177-42	103198	Theodore Burton	02/2007
2919	2^342805-21025	103195	Enzo Doria	06/2013
2920	2^342714+12285	103168	Lelio R Paula	11/2016
2921	18^82178-4481	103156	Enzo Doria	03/2013
2922	2^342665-17349	103153	Enzo Doria	05/2013
2923	2^342612+175	103137	Lelio R Paula	08/2011
2924	5*2^342585-3	103130	Lelio R Paula	09/2014
2925	2^342503-19209	103104	Enzo Doria	05/2013
2926	2^342476+51	103096	Lelio R Paula	08/2011
2927	2^342460-18885	103091	Enzo Doria	05/2013
2928	7^121968+82	103075	Lelio R Paula	10/2016
2929	2^342392-108863	103071	Enzo Doria	03/2014
2930	3^216014+28	103065	Lelio R Paula	11/2016
2931	2^342353-108879	103059	Enzo Doria	03/2014
2932	10^103055+276081	103056	Patrick De Geest	12/2016
2933	10^103055-53	103055	Lelio R Paula	11/2016
2934	7^121933+4	103046	Lelio R Paula	11/2014
2935	19^80560-68	103017	Lelio R Paula	10/2016
2936	2^342209+76607	103016	Enzo Doria	05/2016
2938	328^40945+40945^328	103013	Norbert Schneider	12/2014
2937	12^95454-91	103013	Lelio R Paula	10/2016
2939	65^56809-64^56809	102990	Robert Price	08/2013
2940	5^147338-6	102985	Lelio R Paula	11/2014
2941	2^342084-112739	102978	Enzo Doria	06/2014
2942	9*6^132330+7	102974	Lelio R Paula	11/2014
2943	2^342034-16737	102963	Enzo Doria	05/2013
2944	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
2945	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
2946	2^341991-17421	102950	Enzo Doria	05/2013
2947	2^341969-112225	102943	Enzo Doria	06/2014
2948	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
2949	2^341859+1869413	102910	Enzo Doria	05/2016
2950	10^102909+61	102910	Lelio R Paula	11/2016
2951	10^102909-67049	102909	Patrick De Geest	12/2016
2952	2^341659+1836773	102850	Enzo Doria	03/2016
2953	2^341608-110639	102835	Enzo Doria	05/2014
2954	10^102824+49	102825	Lelio R Paula	11/2016
2955	10^102824-168011	102824	Patrick De Geest	12/2016
2956	11^98708-8	102794	Lelio R Paula	10/2016
2957	2^341466+4429	102792	Lelio R Paula	09/2011
2958	2^341460-107	102790	Lelio R Paula	08/2011
2959	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
2960	2^341355+21	102759	Lelio R Paula	08/2011
2961	2^341246+40755	102726	Lelio R Paula	11/2016
2962	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
2963	7^121547+78	102720	Lelio R Paula	10/2016
2964	2^341223-461197	102719	Enzo Doria	06/2015
2965	2^341190-20577	102709	Enzo Doria	06/2013
2966	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
2967	6^131976-65	102698	Lelio R Paula	10/2016
2968	2^341134+2533	102692	Henri Lifchitz	09/2005
2969	13^92184-54	102688	Lelio R Paula	10/2016
2970	2^341116-20873	102687	Enzo Doria	06/2013
2971	2^341094-19953	102680	Enzo Doria	06/2013
2972	2^341053+129	102668	Lelio R Paula	08/2011
2973	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
2974	7^121471+94	102655	Lelio R Paula	10/2016
2976	2^341004-173	102653	Lelio R Paula	08/2011
2975	20^78901+3	102653	Lelio R Paula	10/2016
2977	5^146853-52	102646	Lelio R Paula	10/2016
2978	2^340969-216931	102642	Enzo Doria	05/2014
2979	2^340952+1870021	102637	Enzo Doria	05/2016
2980	5*2^340940-3	102634	Lelio R Paula	08/2014
2981	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
2982	(4*10^102612+83)/3	102613	Robert Price	02/2018
2983	75^54717+74	102598	Norbert Schneider	01/2015
2984	2^340806-20393	102593	Enzo Doria	06/2013
2985	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
2986	6^131821+77	102577	Lelio R Paula	10/2016
2987	2^340688-29	102558	Henri Lifchitz	05/2005
2988	2^340685-109101	102557	Enzo Doria	04/2014
2989	65^56567-64	102552	Norbert Schneider	11/2014
2990	2^340547-108897	102515	Enzo Doria	03/2014
2991	7^121268+82	102484	Lelio R Paula	10/2016
2992	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
2993	2^340434-5955	102481	Lelio R Paula	11/2016
2994	(2^340381+47)/7	102465	Lelio R Paula	12/2013
2995	111^50095+110	102461	Norbert Schneider	04/2017
2996	2^340291-20301	102438	Enzo Doria	06/2013
2997	12^94915+89	102431	Lelio R Paula	10/2016
2998	2^340208-20373	102413	Enzo Doria	06/2013
2999	6^131598-17273	102404	Enzo Doria	02/2013
3000	2^340115-21181	102385	Enzo Doria	06/2013

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Probable Primes Top 10000

(205869 PRPs in the top)