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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^354157-17041	106612	Enzo Doria	05/2013
2752	12^98778+73	106600	Lelio R Paula	02/2017
2753	2^354064+1870651	106584	Enzo Doria	05/2016
2754	2^353992-57	106563	Lelio R Paula	10/2011
2755	(7*10^106516+113)/3	106517	Robert Price	02/2018
2756	2^353832-1853849	106515	Enzo Doria	09/2015
2757	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
2758	2^353794-18453	106503	Enzo Doria	05/2013
2759	2^353728+7695	106483	Lelio R Paula	01/2017
2760	2^353672-303	106466	Yves Minet	02/2012
2761	6^136811+101	106460	Lelio R Paula	02/2017
2762	2^353641+1871981	106457	Enzo Doria	05/2016
2763	(8*10^106454-29)/3	106455	Robert Price	07/2018
2764	2^353553+54615	106431	Lelio R Paula	01/2017
2765	2^353544-18897	106428	Enzo Doria	05/2013
2766	6^136729-133	106396	Lelio R Paula	02/2017
2767	2^353418+1605	106390	Lelio R Paula	01/2017
2768	2^353387+65	106381	Lelio R Paula	10/2011
2769	2^353372+74311	106376	Enzo Doria	04/2016
2770	2^353344-3693	106368	Yves Minet	03/2017
2771	2^353277-20089	106347	Enzo Doria	06/2013
2772	2^353275+72173	106347	Enzo Doria	04/2016
2773	2^353268-17705	106345	Enzo Doria	05/2013
2774	2^353267-19857	106344	Enzo Doria	06/2013
2775	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
2776	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
2777	2^353025+72257	106272	Enzo Doria	04/2016
2778	2^352932-20345	106244	Enzo Doria	06/2013
2779	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
2780	2^352883-187	106229	Lelio R Paula	10/2011
2781	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
2782	2^352814-131	106208	Lelio R Paula	10/2011
2783	2^352752+73951	106189	Enzo Doria	04/2016
2784	6^136434+5	106167	Lelio R Paula	11/2014
2785	7*5^151872-8	106155	Lelio R Paula	11/2014
2786	105^52520-2	106153	Lelio R Paula	10/2017
2787	2^352601-1604809	106144	Enzo Doria	05/2015
2788	12^98353-43	106141	Lelio R Paula	02/2017
2789	2^352585-18901	106139	Enzo Doria	05/2013
2790	(2^352554-3)/193	106128	Lelio R Paula	12/2013
2791	2^352540+15015	106126	Lelio R Paula	01/2017
2792	2^352524-3149	106121	Yves Minet	10/2014
2793	2^352486-1858781	106109	Enzo Doria	04/2016
2794	2^352444+12705	106097	Lelio R Paula	01/2017
2795	2^352228-18953	106032	Enzo Doria	05/2013
2796	2^352107+1872533	105995	Enzo Doria	05/2016
2797	2^352066-2591	105983	Yves Minet	07/2014
2798	2^352030+715	105972	Lelio R Paula	10/2011
2799	9*6^136176-5	105967	Lelio R Paula	11/2014
2800	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
2801	155^48377+2	105962	Lelio R Paula	08/2013
2802	2^351865+1869707	105922	Enzo Doria	05/2016
2803	2^351831+23	105912	Lelio R Paula	10/2011
2804	9*2^351784-5	105899	Lelio R Paula	09/2014
2805	2^351671-112387	105864	Enzo Doria	06/2014
2806	2^351669-109501	105863	Enzo Doria	04/2014
2807	2^351644+74731	105856	Enzo Doria	04/2016
2808	13^95025-42	105853	Lelio R Paula	12/2016
2809	2^351599+15015	105842	Lelio R Paula	01/2017
2810	19^82763+90	105834	Lelio R Paula	01/2017
2811	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
2812	20^81329-51	105812	Lelio R Paula	01/2017
2813	(5*10^105811+211)/9	105811	Robert Price	02/2018
2814	2^351483+28425	105807	Lelio R Paula	01/2017
2815	15^89960+86	105802	Lelio R Paula	02/2017
2816	2^351460-17289	105801	Enzo Doria	05/2013
2817	19^82735+22	105798	Lelio R Paula	01/2017
2818	2^351435-109077	105793	Enzo Doria	04/2014
2819	2^351393+1089	105780	Lelio R Paula	01/2017
2820	2^351364+72631	105772	Enzo Doria	04/2016
2821	2^351305+1872467	105754	Enzo Doria	05/2016
2822	3^221649+16	105754	Lelio R Paula	11/2016
2823	8*3^221637-5	105749	Lelio R Paula	09/2014
2824	2^351279-2780449	105746	Enzo Doria	03/2016
2825	15^89903-26	105735	Lelio R Paula	02/2017
2826	2^351213-73	105726	Lelio R Paula	10/2011
2827	2^351192-4589	105720	Yves Minet	07/2011
2828	20^81250-33	105709	Lelio R Paula	12/2016
2829	2^351076-113159	105685	Enzo Doria	07/2014
2830	93^53688-2	105684	Lelio R Paula	09/2013
2831	2^351060-4559	105680	Yves Minet	07/2011
2832	11^101473-750	105674	Enzo Doria	11/2012
2833	3*5^151181-8	105672	Lelio R Paula	11/2014
2834	15^89831-34	105650	Lelio R Paula	02/2017
2836	11^101448-360	105648	Enzo Doria	08/2012
2835	3*7^125011+4	105648	Lelio R Paula	11/2014
2837	2^350943-113269	105645	Enzo Doria	07/2014
2838	2^350868-19725	105622	Enzo Doria	06/2013
2839	2^350858-59291	105619	Enzo Doria	10/2015
2840	2^350851+135	105617	Lelio R Paula	10/2011
2841	2^350841-741	105614	Lelio R Paula	01/2017
2842	8*10^105571+3	105572	Robert Price	08/2015
2843	2^350674-78557	105564	Jorge Menendez	03/2018
2844	2*5^151026-3	105563	Lelio R Paula	11/2014
2845	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
2846	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
2847	3^221211+236	105545	Lelio R Paula	11/2016
2848	(32*10^105530-77)/9	105531	Robert Price	06/2018
2849	10^105515+33	105516	Lelio R Paula	11/2016
2850	10^105515-41033	105515	Patrick De Geest	12/2016
2851	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
2852	17^85732-72	105489	Lelio R Paula	01/2017
2853	2^350307-110329	105453	Enzo Doria	05/2014
2854	2^350253-20365	105437	Enzo Doria	06/2013
2855	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
2856	2^350139-109009	105403	Enzo Doria	04/2014
2857	3*5^150763+4	105380	Lelio R Paula	11/2014
2858	12^97643+91	105375	Lelio R Paula	02/2017
2859	6*5^150744-7	105367	Lelio R Paula	11/2014
2860	2^349996-112169	105360	Enzo Doria	06/2014
2861	11^101142-1080	105329	Enzo Doria	12/2012
2862	(68*10^105320-41)/9	105321	Robert Price	10/2013
2863	3^220712-9934	105307	Enzo Doria	05/2014
2864	7*10^105296+9	105297	Robert Price	09/2015
2865	2^349739+1873373	105282	Enzo Doria	06/2016
2866	7^124574+24	105278	Lelio R Paula	11/2016
2867	2^349708-20957	105273	Enzo Doria	06/2013
2868	2^349649-20469	105255	Enzo Doria	06/2013
2869	2^349607-20109	105243	Enzo Doria	06/2013
2870	2^349594-19085	105239	Enzo Doria	05/2013
2871	2^349530+1874479	105220	Enzo Doria	06/2016
2872	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
2873	3^220464-112852	105189	Enzo Doria	07/2014
2874	2^349419-17349	105186	Enzo Doria	05/2013
2875	2^349400-2579	105180	Yves Minet	07/2014
2876	8*5^150471+3	105176	Lelio R Paula	11/2014
2877	13^94403+94	105160	Lelio R Paula	12/2016
2878	2^349301-112309	105151	Enzo Doria	06/2014
2879	9*2^349220+5	105127	Lelio R Paula	09/2014
2880	7*3^220317+8	105119	Lelio R Paula	09/2014
2881	7^124386+88	105119	Lelio R Paula	11/2016
2882	2^349171-19657	105111	Enzo Doria	06/2013
2883	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
2884	(2^349111-5)/3	105093	Lelio R Paula	12/2013
2885	2^348981-2797573	105054	Enzo Doria	04/2016
2886	2^348869-6555	105021	Lelio R Paula	01/2017
2887	5^150217+78	104998	Lelio R Paula	11/2016
2888	2^348703-113005	104971	Enzo Doria	06/2014
2890	2^348612-809	104943	Yves Minet	05/2013
2889	(73*10^104942-1)/9	104943	Robert Price	01/2015
2891	2^348583-350407	104934	Enzo Doria	06/2015
2892	2^348531-949	104919	Yves Minet	05/2012
2893	20^80636-59	104910	Lelio R Paula	12/2016
2894	2^348437+35	104890	Lelio R Paula	09/2011
2895	2^348348+135	104864	Lelio R Paula	09/2011
2896	(2^348284+9)/25	104843	Lelio R Paula	12/2013
2897	75^55914-74	104843	Norbert Schneider	01/2015
2898	2^348268+255255	104840	Lelio R Paula	01/2017
2899	5^149985-52	104836	Lelio R Paula	11/2016
2900	2^348224-20249	104826	Enzo Doria	06/2013
2901	2^348212-20105	104823	Enzo Doria	06/2013
2902	20^80562+19	104814	Lelio R Paula	12/2016
2903	2*10^104811-87	104812	Robert Price	04/2018
2904	2^348149-20053	104804	Enzo Doria	06/2013
2905	2^348095-171	104788	Lelio R Paula	09/2011
2906	2^348003-20377	104760	Enzo Doria	06/2013
2907	2^347994-741	104757	Lelio R Paula	12/2016
2908	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
2909	2^347910-109937	104732	Enzo Doria	04/2014
2910	5^149794+28	104702	Lelio R Paula	11/2016
2911	105^51800-2	104698	Lelio R Paula	10/2017
2912	(16^86939+3^86939)/19	104684	Robert Price	06/2013
2913	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
2914	2^347731-18609	104678	Enzo Doria	05/2013
2915	4*6^134519+7	104677	Lelio R Paula	11/2014
2916	2^347612-18545	104642	Enzo Doria	05/2013
2917	6^134465+95	104635	Lelio R Paula	11/2016
2918	2^347517-17301	104614	Enzo Doria	05/2013
2919	3^219222-310	104596	Lelio R Paula	11/2016
2920	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
2921	2^347372-17853	104570	Enzo Doria	05/2013
2922	2^347314+99	104552	Lelio R Paula	09/2011
2923	2^347300-22233	104548	Enzo Doria	06/2013
2924	2^347287-19845	104544	Enzo Doria	06/2013
2925	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
2926	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
2927	7*2^347239-3	104531	Lelio R Paula	09/2014
2928	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
2929	5*3^219047+8	104513	Lelio R Paula	09/2014
2930	2^347148-109073	104502	Enzo Doria	04/2014
2931	2^347129-20145	104497	Enzo Doria	06/2013
2932	2^346923-19585	104435	Enzo Doria	05/2013
2933	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
2934	2^346854+346854^2+1	104414	Robert Price	06/2014
2935	2^346834+11715	104408	Lelio R Paula	04/2015
2936	79^55009+78	104387	Norbert Schneider	02/2015
2937	3^218744+58	104368	Lelio R Paula	11/2016
2938	2^346649+65	104352	Lelio R Paula	09/2011
2939	2^346638-17265	104349	Enzo Doria	05/2013
2940	2^346527-111817	104316	Enzo Doria	05/2014
2941	6^134055+101	104316	Lelio R Paula	11/2016
2942	6^134013+163	104283	Lelio R Paula	11/2016
2943	18^83049-89	104250	Lelio R Paula	01/2017
2944	2^346213+484049	104221	Enzo Doria	04/2017
2945	18^83021-91	104214	Lelio R Paula	01/2017
2946	10^104212+128779	104213	Patrick De Geest	05/2016
2947	10^104212+237447	104213	Patrick De Geest	05/2016
2948	10^104212+242139	104213	Patrick De Geest	05/2016
2949	10^104212+269199	104213	Patrick De Geest	05/2016
2950	(10^104212-71)/1	104212	Serge Batalov	12/2014
2951	2^346078+7695	104180	Lelio R Paula	12/2016
2952	2^346055-19537	104173	Enzo Doria	05/2013
2953	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
2954	2^346037-20125	104168	Enzo Doria	06/2013
2955	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
2956	6^133854-17993	104159	Enzo Doria	03/2013
2957	2^345990+1874239	104154	Enzo Doria	06/2016
2958	2^345988-20373	104153	Enzo Doria	06/2013
2959	(26*10^104132-503)/9	104133	Robert Price	07/2018
2960	3*5^148968+8	104125	Lelio R Paula	11/2014
2961	(7*10^104113+53)/3	104114	Robert Price	05/2018
2962	p(21253)#/2+8	104113	Robert Price	01/2017
2963	322^41507+41507^322	104094	Norbert Schneider	12/2014
2964	6^133768-17423	104092	Enzo Doria	03/2013
2965	2^345786-19557	104092	Enzo Doria	05/2013
2966	171^46606-2	104072	Lelio R Paula	10/2017
2967	2^345704-149	104068	Lelio R Paula	09/2011
2968	6^133704-17273	104042	Enzo Doria	02/2013
2969	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
2970	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
2971	2^345547+11	104021	Lelio R Paula	09/2011
2972	2^345504+723	104008	Lelio R Paula	09/2011
2973	2^345498-20037	104006	Enzo Doria	06/2013
2974	18^82854-37	104005	Lelio R Paula	01/2017
2975	2^345486-109065	104002	Enzo Doria	04/2014
2976	2^345487-1851507	104002	Enzo Doria	08/2015
2977	2^345476+777	103999	Lelio R Paula	09/2011
2978	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
2979	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
2980	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
2981	2^345106-112181	103888	Enzo Doria	06/2014
2982	2^345079+99	103880	Lelio R Paula	09/2011
2983	11^99736-1500	103865	Enzo Doria	12/2012
2984	2^344842-20157	103808	Enzo Doria	06/2013
2985	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
2986	2^344802-20765	103796	Enzo Doria	06/2013
2987	2^344794-3821	103794	Yves Minet	05/2011
2988	2^344782-109103	103790	Enzo Doria	04/2014
2989	3^217521-112292	103784	Enzo Doria	06/2014
2990	2^344759-3505	103783	Lelio R Paula	11/2016
2991	2^344735-147	103776	Lelio R Paula	09/2011
2992	L(496533)-p(496533)	103770	Robert Price	02/2018
2993	2*10^103749-69	103750	Robert Price	03/2018
2994	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
2995	2^344607-108891	103738	Enzo Doria	03/2014
2996	2^344541-19561	103718	Enzo Doria	05/2013
2997	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
2998	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
2999	2^344444-455	103688	Yves Minet	03/2012
3000	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017

Find by discoverer :

PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)