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	2^340115-21181	102385	Enzo Doria	06/2013
2752	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
2753	89^52511-88^52511	102365	Robert Price	06/2015
2754	3^214539-112756	102362	Enzo Doria	07/2014
2755	2^340000-19877	102351	Enzo Doria	06/2013
2756	2^339990-114845	102348	Enzo Doria	05/2015
2757	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
2758	20^78661-99	102341	Lelio R Paula	09/2016
2759	2^339951-19585	102336	Enzo Doria	05/2013
2760	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
2761	2^339889+29327	102317	Yves Minet	06/2010
2762	2^339834-109493	102301	Enzo Doria	04/2014
2763	(11^98221-5^98221)/6	102286	Robert Price	01/2013
2764	3^214365+1820	102279	Lelio R Paula	10/2016
2765	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
2766	2^339694-16995	102259	Lelio R Paula	09/2016
2767	7^120985-38	102245	Lelio R Paula	10/2016
2768	10^102244+122961	102245	Patrick De Geest	12/2016
2769	10^102244-27	102244	Lelio R Paula	09/2016
2770	7^120982-62	102242	Lelio R Paula	10/2016
2771	4*6^131382-5	102236	Lelio R Paula	11/2014
2772	2^339586-1091	102226	Yves Minet	11/2012
2773	11^98161-3072000	102225	Enzo Doria	12/2012
2774	9*7^120961-4	102225	Lelio R Paula	11/2014
2775	5*3^214250+2	102224	Serge Batalov	10/2010
2776	12^94713-59	102213	Lelio R Paula	10/2016
2777	12^94705+89	102204	Lelio R Paula	10/2016
2778	2^339407-177	102172	Lelio R Paula	08/2011
2779	2^339355+65	102157	Lelio R Paula	07/2011
2780	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
2781	2^339168+21	102100	Lelio R Paula	07/2011
2782	2^339167-108807	102100	Enzo Doria	03/2014
2783	2^339156+163	102097	Lelio R Paula	08/2011
2784	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
2785	2^338891-18885	102017	Enzo Doria	05/2013
2786	2^338829-113239	101998	Enzo Doria	07/2014
2787	2^338828-113297	101998	Enzo Doria	07/2014
2788	2^338796+93	101988	Donovan Johnson	06/2008
2789	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
2791	2^338682-19865	101954	Enzo Doria	06/2013
2790	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
2792	2^338568+37	101920	Lelio R Paula	07/2011
2793	2^338559-1858777	101917	Enzo Doria	04/2016
2794	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
2795	2^338497-17041	101898	Enzo Doria	05/2013
2796	2^338475+54615	101892	Lelio R Paula	10/2016
2797	2^338426-19797	101877	Enzo Doria	06/2013
2798	2^338368-20369	101859	Enzo Doria	06/2013
2799	2^338366+74179	101859	Enzo Doria	04/2016
2800	2^338280-19745	101833	Enzo Doria	06/2013
2801	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
2802	6^130841+103	101815	Lelio R Paula	10/2016
2803	2^338122-20117	101785	Enzo Doria	06/2013
2804	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
2805	35^65917-7092	101781	Enzo Doria	03/2013
2806	2^338010-19833	101752	Enzo Doria	06/2013
2807	3^213215-76	101730	Lelio R Paula	09/2016
2808	2^337930+63	101728	Lelio R Paula	07/2011
2809	2^337920+1869661	101725	Enzo Doria	05/2016
2810	2^337859-19645	101706	Enzo Doria	05/2013
2811	2^337754+1869169	101675	Enzo Doria	05/2016
2812	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
2813	11^97605-24	101646	Lelio R Paula	10/2016
2814	8^112539-112539	101633	Robert Price	01/2014
2815	2^337515-19869	101603	Enzo Doria	06/2013
2816	2^337473+719	101590	Lelio R Paula	08/2011
2817	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
2818	2^337452-108815	101584	Enzo Doria	03/2014
2819	2^337453+1185	101584	Lelio R Paula	09/2016
2820	2^337410-113561	101571	Enzo Doria	08/2014
2821	2^337387+855	101564	Lelio R Paula	09/2016
2822	2^337367-17295	101558	Lelio R Paula	09/2016
2823	2^337342-109035	101551	Enzo Doria	04/2014
2824	2^337267-19	101528	Lelio R Paula	07/2011
2825	2^337183-19989	101503	Enzo Doria	06/2013
2826	2^337149+72425	101492	Enzo Doria	04/2016
2827	2^337101-20241	101478	Enzo Doria	06/2013
2828	2^337035-20001	101458	Enzo Doria	06/2013
2829	2^337017-16995	101453	Lelio R Paula	09/2016
2830	2^336979-115315	101441	Enzo Doria	06/2015
2831	2^336970-20885	101439	Enzo Doria	06/2013
2832	2^336958+79	101435	Lelio R Paula	10/2009
2833	2^336942+169	101430	Lelio R Paula	10/2009
2834	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
2835	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
2836	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
2837	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
2838	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
2839	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
2840	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
2841	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
2842	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
2843	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
2844	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
2845	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
2846	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
2847	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
2848	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
2849	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
2850	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
2851	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
2852	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
2853	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
2854	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
2855	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
2856	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
2857	2^336842+94065	101400	Lelio R Paula	09/2016
2858	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
2859	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
2860	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
2861	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
2862	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
2863	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
2864	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
2865	10^101369+203811	101370	Patrick De Geest	11/2016
2866	10^101369-99	101369	Lelio R Paula	09/2016
2867	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
2868	2^336701-113563	101358	Enzo Doria	08/2014
2869	2^336644-109023	101340	Enzo Doria	04/2014
2870	2^336601-21081	101327	Enzo Doria	06/2013
2871	20^77869+63	101310	Lelio R Paula	09/2016
2872	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
2874	6^130179-137	101299	Lelio R Paula	10/2016
2873	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
2875	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
2876	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
2877	2^336369-19753	101258	Enzo Doria	05/2013
2878	2^336350-344291	101252	Enzo Doria	07/2015
2879	2^336243-108777	101220	Enzo Doria	03/2014
2880	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
2881	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
2882	2^336150-20393	101192	Enzo Doria	06/2013
2883	2^336112-1865249	101180	Enzo Doria	03/2016
2884	2^336103-109015	101178	Enzo Doria	04/2014
2885	13^90809-96	101157	Lelio R Paula	10/2016
2886	19^79098-30	101147	Lelio R Paula	10/2016
2887	19^79095+88	101144	Lelio R Paula	10/2016
2888	15^85976+32	101116	Lelio R Paula	10/2016
2889	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
2890	(4^167933+17)/3	101106	Robert Price	02/2017
2891	2^335858+153	101104	Lelio R Paula	10/2009
2892	6^129918-35	101096	Lelio R Paula	10/2016
2893	3^211885-70	101095	Lelio R Paula	09/2016
2894	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
2895	2^335818-20033	101092	Enzo Doria	06/2013
2896	2^335813-110083	101090	Enzo Doria	04/2014
2897	2^335804+2155	101088	Lelio R Paula	09/2016
2898	2^335784-16145	101082	Enzo Doria	04/2013
2899	11^97051+62	101069	Lelio R Paula	10/2016
2900	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
2901	2^335658-94395	101044	Lelio R Paula	09/2016
2902	2^335586+169	101022	Lelio R Paula	10/2009
2903	47599!2+1024	100991	Robert Price	02/2015
2904	2^335468-18629	100986	Enzo Doria	05/2013
2905	2^335454-20961	100982	Enzo Doria	06/2013
2906	10^100978+61	100979	Lelio R Paula	09/2016
2907	10^100978-156437	100978	Patrick De Geest	11/2016
2908	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
2909	2^335403-1859167	100967	Enzo Doria	03/2016
2910	9*2^335364-5	100956	Lelio R Paula	08/2014
2911	2^335349+72287	100951	Enzo Doria	04/2016
2912	2^335329+16095	100945	Lelio R Paula	09/2016
2913	2^335237-20893	100917	Enzo Doria	06/2013
2914	2^335222-19337	100912	Enzo Doria	05/2013
2915	2^335222-109985	100912	Enzo Doria	04/2014
2916	2^335182-17237	100900	Enzo Doria	05/2013
2917	2^335043-16737	100858	Enzo Doria	05/2013
2918	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
2919	2^335038-20633	100857	Enzo Doria	06/2013
2920	2^335031+1873373	100855	Enzo Doria	06/2016
2921	3^211354-8816	100842	Enzo Doria	05/2014
2922	2^334984-112757	100841	Enzo Doria	06/2014
2924	2^334857+48527	100803	Lelio R Paula	08/2011
2923	12^93406+29	100803	Lelio R Paula	10/2016
2925	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
2926	2^334809-13	100788	Lelio R Paula	04/2011
2927	(82*10^100780-1)/9	100781	Robert Price	12/2014
2928	(2^334779+47)/5	100778	Lelio R Paula	12/2013
2929	2^334751+2049	100771	Lelio R Paula	09/2016
2930	13^90443-98	100749	Lelio R Paula	10/2016
2931	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
2932	15^85639-28	100720	Lelio R Paula	10/2016
2933	2^334562+577294575	100711	Lelio R Paula	09/2016
2934	4*3^211077-5	100710	Lelio R Paula	08/2014
2935	2^334524+145	100702	Lelio R Paula	07/2009
2936	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
2937	2^334294-113111	100633	Enzo Doria	07/2014
2938	6^129308-17723	100622	Enzo Doria	03/2013
2939	6^129305+95	100619	Lelio R Paula	10/2016
2940	2^334244-1167	100618	Lelio R Paula	09/2016
2941	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
2942	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
2943	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
2944	13^90251+24	100535	Lelio R Paula	10/2016
2945	2^333963+789	100533	Lelio R Paula	08/2011
2946	2^333919-1840087	100520	Enzo Doria	06/2015
2947	2^333911+72623	100518	Enzo Doria	04/2016
2948	18^80064-67	100503	Lelio R Paula	10/2016
2949	5^143742-48	100472	Lelio R Paula	10/2016
2950	2^333757-112123	100471	Enzo Doria	06/2014
2951	2^333603-108861	100425	Enzo Doria	03/2014
2952	9*7^118818-2	100414	Lelio R Paula	11/2014
2953	2^333546-17097	100408	Enzo Doria	05/2013
2954	17^81597+72	100401	Lelio R Paula	10/2016
2955	p(20559)#/2+8	100384	Robert Price	01/2017
2956	11^96390-24	100380	Lelio R Paula	10/2016
2957	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
2958	2^333354+763	100350	Lelio R Paula	08/2011
2959	2^333289-109483	100330	Enzo Doria	04/2014
2960	2^333240-2790209	100316	Enzo Doria	03/2016
2961	(2^333227-2^166614+1)/5	100311		11/2006
2962	2^333225+719	100311	Lelio R Paula	08/2011
2963	2^333221-2785333	100310	Enzo Doria	10/2015
2964	76^53332-75	100308	Norbert Schneider	02/2015
2965	6^128892-17573	100298	Enzo Doria	03/2013
2966	2^333105-113215	100275	Enzo Doria	07/2014
2967	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
2968	17^81476-74	100253	Lelio R Paula	10/2016
2969	17^81417-16	100180	Theodore Burton	11/2005
2970	2^332739-113215	100165	Enzo Doria	07/2014
2971	2^332730-1865621	100162	Enzo Doria	03/2016
2972	91^51127-2	100160	Lelio R Paula	09/2013
2973	15^85159-32	100155	Lelio R Paula	10/2016
2974	6^128661+97	100118	Lelio R Paula	10/2016
2975	19^78285+40	100108	Lelio R Paula	07/2016
2976	6^128640+5	100102	Lelio R Paula	11/2014
2977	6^128565-127	100044	Lelio R Paula	08/2016
2978	2^332309-133	100035	Lelio R Paula	02/2011
2979	2^332307+731	100035	Lelio R Paula	07/2011
2980	2^332301+12927	100033	Lelio R Paula	04/2013
2981	12^92684-13	100023	Lelio R Paula	07/2016
2997	10^100000+342909	100001	Milton L. Brown	12/2007
2990	10^100000+1751769	100001	Robert Price	08/2012
2991	10^100000+2155489	100001	Robert Price	10/2012
2992	10^100000+2483527	100001	Robert Price	12/2012
2993	10^100000+2503087	100001	Robert Price	12/2012
2994	10^100000+2686179	100001	Robert Price	12/2012
2995	10^100000+2688933	100001	Robert Price	12/2012
2996	10^100000+3667159	100001	Robert Price	08/2013
2998	10^100000+3938473	100001	Robert Price	05/2015
2999	10^100000+3979761	100001	Robert Price	05/2015
3000	10^100000+4293973	100001	Robert Price	09/2015
2982	10^100000+5354043	100001	Robert Price	05/2016
2983	10^100000+5717979	100001	Robert Price	05/2016
2984	10^100000+6080631	100001	Robert Price	07/2016
2985	10^100000+6308469	100001	Robert Price	07/2016
2986	10^100000+6512023	100001	Robert Price	08/2016
2987	10^100000+6596557	100001	Robert Price	08/2016
2988	10^100000+7115409	100001	Robert Price	10/2016
2989	10^100000+7235803	100001	Robert Price	10/2016

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PRP Records

Probable Primes Top 10000

(177649 PRPs in the top)