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	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
2752	2^400571-15	120584	Lelio R Paula	10/2013
2753	(10^120574+359)/9	120574	Serge Batalov	12/2014
2754	2^400424-216413	120540	Enzo Doria	04/2013
2755	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
2756	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2758	2^400166+1874899	120462	Enzo Doria	06/2016
2757	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
2759	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
2760	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2761	2^399966+73759	120402	Enzo Doria	04/2016
2762	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2763	2^399918-95	120388	Lelio R Paula	04/2013
2764	(49*10^120380-139)/9	120381	Robert Price	03/2019
2765	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
2766	2^399792-1849259	120350	Enzo Doria	08/2015
2767	9*10^120342-7	120343	Robert Price	09/2015
2768	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
2769	(13*10^120306-37)/3	120307	Robert Price	01/2019
2770	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
2771	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
2772	2^399526-1861721	120270	Enzo Doria	11/2015
2773	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2774	2^399322-2798111	120208	Enzo Doria	04/2016
2775	72^64693-71^64693	120157	Robert Price	03/2014
2776	2^399111-28489	120145	Enzo Doria	08/2015
2778	2^398877+105	120074	Donovan Johnson	01/2006
2777	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2779	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2780	2^398710+57	120024	Lelio R Paula	04/2013
2781	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
2782	2^398691-115057	120018	Enzo Doria	06/2015
2783	L(574219)	120005	Renaud Lifchitz	03/2004
2784	2^398571+60413	119982	Yves Minet	03/2011
2785	p(24179)#/2-64	119949	Robert Price	04/2017
2786	2^398448+1872001	119945	Enzo Doria	05/2016
2787	634^42803+42803^634	119938	Norbert Schneider	07/2019
2788	(68*10^119931-11)/3	119933	Robert Price	01/2020
2789	8*10^119930-3	119931	Ray Chandler	04/2011
2790	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
2791	(10^119880+179)/9	119880	Serge Batalov	12/2014
2792	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
2793	(10^119836+77)/3	119836	Robert Price	01/2018
2794	2^398029+1872527	119819	Enzo Doria	05/2016
2795	2^397897-113541	119779	Enzo Doria	08/2014
2796	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
2797	(19*10^119716+101)/3	119717	Robert Price	09/2019
2798	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
2799	77*10^119688+3	119690	Robert Price	06/2020
2800	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
2801	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
2802	2^397426+73849	119638	Enzo Doria	04/2016
2803	2^396933-112723	119489	Enzo Doria	06/2014
2804	11^114738-150	119488	Enzo Doria	10/2012
2805	(4*10^119474+149)/9	119474	Robert Price	04/2018
2806	2^396790-21	119446	Lelio R Paula	04/2013
2807	(2^396633-7)/5	119398	Lelio R Paula	04/2014
2808	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
2809	105^59050+104	119352	Norbert Schneider	11/2016
2810	126^56824-125	119352	Norbert Schneider	12/2018
2811	139^55690-138	119345	Norbert Schneider	04/2019
2812	790^41179+41179^790	119322	Norbert Schneider	04/2019
2813	2^396374+73729	119321	Enzo Doria	04/2016
2814	88*10^119295+3	119297	Robert Price	05/2020
2815	2^396258-459491	119286	Enzo Doria	05/2015
2816	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
2817	2^396128-396128-1	119247	Karsten Bonath	06/2018
2818	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
2819	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
2820	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
2821	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
2822	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
2823	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
2824	(30^80599+1)/31	119054	Robert Price	07/2013
2825	(43*10^119024-403)/9	119025	Robert Price	01/2019
2826	6*10^118964+43	118965	Robert Price	07/2020
2827	(8*10^118960+49)/3	118961	Robert Price	05/2020
2828	(194*10^118925-17)/3	118927	Robert Price	09/2020
2829	2^395062-109121	118926	Enzo Doria	04/2014
2830	2^395055-4627	118924	Yves Minet	05/2019
2831	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
2832	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
2833	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
2834	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
2835	(16*10^118852+77)/3	118853	Robert Price	03/2019
2836	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
2837	10^118772-40000000001	118772	Robert Price	09/2020
2838	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
2839	2^394266+71389	118686	Enzo Doria	04/2016
2840	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
2841	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
2842	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
2843	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
2844	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
2845	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
2846	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
2847	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
2848	(17*10^118635+13)/3	118636	Robert Price	01/2019
2849	5^169727+2	118635	Lelio R Paula	08/2013
2850	2^394034-3	118617	M. Frind & P. Underwood	09/2002
2851	(7*10^118607+179)/3	118608	Robert Price	09/2018
2852	3^248572-6242	118599	Enzo Doria	05/2014
2853	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
2854	7^140303-6	118570	Robert Price	11/2014
2855	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
2856	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
2857	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
2858	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
2859	10^118485-50001	118485	Robert Price	08/2020
2860	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
2861	2^393427+75683	118434	Enzo Doria	04/2016
2862	2^393376-114749	118418	Enzo Doria	04/2015
2863	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
2864	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
2865	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
2866	2^393180+73	118359	Lelio R Paula	04/2013
2867	p(23881)#/2+256	118328	Robert Price	05/2017
2868	(10^118324+359)/9	118324	Serge Batalov	12/2014
2869	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
2870	p(23879)#/2+64	118317	Robert Price	03/2017
2871	(238*10^118265-1)/3	118267	Robert Price	04/2020
2873	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
2872	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
2874	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
2875	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
2876	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
2877	2^392516-29219	118160	Enzo Doria	07/2015
2878	66*10^118155+7	118157	Robert Price	07/2020
2879	Phi(177231,10)	118152	Maksym Voznyy	09/2015
2880	2^392413-112123	118129	Enzo Doria	06/2014
2881	(2^392342+5)/27	118106	Lelio R Paula	04/2014
2882	2^392300-1841429	118095	Enzo Doria	06/2015
2883	2^392220+75241	118070	Enzo Doria	04/2016
2884	10^118009+664447	118010	Patrick De Geest	07/2018
2885	10^118009-20001	118009	Robert Price	01/2018
2886	(14*10^117991+61)/3	117992	Robert Price	12/2018
2887	2^391933+5897	117984	Yves Minet	02/2011
2888	2^391912-1849259	117978	Enzo Doria	08/2015
2889	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
2890	(46*10^117902+683)/9	117903	Robert Price	03/2019
2891	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
2892	2^391324+90901	117801	Yves Minet	02/2011
2893	2^391301-1859923	117794	Enzo Doria	03/2016
2894	2^391261-4131	117782	Yves Minet	02/2018
2895	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
2896	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
2897	(85*10^117719+473)/9	117720	Robert Price	01/2020
2898	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
2899	2^390960+1880881	117691	Enzo Doria	11/2016
2900	2^390897-1860553	117672	Enzo Doria	11/2015
2901	2^390889-115003	117670	Enzo Doria	06/2015
2902	2^390779-30337	117637	Paul Bourdelais	02/2012
2903	11^112916-780	117590	Enzo Doria	12/2012
2904	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
2905	(16^97613-5^97613)/11	117537	Robert Price	07/2013
2906	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
2907	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
2908	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
2909	31^78759-30	117459	Theodore Burton	02/2007
2910	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
2911	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
2912	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
2913	3*10^117402+61	117403	Robert Price	09/2020
2914	2^389998+37	117402	Lelio R Paula	03/2013
2915	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
2916	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
2917	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
2918	(13*10^117249+161)/3	117250	Robert Price	11/2018
2919	2^389478+43	117245	Lelio R Paula	03/2013
2920	(298*10^117229-7)/3	117231	Robert Price	06/2020
2921	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
2922	5*10^117205+23	117206	Robert Price	03/2019
2923	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
2924	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
2925	10^117142+209223	117143	Patrick De Geest	04/2018
2927	10^117142-1000000001	117142	Robert Price	03/2018
2926	10^117142-966057	117142	Patrick De Geest	04/2018
2928	10^117135+360577	117136	Patrick De Geest	07/2018
2929	10^117135-401	117135	Robert Price	01/2018
2930	4*10^117123+79	117124	Robert Price	08/2018
2931	2^389033-12797413	117111	Enzo Doria	04/2016
2932	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
2933	2^388960-109505	117089	Enzo Doria	04/2014
2934	7*10^117082-57	117083	Robert Price	06/2020
2935	(2^388928-5)/569	117077	Lelio R Paula	03/2014
2936	2^388888-1529	117067	Yves Minet	01/2013
2937	10^117059+28879	117060	Patrick De Geest	05/2016
2938	(10^117059-71)/1	117059	Serge Batalov	12/2014
2939	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
2940	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
2941	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
2942	(693^41189-1)/692	117005	Michael Stocker	05/2020
2943	(26*10^116999-503)/9	117000	Robert Price	07/2018
2944	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
2945	3^245154-6256	116969	Enzo Doria	05/2014
2946	5*10^116966-43	116967	Robert Price	01/2019
2947	2^388536-113495	116961	Enzo Doria	08/2014
2948	2^388469-43	116941	Lelio R Paula	03/2013
2949	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
2950	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
2951	2^388180+93	116854	Donovan Johnson	07/2008
2952	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
2953	(85*10^116842+293)/9	116843	Robert Price	12/2019
2954	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
2955	2^387946-113261	116784	Enzo Doria	07/2014
2956	2^387745+75557	116723	Enzo Doria	04/2016
2957	(206*10^116687-17)/9	116689	Robert Price	01/2020
2958	(7*10^116684+179)/3	116685	Robert Price	09/2018
2959	2^387554+71455	116666	Enzo Doria	04/2016
2960	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
2961	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
2962	(25*10^116601-331)/9	116602	Robert Price	08/2018
2964	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
2963	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
2965	10^116557+987654321	116558	Robert Price	12/2019
2966	10^116557+9141	116558	Patrick De Geest	02/2020
2967	10^116557-609431	116557	Patrick De Geest	02/2020
2968	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
2969	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
2970	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
2971	2^386947+1869143	116483	Enzo Doria	05/2016
2972	(30^78857-1)/29	116480	Robert Price	12/2011
2973	(2^386903-3)/5	116469	Lelio R Paula	03/2014
2974	2^386389-1864783	116315	Enzo Doria	03/2016
2975	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
2976	297^47012+47012^297	116250	Norbert Schneider	07/2018
2977	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
2978	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
2979	2^385969-823	116189	Yves Minet	05/2012
2980	57^66162+2	116173	Lelio R Paula	08/2013
2981	2^385854+75049	116154	Enzo Doria	04/2016
2982	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
2983	2^385775-109587	116130	Enzo Doria	04/2014
2984	(14*10^116112-101)/3	116113	Robert Price	02/2019
2985	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
2986	2^385622+71839	116084	Enzo Doria	04/2016
2988	2^385564+781	116067	Lelio R Paula	01/2012
2987	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
2989	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
2990	(266*10^116024-17)/3	116026	Robert Price	07/2020
2991	2^385410+71893	116020	Enzo Doria	04/2016
2992	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
2993	(11*10^115910-131)/3	115911	Robert Price	09/2018
2994	2^384953-111943	115883	Paul Bourdelais	02/2012
2995	43^70942-2	115882	Lelio R Paula	04/2014
2996	(94*10^115879-7)/3	115881	Robert Price	03/2020
2997	7*10^115863+3	115864	Robert Price	08/2015
2998	2^384834+93	115847	Donovan Johnson	07/2008
2999	2^384809+71297	115840	Enzo Doria	04/2016
3000	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014

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Probable Primes Top 10000

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