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	2^634470-59861	190995	Enzo Doria	11/2015
2752	2^634368-29519	190964	Enzo Doria	08/2015
2753	(19*10^190935+11)/3	190936	Robert Price	07/2023
2754	2^634188-350609	190910	Enzo Doria	06/2015
2755	(65*10^190899+493)/9	190900	Robert Price	08/2021
2756	(62*10^190795-413)/9	190796	Robert Price	09/2021
2757	(26*10^190789-131)/3	190790	Robert Price	10/2019
2758	(13*10^190732-61)/3	190733	Robert Price	11/2018
2759	3*2^633524+5	190711	Jon Grantham	07/2023
2760	(7*10^190683+143)/3	190684	Robert Price	03/2018
2761	2^633088-113879	190579	Enzo Doria	10/2014
2762	2^633064+1874911	190572	Enzo Doria	06/2016
2763	5*3^399402+2^399402	190564	Jon Grantham	08/2023
2764	(43*10^190547+83)/9	190548	Robert Price	11/2018
2765	99*10^190543+7	190545	Robert Price	05/2021
2766	(299*10^190533+1)/3	190535	Robert Price	04/2020
2767	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
2768	2^632815-15	190497	Stefano Morozzi	07/2022
2769	2^632795-351205	190491	Enzo Doria	06/2015
2770	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
2771	(16*10^190420-19)/3	190421	Robert Price	02/2019
2772	(43*10^190351+101)/9	190352	Robert Price	11/2018
2773	2^632156+78391	190298	Enzo Doria	06/2016
2774	97*10^190295-3	190297	Robert Price	05/2020
2775	2^632082-1851971	190276	Enzo Doria	08/2015
2776	2^632020+1880311	190257	Enzo Doria	09/2016
2777	(5*10^190242-77)/9	190242	Robert Price	04/2021
2778	7*10^190210+13	190211	Robert Price	03/2021
2779	2^631637-462373	190142	Enzo Doria	08/2015
2780	2*10^190126-21	190127	Robert Price	09/2020
2781	(28*10^190105+191)/3	190106	Robert Price	02/2020
2782	2*10^190093+33	190094	Robert Price	11/2021
2783	(68*10^190053-113)/9	190054	Robert Price	03/2021
2784	2^631183+213413	190006	Enzo Doria	09/2023
2785	2^631122-39251	189987	Enzo Doria	08/2015
2786	(26*10^189928-89)/9	189929	Robert Price	06/2018
2787	2^630839-97	189902	Yves Minet	07/2017
2788	99*10^189876-7	189878	Robert Price	07/2020
2789	41147^41147+30^30	189867	Henri Lifchitz	09/2024
2790	2^630359+1788953	189757	Enzo Doria	05/2016
2791	2^630228+1871971	189718	Enzo Doria	05/2016
2792	2^630108+781	189682	Lelio R Paula	08/2013
2793	2^629870-1867811	189610	Enzo Doria	04/2016
2794	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
2795	2^629326+2792929	189447	Enzo Doria	02/2016
2796	4*10^189401+13	189402	Robert Price	02/2021
2797	(10^189385-61)/3	189385	Serge Batalov	12/2014
2798	2^629036+1874011	189359	Enzo Doria	06/2016
2799	2^628930+80779	189327	Enzo Doria	07/2016
2800	(134*10^189309-11)/3	189311	Robert Price	01/2022
2801	9*10^189306-11	189307	Mischa Rodermond	04/2023
2802	3^396740-396740^3	189294	Henri Lifchitz	07/2024
2803	2^628582+1179439	189223	Enzo Doria	06/2016
2804	(44*10^188999-503)/9	189000	Robert Price	12/2018
2805	(16*10^188823+167)/3	188824	Robert Price	06/2019
2806	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
2807	2^627037-2785843	188757	Enzo Doria	10/2015
2808	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
2809	(16*10^188457+161)/3	188458	Robert Price	02/2019
2810	L(901657)	188436	Renaud Lifchitz	11/2008
2811	(19*10^188375+137)/3	188376	Robert Price	03/2022
2812	2^625651+74213	188340	Enzo Doria	04/2016
2813	2^625584-460919	188320	Enzo Doria	06/2015
2814	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
2815	5^269399-3^269399-1	188302	Jon Grantham	08/2023
2816	(14*10^188218+139)/9	188219	Robert Price	11/2021
2817	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
2818	(10^188164+359)/9	188164	Serge Batalov	12/2014
2819	2^624481-113611	187988	Enzo Doria	08/2014
2820	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
2821	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
2822	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
2823	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
2824	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
2825	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
2827	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
2826	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
2828	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
2829	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
2830	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
2831	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
2832	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
2834	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
2833	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
2835	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
2836	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
2837	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
2838	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
2839	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
2840	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
2841	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
2843	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
2842	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
2844	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
2845	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
2846	2^624077-112723	187866	Enzo Doria	07/2014
2847	2^624008+1874941	187846	Enzo Doria	06/2016
2848	2^623870+78679	187804	Enzo Doria	05/2016
2849	2^623714-114035	187757	Enzo Doria	11/2014
2850	2^623651-1834251	187738	Enzo Doria	07/2015
2851	(7*10^187645+53)/3	187646	Robert Price	05/2018
2852	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
2853	2^623146+1879609	187586	Enzo Doria	09/2016
2854	(401*10^187512+13)/9	187514	Robert Price	09/2021
2855	(5*10^187471+91)/3	187472	Robert Price	04/2018
2856	2^622500+81931	187392	Enzo Doria	08/2016
2857	(13*10^187382-157)/9	187383	Robert Price	05/2021
2858	2^622300-1861739	187331	Enzo Doria	12/2015
2859	(22*10^187317-91)/3	187318	Robert Price	02/2022
2860	(38*10^187281+349)/9	187282	Robert Price	10/2018
2861	2^622052+76771	187257	Enzo Doria	05/2016
2862	2^622005-24091	187243	Enzo Doria	08/2013
2863	7*10^187205-57	187206	Robert Price	06/2020
2864	2^621879-351787	187205	Enzo Doria	07/2015
2865	(5*10^187168-53)/3	187169	Robert Price	09/2020
2866	(23*10^187164-143)/3	187165	Robert Price	12/2019
2867	2^621700+79411	187151	Enzo Doria	06/2016
2868	2^621597+39	187120	Jon Grantham	08/2023
2869	(7*10^187101+131)/3	187102	Robert Price	06/2020
2870	(2*10^187062-71)/3	187062	Robert Price	12/2017
2871	V(1118570)	187013	Serge Batalov	07/2024
2872	2^620929-113203	186919	Enzo Doria	07/2014
2873	10^186842+168223	186843	Patrick De Geest	07/2018
2874	10^186842-8001	186842	Robert Price	03/2018
2875	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
2876	2^620347-1777	186744	Lelio R Paula	07/2013
2877	(11*10^186659+133)/9	186660	Robert Price	04/2022
2878	11^179143-4170	186559	Enzo Doria	12/2012
2879	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
2880	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
2881	2*10^186517+33	186518	Robert Price	11/2021
2882	2^619297-2792353	186427	Enzo Doria	02/2016
2883	(49*10^186409+383)/9	186410	Robert Price	04/2019
2884	2^618940-460139	186320	Enzo Doria	06/2015
2885	2^618046+74179	186051	Enzo Doria	04/2016
2886	3*10^186019+11	186020	Robert Price	07/2018
2887	(16*10^185978-19)/3	185979	Robert Price	02/2019
2888	(22*10^185950-7)/3	185951	Robert Price	12/2022
2889	2*10^185930-3	185931	Robert Price	07/2015
2890	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
2891	4*10^185905+91	185906	Robert Price	08/2018
2892	(34*10^185902-601)/9	185903	Robert Price	07/2022
2893	(19*10^185873+131)/3	185874	Robert Price	06/2020
2894	(37*10^185811+377)/9	185812	Robert Price	11/2018
2895	2^617250+9385	185811	Lelio R Paula	07/2013
2896	2^617130+9	185775	Stefano Morozzi	05/2021
2897	39^116749+2	185756	Robert Price	04/2015
2898	2^616924-39719	185713	Enzo Doria	09/2015
2899	2^616712+1867621	185649	Enzo Doria	04/2016
2900	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
2901	8*10^185529-67	185530	Robert Price	08/2019
2902	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
2903	5*2^616124+3	185473	Jon Grantham	07/2023
2904	2^615916+26791	185410	Enzo Doria	12/2023
2905	4*10^185355+9	185356	Robert Price	05/2015
2906	(16*10^185347+89)/3	185348	Robert Price	03/2021
2907	40247^40247-56^56	185327	Henri Lifchitz	08/2024
2908	2^615622+76639	185321	Enzo Doria	05/2016
2909	2^615591+1879223	185312	Enzo Doria	08/2016
2910	2^615587+217013	185311	Enzo Doria	12/2023
2911	2^615503+1876643	185285	Enzo Doria	07/2016
2912	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
2913	(4*10^185221-91)/3	185222	Robert Price	03/2018
2914	(7*10^185221+131)/3	185222	Robert Price	06/2020
2915	(62*10^185216-413)/9	185217	Robert Price	09/2021
2916	(232*10^185180+17)/3	185182	Robert Price	04/2021
2917	56*10^185139-3	185141	Robert Price	03/2020
2918	(28*10^185105+47)/3	185106	Robert Price	02/2021
2919	2^614783-2790097	185069	Enzo Doria	12/2015
2920	2^614745-29323	185057	Enzo Doria	07/2015
2921	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
2922	(49*10^184993-67)/9	184994	Robert Price	03/2019
2923	(5*10^184954-191)/3	184955	Robert Price	05/2021
2924	(14*10^184950+211)/9	184951	Robert Price	04/2018
2925	2^614360+215221	184941	Enzo Doria	11/2023
2926	2^614315+81353	184928	Enzo Doria	08/2016
2927	2^614294-1849961	184921	Enzo Doria	08/2015
2928	2^614266+1877809	184913	Enzo Doria	08/2016
2929	(185*10^184878-11)/3	184880	Robert Price	10/2020
2930	91*10^184867-9	184869	Robert Price	06/2021
2931	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
2932	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
2933	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
2934	(85*10^184768+77)/9	184769	Robert Price	07/2022
2935	2^613715-1860727	184747	Enzo Doria	11/2015
2936	(4*10^184730+89)/3	184731	Robert Price	08/2021
2937	2*10^184723+41	184724	Robert Price	05/2018
2938	(49*10^184703+293)/9	184704	Robert Price	03/2021
2939	2^613487-349987	184678	Enzo Doria	07/2015
2940	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
2941	14^161089-161089^14	184629	Serge Batalov	05/2016
2942	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
2943	2^613033-114621	184542	Enzo Doria	05/2015
2944	3*2^612759+5	184460	Jon Grantham	07/2023
2945	2^612587+213413	184408	Enzo Doria	09/2023
2946	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
2947	2^612424+212341	184358	Enzo Doria	08/2023
2948	2^612341-1604809	184334	Enzo Doria	05/2015
2949	(11*10^184308-161)/3	184309	Robert Price	11/2021
2950	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
2951	(14*10^184150+37)/3	184151	Robert Price	12/2018
2952	2^611731-4837	184150	Yves Minet	08/2018
2953	3*10^184124-7	184125	Robert Price	08/2015
2954	2^611644+29371	184124	Enzo Doria	02/2024
2955	9*10^184122-11	184123	Mischa Rodermond	04/2023
2956	2^611628-24537	184119	Enzo Doria	08/2013
2957	3*10^184110+13	184111	Robert Price	07/2018
2958	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
2959	(194*10^184093+1)/3	184095	Robert Price	01/2022
2960	2^611460+71881	184068	Enzo Doria	04/2016
2961	4*10^184004-63	184005	Robert Price	10/2018
2962	2^611111+84083	183963	Boyan Hu	05/2024
2963	2^610982-1867301	183924	Enzo Doria	03/2016
2964	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
2965	3*10^183872-49	183873	Robert Price	07/2018
2966	2^610597+1178897	183809	Enzo Doria	05/2016
2967	(8*10^183773-269)/9	183773	Robert Price	09/2021
2968	(65*10^183768-29)/9	183769	Robert Price	01/2021
2969	(17*10^183764+31)/3	183765	Robert Price	01/2019
2970	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
2971	2^610401+1277	183750	Lelio R Paula	07/2013
2972	2^610356-1849019	183736	Enzo Doria	08/2015
2973	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
2974	23*10^183710-7	183712	Robert Price	02/2020
2975	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
2976	(4*10^183659+149)/9	183659	Robert Price	04/2018
2977	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
2978	(11^176327-1)/31738870	183619	Paul Vanderveen	05/2025
2979	7*10^183596+39	183597	Robert Price	01/2023
2980	2^609846-1834251	183582	Enzo Doria	07/2015
2981	10^183546+1547323	183547	Patrick De Geest	02/2021
2983	10^183546-800000001	183546	Robert Price	09/2020
2982	10^183546-584297	183546	Patrick De Geest	02/2021
2984	7*10^183511+39	183512	Robert Price	01/2023
2985	(23*10^183477-71)/3	183478	Robert Price	07/2020
2986	11^176176-240	183469	Enzo Doria	11/2012
2987	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
2988	6*10^183429+53	183430	Robert Price	05/2020
2989	(28*10^183403+191)/3	183404	Robert Price	02/2020
2990	U(1096855)	183383	Serge Batalov	07/2024
2991	(5^262337-1)/363486427756606700767551233751524443601036	183325	Paul Vanderveen	05/2025
2992	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
2993	2^608965-113989	183317	Enzo Doria	10/2014
2994	A005165(43592)	183312	Serge Batalov	07/2017
2995	(61*10^183294+119)/9	183295	Robert Price	05/2019
2996	2^608814-461261	183272	Enzo Doria	06/2015
2997	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
2998	2^608541-608541^2	183190	Henri Lifchitz	02/2018
2999	2^608293+143807	183115	Enzo Doria	10/2016
3000	2^608164-462419	183076	Enzo Doria	08/2015

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