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	2^649102-59351	195400	Enzo Doria	10/2015
2752	(2*10^195399+529)/9	195399	Robert Price	01/2018
2753	(202*10^195383-13)/9	195385	Robert Price	01/2020
2754	2^648988+1178971	195365	Enzo Doria	06/2016
2755	2^648975-114319	195361	Enzo Doria	02/2015
2756	(11*10^195350-137)/9	195351	Robert Price	01/2018
2757	2^648619-24835	195254	Enzo Doria	09/2013
2758	5*10^195250-21	195251	Robert Price	12/2021
2759	(14*10^195234-83)/3	195235	Robert Price	12/2018
2760	5*10^195221+81	195222	Robert Price	03/2019
2761	10^195143-5001	195143	Robert Price	12/2021
2762	2^648190-24737	195125	Enzo Doria	09/2013
2763	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
2764	(29*10^195098-197)/3	195099	Robert Price	08/2021
2765	10^195060+89701	195061	Patrick De Geest	02/2021
2767	10^195060-40000000001	195060	Robert Price	09/2020
2766	10^195060-110337	195060	Patrick De Geest	02/2021
2768	56*10^195032-3	195034	Robert Price	03/2020
2769	11^187185-90	194934	Enzo Doria	09/2012
2770	2^647545-25	194931	Boyan Hu	12/2024
2771	2^647468+220141	194908	Enzo Doria	03/2024
2772	(83^101533-1)/91545628589416644493342	194827	Paul Vanderveen	06/2025
2773	(86*10^194818-437)/9	194819	Robert Price	03/2021
2774	7^230492-230492^7	194789	Henri Lifchitz	07/2024
2775	2^647068+77281	194787	Enzo Doria	05/2016
2776	2*10^194716-93	194717	Robert Price	12/2021
2777	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
2778	F(931517)	194676	Henri Lifchitz	09/2008
2779	4*10^194668+49	194669	Robert Price	01/2019
2780	2^646589+1179407	194643	Enzo Doria	06/2016
2781	2^646289-114621	194553	Enzo Doria	05/2015
2782	2^646236-39659	194537	Enzo Doria	09/2015
2783	(16*10^194536+53)/3	194537	Robert Price	03/2019
2784	2^646161-59833	194514	Enzo Doria	11/2015
2785	(17*10^194502+31)/3	194503	Robert Price	01/2019
2786	(19*10^194428+287)/9	194429	Robert Price	10/2021
2787	2*10^194413+3	194414	Robert Price	07/2015
2788	2^645360-1848599	194273	Enzo Doria	08/2015
2789	22470^44641+44641^22470	194260	Norbert Schneider	08/2023
2790	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
2791	Phi(293127,10)	194041	Makoto Kamada	12/2023
2792	2*10^193981-43	193982	Robert Price	04/2018
2793	2^644382+75169	193979	Enzo Doria	04/2016
2794	2^644304-1861409	193955	Enzo Doria	11/2015
2795	(29*10^193950-23)/3	193951	Robert Price	03/2022
2796	5*10^193907-9	193908	Robert Price	05/2015
2797	2^644043+1876703	193877	Enzo Doria	07/2016
2798	2*10^193841-63	193842	Robert Price	01/2022
2799	2^643735+1879733	193784	Enzo Doria	09/2016
2800	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
2801	9*10^193712+71	193713	Robert Price	08/2020
2802	2^643216-286565	193628	Enzo Doria	07/2015
2803	2^643204+215011	193624	Enzo Doria	11/2023
2804	10^193566+1126339	193567	Patrick De Geest	09/2022
2806	10^193566-10000000001	193566	Robert Price	04/2021
2805	10^193566-454041	193566	Patrick De Geest	08/2021
2808	2^642888-24965	193529	Enzo Doria	09/2013
2807	2^642889+25367	193529	Enzo Doria	11/2023
2809	2^642448-114825	193397	Enzo Doria	05/2015
2810	2^642437-1856623	193393	Enzo Doria	10/2015
2811	2^642039-59797	193273	Enzo Doria	11/2015
2812	2^641987+39	193258	Jon Grantham	08/2023
2813	10^193230+513861	193231	Patrick De Geest	07/2018
2814	10^193230-8001	193230	Robert Price	03/2018
2815	(62*10^193225-233)/9	193226	Robert Price	02/2022
2816	2^641692-286349	193169	Enzo Doria	07/2015
2817	2^641690-24737	193168	Enzo Doria	09/2013
2818	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
2819	2^641514+1876549	193115	Enzo Doria	07/2016
2820	2^640888-2785619	192927	Enzo Doria	10/2015
2821	2^640874-2783741	192923	Enzo Doria	09/2015
2822	10^192922+192207	192923	Patrick De Geest	08/2021
2823	10^192922-7001	192922	Robert Price	04/2021
2824	2^640854+25	192917	Stefano Morozzi	05/2021
2825	34*10^192868-9	192870	Robert Price	06/2020
2826	(46*10^192841+683)/9	192842	Robert Price	03/2019
2827	2^640181+467	192714	Lelio R Paula	08/2013
2828	2^640072+27541	192681	Enzo Doria	01/2024
2829	(10^192700)/(192700^10)	192648	Henri Lifchitz	05/2025
2830	2^639536-1850249	192520	Enzo Doria	08/2015
2831	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
2832	5*10^192422-43	192423	Robert Price	01/2019
2833	2^639110-2792441	192392	Enzo Doria	02/2016
2834	(241^80761-1)/240	192372	Anonymous	04/2024
2835	2^638955-29827	192345	Enzo Doria	08/2015
2836	15^163539+14	192337	Alfred Reich	10/2023
2837	2^638713-2784223	192272	Enzo Doria	10/2015
2838	(10^192216+7)/149	192214	Alfred Reich	07/2021
2839	2^638490-113507	192205	Enzo Doria	08/2014
2840	2^638189-39943	192115	Enzo Doria	09/2015
2841	2^638110+1877119	192091	Enzo Doria	07/2016
2842	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440	192083	Sergey Batalov	05/2024
2843	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)	192083	Sergey Batalov	05/2024
2844	2^638066-2785211	192078	Enzo Doria	10/2015
2845	(35*10^191973-341)/9	191974	Robert Price	08/2021
2846	(112*10^191900+17)/3	191902	Robert Price	03/2020
2847	2^637475-115309	191900	Enzo Doria	07/2015
2848	(68*10^191754-113)/9	191755	Robert Price	03/2021
2849	2^636930-11	191736	Stefano Morozzi	07/2022
2850	(47*10^191732+259)/9	191733	Robert Price	03/2022
2851	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
2852	2^636661+1876577	191655	Enzo Doria	07/2016
2853	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
2854	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
2855	fibonacci(916540)-2	191546	Jon Grantham	08/2023
2856	2^636177-1855123	191509	Enzo Doria	09/2015
2857	2^636158-113627	191503	Enzo Doria	08/2014
2858	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
2859	2^636035+79823	191466	Enzo Doria	06/2016
2860	2^636011-1860847	191459	Enzo Doria	11/2015
2861	2^635926-1860611	191433	Enzo Doria	11/2015
2862	3*2^635755+5	191382	Jon Grantham	07/2023
2863	3*10^191152-7	191153	Robert Price	08/2015
2864	2^634883-1865677	191119	Enzo Doria	02/2016
2865	2^634801+1871957	191095	Enzo Doria	05/2016
2866	(77*10^191080+157)/9	191081	Robert Price	05/2022
2867	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
2868	9*10^191018-41	191019	Robert Price	08/2020
2869	2^634470-59861	190995	Enzo Doria	11/2015
2870	2^634368-29519	190964	Enzo Doria	08/2015
2871	(19*10^190935+11)/3	190936	Robert Price	07/2023
2872	2^634188-350609	190910	Enzo Doria	06/2015
2873	(65*10^190899+493)/9	190900	Robert Price	08/2021
2874	(62*10^190795-413)/9	190796	Robert Price	09/2021
2875	(26*10^190789-131)/3	190790	Robert Price	10/2019
2876	(13*10^190732-61)/3	190733	Robert Price	11/2018
2877	3*2^633524+5	190711	Jon Grantham	07/2023
2878	(7*10^190683+143)/3	190684	Robert Price	03/2018
2879	2^633088-113879	190579	Enzo Doria	10/2014
2880	2^633064+1874911	190572	Enzo Doria	06/2016
2881	5*3^399402+2^399402	190564	Jon Grantham	08/2023
2882	(43*10^190547+83)/9	190548	Robert Price	11/2018
2883	99*10^190543+7	190545	Robert Price	05/2021
2884	(299*10^190533+1)/3	190535	Robert Price	04/2020
2885	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
2886	2^632815-15	190497	Stefano Morozzi	07/2022
2887	2^632795-351205	190491	Enzo Doria	06/2015
2888	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
2889	(16*10^190420-19)/3	190421	Robert Price	02/2019
2890	(43*10^190351+101)/9	190352	Robert Price	11/2018
2891	2^632156+78391	190298	Enzo Doria	06/2016
2892	97*10^190295-3	190297	Robert Price	05/2020
2893	2^632082-1851971	190276	Enzo Doria	08/2015
2894	2^632020+1880311	190257	Enzo Doria	09/2016
2895	(5*10^190242-77)/9	190242	Robert Price	04/2021
2896	7*10^190210+13	190211	Robert Price	03/2021
2897	2^631637-462373	190142	Enzo Doria	08/2015
2898	2*10^190126-21	190127	Robert Price	09/2020
2899	(28*10^190105+191)/3	190106	Robert Price	02/2020
2900	2*10^190093+33	190094	Robert Price	11/2021
2901	(68*10^190053-113)/9	190054	Robert Price	03/2021
2902	2^631183+213413	190006	Enzo Doria	09/2023
2903	2^631122-39251	189987	Enzo Doria	08/2015
2904	(26*10^189928-89)/9	189929	Robert Price	06/2018
2905	2^630839-97	189902	Yves Minet	07/2017
2906	99*10^189876-7	189878	Robert Price	07/2020
2907	41147^41147+30^30	189867	Henri Lifchitz	09/2024
2908	2^630359+1788953	189757	Enzo Doria	05/2016
2909	2^630228+1871971	189718	Enzo Doria	05/2016
2910	2^630108+781	189682	Lelio R Paula	08/2013
2911	2^629870-1867811	189610	Enzo Doria	04/2016
2912	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
2913	2^629326+2792929	189447	Enzo Doria	02/2016
2914	4*10^189401+13	189402	Robert Price	02/2021
2915	(10^189385-61)/3	189385	Serge Batalov	12/2014
2916	2^629036+1874011	189359	Enzo Doria	06/2016
2917	2^628930+80779	189327	Enzo Doria	07/2016
2918	(134*10^189309-11)/3	189311	Robert Price	01/2022
2919	9*10^189306-11	189307	Mischa Rodermond	04/2023
2920	3^396740-396740^3	189294	Henri Lifchitz	07/2024
2921	2^628582+1179439	189223	Enzo Doria	06/2016
2922	(44*10^188999-503)/9	189000	Robert Price	12/2018
2923	(16*10^188823+167)/3	188824	Robert Price	06/2019
2924	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
2925	2^627037-2785843	188757	Enzo Doria	10/2015
2926	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
2927	(16*10^188457+161)/3	188458	Robert Price	02/2019
2928	L(901657)	188436	Renaud Lifchitz	11/2008
2929	(19*10^188375+137)/3	188376	Robert Price	03/2022
2930	2^625651+74213	188340	Enzo Doria	04/2016
2931	2^625584-460919	188320	Enzo Doria	06/2015
2932	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
2933	5^269399-3^269399-1	188302	Jon Grantham	08/2023
2934	(14*10^188218+139)/9	188219	Robert Price	11/2021
2935	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
2936	(10^188164+359)/9	188164	Serge Batalov	12/2014
2937	2^624481-113611	187988	Enzo Doria	08/2014
2938	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
2939	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
2940	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
2941	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
2942	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
2943	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
2945	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
2944	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
2946	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
2947	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
2948	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
2949	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
2950	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
2952	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
2951	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
2953	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
2954	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
2955	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
2956	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
2957	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
2958	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
2959	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
2961	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
2960	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
2962	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
2963	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
2964	2^624077-112723	187866	Enzo Doria	07/2014
2965	2^624008+1874941	187846	Enzo Doria	06/2016
2966	2^623870+78679	187804	Enzo Doria	05/2016
2967	2^623714-114035	187757	Enzo Doria	11/2014
2968	2^623651-1834251	187738	Enzo Doria	07/2015
2969	(7*10^187645+53)/3	187646	Robert Price	05/2018
2970	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
2971	2^623146+1879609	187586	Enzo Doria	09/2016
2972	(401*10^187512+13)/9	187514	Robert Price	09/2021
2973	(5*10^187471+91)/3	187472	Robert Price	04/2018
2974	2^622500+81931	187392	Enzo Doria	08/2016
2975	(13*10^187382-157)/9	187383	Robert Price	05/2021
2976	2^622300-1861739	187331	Enzo Doria	12/2015
2977	(22*10^187317-91)/3	187318	Robert Price	02/2022
2978	(38*10^187281+349)/9	187282	Robert Price	10/2018
2979	2^622052+76771	187257	Enzo Doria	05/2016
2980	2^622005-24091	187243	Enzo Doria	08/2013
2981	7*10^187205-57	187206	Robert Price	06/2020
2982	2^621879-351787	187205	Enzo Doria	07/2015
2983	(5*10^187168-53)/3	187169	Robert Price	09/2020
2984	(23*10^187164-143)/3	187165	Robert Price	12/2019
2985	2^621700+79411	187151	Enzo Doria	06/2016
2986	2^621597+39	187120	Jon Grantham	08/2023
2987	(7*10^187101+131)/3	187102	Robert Price	06/2020
2988	(2*10^187062-71)/3	187062	Robert Price	12/2017
2989	V(1118570)	187013	Serge Batalov	07/2024
2990	2^620929-113203	186919	Enzo Doria	07/2014
2991	10^186842+168223	186843	Patrick De Geest	07/2018
2992	10^186842-8001	186842	Robert Price	03/2018
2993	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
2994	2^620347-1777	186744	Lelio R Paula	07/2013
2995	(11*10^186659+133)/9	186660	Robert Price	04/2022
2996	11^179143-4170	186559	Enzo Doria	12/2012
2997	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
2998	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
2999	2*10^186517+33	186518	Robert Price	11/2021
3000	2^619297-2792353	186427	Enzo Doria	02/2016

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Probable Primes Top 10000

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