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	(299*10^197426+1)/3	197428	Robert Price	04/2020
2752	2^655682-1849121	197380	Enzo Doria	08/2015
2753	4*10^197268-89	197269	Robert Price	11/2018
2754	(11*10^197198-89)/3	197199	Robert Price	05/2021
2755	2^655045-49603	197189	Enzo Doria	10/2015
2756	2^655000-2784089	197175	Enzo Doria	10/2015
2757	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
2758	(4*10^197061+41)/9	197061	Serge Batalov	11/2022
2759	(154*10^197005+17)/9	197007	Robert Price	06/2022
2760	2^654400-39719	196995	Enzo Doria	09/2015
2761	(5^281807-2^281807)/3	196975	Jon Grantham	08/2023
2762	(14*10^196965-221)/9	196966	Robert Price	04/2018
2763	(7^233069-1)/52258731186	196956	Paul Vanderveen	05/2025
2764	2^654216-459995	196939	Enzo Doria	06/2015
2765	(17*10^196921+31)/3	196922	Robert Price	01/2019
2766	(14*10^196885-89)/3	196886	Robert Price	05/2020
2767	3*10^196881-59	196882	Robert Price	09/2018
2768	2^653851+82295	196829	Enzo Doria	09/2016
2769	(38*10^196792+691)/9	196793	Robert Price	10/2018
2770	(65*10^196768+493)/9	196769	Robert Price	08/2021
2772	2^653636-29429	196765	Enzo Doria	08/2015
2771	2^653638-11	196765	Stefano Morozzi	07/2022
2773	2^653601-69673	196754	Enzo Doria	02/2016
2774	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
2775	2^652786-1852571	196509	Enzo Doria	08/2015
2776	2^652752-1325	196498	Yves Minet	07/2015
2777	2^652470-1859141	196414	Enzo Doria	10/2015
2778	2^652346+29329	196376	Enzo Doria	02/2024
2779	2^652307+1877483	196364	Enzo Doria	08/2016
2780	2^652293-115273	196360	Enzo Doria	06/2015
2781	(47*10^196281+403)/9	196282	Robert Price	03/2019
2782	2^652025+218027	196280	Enzo Doria	01/2024
2783	2^652004+23961	196273	Enzo Doria	10/2023
2784	(7*10^196125-31)/3	196126	Robert Price	12/2021
2785	33^129128+129128^33	196083	Norbert Schneider	06/2022
2786	6*10^196070+73	196071	Robert Price	04/2019
2787	2^651218-1868201	196037	Enzo Doria	04/2016
2788	2^651047-49687	195985	Enzo Doria	10/2015
2789	10^195968-700001	195968	Robert Price	08/2021
2790	fibonacci(937485)+3	195923	Jon Grantham	08/2023
2791	(29*10^195875-197)/3	195876	Robert Price	08/2021
2792	(25*10^195808-97)/9	195809	Robert Price	01/2022
2793	2^650285-2785333	195756	Enzo Doria	10/2015
2794	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
2795	(29*10^195648-41)/3	195649	Tyler Busby	03/2024
2796	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
2797	2^649811+1877573	195613	Enzo Doria	08/2016
2798	2^649662-170531	195568	Hans Havermann	10/2018
2799	2^649586+182839	195545	Enzo Doria	11/2016
2800	2^649537-1867363	195531	Enzo Doria	04/2016
2801	2^649536-1861499	195530	Enzo Doria	12/2015
2802	2^649493+25907	195517	Enzo Doria	11/2023
2803	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
2804	2^649102-59351	195400	Enzo Doria	10/2015
2805	(2*10^195399+529)/9	195399	Robert Price	01/2018
2806	(202*10^195383-13)/9	195385	Robert Price	01/2020
2807	2^648988+1178971	195365	Enzo Doria	06/2016
2808	2^648975-114319	195361	Enzo Doria	02/2015
2809	(11*10^195350-137)/9	195351	Robert Price	01/2018
2810	2^648619-24835	195254	Enzo Doria	09/2013
2811	5*10^195250-21	195251	Robert Price	12/2021
2812	(14*10^195234-83)/3	195235	Robert Price	12/2018
2813	5*10^195221+81	195222	Robert Price	03/2019
2814	10^195143-5001	195143	Robert Price	12/2021
2815	2^648190-24737	195125	Enzo Doria	09/2013
2816	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
2817	(29*10^195098-197)/3	195099	Robert Price	08/2021
2818	10^195060+89701	195061	Patrick De Geest	02/2021
2820	10^195060-40000000001	195060	Robert Price	09/2020
2819	10^195060-110337	195060	Patrick De Geest	02/2021
2821	56*10^195032-3	195034	Robert Price	03/2020
2822	11^187185-90	194934	Enzo Doria	09/2012
2823	2^647545-25	194931	Boyan Hu	12/2024
2824	2^647468+220141	194908	Enzo Doria	03/2024
2825	(83^101533-1)/91545628589416644493342	194827	Paul Vanderveen	06/2025
2826	(86*10^194818-437)/9	194819	Robert Price	03/2021
2827	7^230492-230492^7	194789	Henri Lifchitz	07/2024
2828	2^647068+77281	194787	Enzo Doria	05/2016
2829	2*10^194716-93	194717	Robert Price	12/2021
2830	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
2831	F(931517)	194676	Henri Lifchitz	09/2008
2832	4*10^194668+49	194669	Robert Price	01/2019
2833	2^646589+1179407	194643	Enzo Doria	06/2016
2834	2^646289-114621	194553	Enzo Doria	05/2015
2835	2^646236-39659	194537	Enzo Doria	09/2015
2836	(16*10^194536+53)/3	194537	Robert Price	03/2019
2837	2^646161-59833	194514	Enzo Doria	11/2015
2838	(17*10^194502+31)/3	194503	Robert Price	01/2019
2839	(19*10^194428+287)/9	194429	Robert Price	10/2021
2840	2*10^194413+3	194414	Robert Price	07/2015
2841	2^645360-1848599	194273	Enzo Doria	08/2015
2842	22470^44641+44641^22470	194260	Norbert Schneider	08/2023
2843	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
2844	Phi(293127,10)	194041	Makoto Kamada	12/2023
2845	2*10^193981-43	193982	Robert Price	04/2018
2846	2^644382+75169	193979	Enzo Doria	04/2016
2847	2^644304-1861409	193955	Enzo Doria	11/2015
2848	(29*10^193950-23)/3	193951	Robert Price	03/2022
2849	5*10^193907-9	193908	Robert Price	05/2015
2850	2^644043+1876703	193877	Enzo Doria	07/2016
2851	2*10^193841-63	193842	Robert Price	01/2022
2852	2^643735+1879733	193784	Enzo Doria	09/2016
2853	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
2854	9*10^193712+71	193713	Robert Price	08/2020
2855	2^643216-286565	193628	Enzo Doria	07/2015
2856	2^643204+215011	193624	Enzo Doria	11/2023
2857	10^193566+1126339	193567	Patrick De Geest	09/2022
2859	10^193566-10000000001	193566	Robert Price	04/2021
2858	10^193566-454041	193566	Patrick De Geest	08/2021
2861	2^642888-24965	193529	Enzo Doria	09/2013
2860	2^642889+25367	193529	Enzo Doria	11/2023
2862	2^642448-114825	193397	Enzo Doria	05/2015
2863	2^642437-1856623	193393	Enzo Doria	10/2015
2864	2^642039-59797	193273	Enzo Doria	11/2015
2865	2^641987+39	193258	Jon Grantham	08/2023
2866	10^193230+513861	193231	Patrick De Geest	07/2018
2867	10^193230-8001	193230	Robert Price	03/2018
2868	(62*10^193225-233)/9	193226	Robert Price	02/2022
2869	2^641692-286349	193169	Enzo Doria	07/2015
2870	2^641690-24737	193168	Enzo Doria	09/2013
2871	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
2872	2^641514+1876549	193115	Enzo Doria	07/2016
2873	2^640888-2785619	192927	Enzo Doria	10/2015
2874	2^640874-2783741	192923	Enzo Doria	09/2015
2875	10^192922+192207	192923	Patrick De Geest	08/2021
2876	10^192922-7001	192922	Robert Price	04/2021
2877	2^640854+25	192917	Stefano Morozzi	05/2021
2878	34*10^192868-9	192870	Robert Price	06/2020
2879	(46*10^192841+683)/9	192842	Robert Price	03/2019
2880	2^640181+467	192714	Lelio R Paula	08/2013
2881	2^640072+27541	192681	Enzo Doria	01/2024
2882	(10^192700)/(192700^10)	192648	Henri Lifchitz	05/2025
2883	2^639536-1850249	192520	Enzo Doria	08/2015
2884	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
2885	5*10^192422-43	192423	Robert Price	01/2019
2886	2^639110-2792441	192392	Enzo Doria	02/2016
2887	(241^80761-1)/240	192372	Anonymous	04/2024
2888	2^638955-29827	192345	Enzo Doria	08/2015
2889	15^163539+14	192337	Alfred Reich	10/2023
2890	2^638713-2784223	192272	Enzo Doria	10/2015
2891	(10^192216+7)/149	192214	Alfred Reich	07/2021
2892	2^638490-113507	192205	Enzo Doria	08/2014
2893	2^638189-39943	192115	Enzo Doria	09/2015
2894	2^638110+1877119	192091	Enzo Doria	07/2016
2895	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
2896	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
2897	2^638066-2785211	192078	Enzo Doria	10/2015
2898	(35*10^191973-341)/9	191974	Robert Price	08/2021
2899	(112*10^191900+17)/3	191902	Robert Price	03/2020
2900	2^637475-115309	191900	Enzo Doria	07/2015
2901	(68*10^191754-113)/9	191755	Robert Price	03/2021
2902	2^636930-11	191736	Stefano Morozzi	07/2022
2903	(47*10^191732+259)/9	191733	Robert Price	03/2022
2904	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
2905	2^636661+1876577	191655	Enzo Doria	07/2016
2906	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
2907	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
2908	fibonacci(916540)-2	191546	Jon Grantham	08/2023
2909	2^636177-1855123	191509	Enzo Doria	09/2015
2910	2^636158-113627	191503	Enzo Doria	08/2014
2911	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
2912	2^636035+79823	191466	Enzo Doria	06/2016
2913	2^636011-1860847	191459	Enzo Doria	11/2015
2914	2^635926-1860611	191433	Enzo Doria	11/2015
2915	3*2^635755+5	191382	Jon Grantham	07/2023
2916	3*10^191152-7	191153	Robert Price	08/2015
2917	2^634883-1865677	191119	Enzo Doria	02/2016
2918	2^634801+1871957	191095	Enzo Doria	05/2016
2919	(77*10^191080+157)/9	191081	Robert Price	05/2022
2920	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
2921	9*10^191018-41	191019	Robert Price	08/2020
2922	2^634470-59861	190995	Enzo Doria	11/2015
2923	2^634368-29519	190964	Enzo Doria	08/2015
2924	(19*10^190935+11)/3	190936	Robert Price	07/2023
2925	2^634188-350609	190910	Enzo Doria	06/2015
2926	(65*10^190899+493)/9	190900	Robert Price	08/2021
2927	(62*10^190795-413)/9	190796	Robert Price	09/2021
2928	(26*10^190789-131)/3	190790	Robert Price	10/2019
2929	(13*10^190732-61)/3	190733	Robert Price	11/2018
2930	3*2^633524+5	190711	Jon Grantham	07/2023
2931	(7*10^190683+143)/3	190684	Robert Price	03/2018
2932	2^633088-113879	190579	Enzo Doria	10/2014
2933	2^633064+1874911	190572	Enzo Doria	06/2016
2934	5*3^399402+2^399402	190564	Jon Grantham	08/2023
2935	(43*10^190547+83)/9	190548	Robert Price	11/2018
2936	99*10^190543+7	190545	Robert Price	05/2021
2937	(299*10^190533+1)/3	190535	Robert Price	04/2020
2938	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
2939	2^632815-15	190497	Stefano Morozzi	07/2022
2940	2^632795-351205	190491	Enzo Doria	06/2015
2941	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
2942	(16*10^190420-19)/3	190421	Robert Price	02/2019
2943	(43*10^190351+101)/9	190352	Robert Price	11/2018
2944	2^632156+78391	190298	Enzo Doria	06/2016
2945	97*10^190295-3	190297	Robert Price	05/2020
2946	2^632082-1851971	190276	Enzo Doria	08/2015
2947	2^632020+1880311	190257	Enzo Doria	09/2016
2948	(5*10^190242-77)/9	190242	Robert Price	04/2021
2949	7*10^190210+13	190211	Robert Price	03/2021
2950	2^631637-462373	190142	Enzo Doria	08/2015
2951	2*10^190126-21	190127	Robert Price	09/2020
2952	(28*10^190105+191)/3	190106	Robert Price	02/2020
2953	2*10^190093+33	190094	Robert Price	11/2021
2954	(68*10^190053-113)/9	190054	Robert Price	03/2021
2955	2^631183+213413	190006	Enzo Doria	09/2023
2956	2^631122-39251	189987	Enzo Doria	08/2015
2957	(26*10^189928-89)/9	189929	Robert Price	06/2018
2958	2^630839-97	189902	Yves Minet	07/2017
2959	99*10^189876-7	189878	Robert Price	07/2020
2960	41147^41147+30^30	189867	Henri Lifchitz	09/2024
2961	2^630359+1788953	189757	Enzo Doria	05/2016
2962	2^630228+1871971	189718	Enzo Doria	05/2016
2963	2^630108+781	189682	Lelio R Paula	08/2013
2964	2^629870-1867811	189610	Enzo Doria	04/2016
2965	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
2966	2^629326+2792929	189447	Enzo Doria	02/2016
2967	4*10^189401+13	189402	Robert Price	02/2021
2968	(10^189385-61)/3	189385	Serge Batalov	12/2014
2969	2^629036+1874011	189359	Enzo Doria	06/2016
2970	2^628930+80779	189327	Enzo Doria	07/2016
2971	(134*10^189309-11)/3	189311	Robert Price	01/2022
2972	9*10^189306-11	189307	Mischa Rodermond	04/2023
2973	3^396740-396740^3	189294	Henri Lifchitz	07/2024
2974	2^628582+1179439	189223	Enzo Doria	06/2016
2975	(44*10^188999-503)/9	189000	Robert Price	12/2018
2976	(16*10^188823+167)/3	188824	Robert Price	06/2019
2977	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
2978	2^627037-2785843	188757	Enzo Doria	10/2015
2979	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
2980	(16*10^188457+161)/3	188458	Robert Price	02/2019
2981	L(901657)	188436	Renaud Lifchitz	11/2008
2982	(19*10^188375+137)/3	188376	Robert Price	03/2022
2983	2^625651+74213	188340	Enzo Doria	04/2016
2984	2^625584-460919	188320	Enzo Doria	06/2015
2985	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
2986	5^269399-3^269399-1	188302	Jon Grantham	08/2023
2987	(14*10^188218+139)/9	188219	Robert Price	11/2021
2988	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
2989	(10^188164+359)/9	188164	Serge Batalov	12/2014
2990	2^624481-113611	187988	Enzo Doria	08/2014
2991	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
2992	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
2993	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
2994	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
2995	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
2996	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
2998	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
2997	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
2999	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3000	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019

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Probable Primes Top 10000

(301979 PRPs in the top)