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	2^460078-69581	138498	Enzo Doria	12/2015
2752	37384^5065+5065^37384	138492	Hans Havermann	05/2021
2753	34774^9585+9585^34774	138456	Hans Havermann	05/2021
2754	10^138444-5001	138444	Robert Price	12/2021
2755	2^459768+1531	138404	Lelio R Paula	06/2012
2756	(266*10^138328-17)/3	138330	Robert Price	07/2020
2757	32963^15696+15696^32963	138306	Hans Havermann	05/2021
2758	2^459343-113611	138277	Enzo Doria	08/2014
2759	(28*10^138240+113)/3	138241	Robert Price	03/2020
2760	2^459199+1874393	138233	Enzo Doria	06/2016
2761	33339^14002+14002^33339	138230	Hans Havermann	05/2021
2762	2^459063-345307	138192	Enzo Doria	06/2015
2763	2*10^138162-43	138163	Robert Price	04/2018
2764	2^458927-112747	138151	Enzo Doria	06/2014
2765	2^458927-69217	138151	Enzo Doria	11/2015
2766	30907^29458+29458^30907	138130	Hans Havermann	05/2021
2767	32882^15837+15837^32882	138094	Hans Havermann	05/2021
2768	39252^3295+3295^39252	138083	Hans Havermann	05/2021
2769	33789^12190+12190^33789	138062	Hans Havermann	06/2021
2770	555555*2^458524+1513	138036	Darren Bedwell	08/2009
2771	30931^29002+29002^30931	138028	Hans Havermann	05/2021
2772	2^458465+2^32+1	138012	T. D. Noe	06/2007
2773	32206^19275+19275^32206	138003	Hans Havermann	05/2021
2774	2^458321-113053	137969	Enzo Doria	07/2014
2775	2^458298+79459	137962	Enzo Doria	06/2016
2776	2^458248-21815	137947	Enzo Doria	07/2013
2777	2^458194+1876549	137931	Enzo Doria	07/2016
2778	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
2779	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
2780	2^457937+57	137853	Lelio R Paula	09/2017
2781	(8*10^137845+13)/3	137846	Robert Price	06/2018
2782	2^457822+105	137819	Donovan Johnson	06/2006
2783	2^457754-113711	137798	Enzo Doria	09/2014
2784	11^132315-360	137792	Enzo Doria	09/2012
2785	32072^19689+19689^32072	137725	Hans Havermann	06/2021
2786	44592^1225+1225^44592	137707	Hans Havermann	05/2021
2787	2^457347-37	137676	Lelio R Paula	09/2017
2788	2^457322-2786393	137668	Enzo Doria	10/2015
2789	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
2790	34015^11134+11134^34015	137647	Hans Havermann	06/2021
2791	2^457240-59939	137643	Enzo Doria	10/2015
2792	(856*10^137633-1)/9	137635	Robert Price	03/2020
2793	36232^6289+6289^36232	137631	Hans Havermann	05/2021
2794	2^457120-21575	137607	Enzo Doria	07/2013
2796	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
2795	30963^27722+27722^30963	137564	Hans Havermann	04/2021
2797	33722^12003+12003^33722	137562	Hans Havermann	06/2021
2798	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
2799	41901^1918+1918^41901	137555	Hans Havermann	06/2021
2800	32930^15021+15021^32930	137539	Hans Havermann	05/2021
2801	31178^25785+25785^31178	137538	Hans Havermann	05/2021
2802	419^52446+52446^419	137525	Norbert Schneider	11/2020
2803	2^456796-113513	137510	Enzo Doria	08/2014
2804	31788^21137+21137^31788	137485	Hans Havermann	04/2021
2805	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
2806	2^456503-114361	137422	Enzo Doria	01/2015
2807	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
2808	36248^6147+6147^36248	137332	Hans Havermann	05/2021
2809	31986^19651+19651^31986	137329	Hans Havermann	05/2021
2810	31817^20656+20656^31817	137292	Hans Havermann	05/2021
2811	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
2812	2^455922+76249	137247	Enzo Doria	05/2016
2813	31310^24171+24171^31310	137241	Hans Havermann	05/2021
2814	14^119741-119741^14	137239	Serge Batalov	04/2016
2815	35014^8297+8297^35014	137218	Hans Havermann	05/2021
2816	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
2818	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
2817	124^65536+57^65536	137195	Serge Batalov	03/2018
2819	2^455689+72677	137177	Enzo Doria	04/2016
2820	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
2821	31287^24128+24128^31287	137116	Hans Havermann	05/2021
2822	(37^87421-1)/36	137093	Robert Price	03/2012
2823	36233^6070+6070^36233	137077	Hans Havermann	05/2021
2824	38418^3697+3697^38418	137070	Hans Havermann	04/2021
2825	2^455323-57	137066	Lelio R Paula	09/2017
2826	(56*10^137019+583)/9	137020	Robert Price	08/2021
2827	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
2828	2^455025-112723	136977	Enzo Doria	06/2014
2829	33876^11039+11039^33876	136959	Hans Havermann	05/2021
2830	35142^7873+7873^35142	136919	Hans Havermann	05/2021
2831	66*10^136894+7	136896	Robert Price	07/2020
2832	2^454675-1777	136871	Yves Minet	10/2011
2833	31676^20931+20931^31676	136866	Hans Havermann	05/2021
2834	3*10^136829+29	136830	Robert Price	05/2018
2835	4*10^136813-57	136814	Robert Price	10/2018
2836	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
2837	37359^4588+4588^37359	136795	Hans Havermann	05/2021
2838	2^454348-53	136773	Lelio R Paula	09/2017
2839	31^91680-2	136729	Lelio R Paula	05/2017
2840	2^454199-113697	136728	Enzo Doria	09/2014
2841	30785^27622+27622^30785	136725	Hans Havermann	05/2021
2842	32973^14014+14014^32973	136725	Hans Havermann	05/2021
2844	7*10^136716+69	136717	Robert Price	07/2019
2843	36002^6273+6273^36002	136717	Hans Havermann	05/2021
2845	6*10^136692+53	136693	Robert Price	05/2020
2846	(13*10^136687+47)/3	136688	Robert Price	10/2018
2847	2^453935-2791357	136649	Enzo Doria	01/2016
2848	2^453906-69131	136640	Enzo Doria	11/2015
2849	33232^12915+12915^33232	136620	Hans Havermann	05/2021
2850	2^453791+1873913	136605	Enzo Doria	06/2016
2851	34166^9951+9951^34166	136592	Hans Havermann	05/2021
2852	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
2853	31102^24635+24635^31102	136587	Hans Havermann	05/2021
2854	580^49413+49413^580	136550	Norbert Schneider	02/2019
2855	2^453503-2788297	136519	Enzo Doria	11/2015
2856	34989^7958+7958^34989	136486	Hans Havermann	12/2020
2857	31007^25158+25158^31007	136452	Hans Havermann	11/2020
2858	2^453267-113827	136447	Enzo Doria	09/2014
2859	32234^17085+17085^32234	136435	Hans Havermann	12/2020
2860	2^453102+1877629	136398	Enzo Doria	08/2016
2861	31016^24981+24981^31016	136397	Hans Havermann	12/2020
2862	(62*10^136384-791)/9	136385	Robert Price	06/2019
2863	34171^9798+9798^34171	136382	Hans Havermann	12/2020
2864	(17*10^136354-113)/3	136355	Robert Price	06/2021
2865	32756^14541+14541^32756	136350	Hans Havermann	11/2020
2866	32205^17086+17086^32205	136313	Hans Havermann	12/2020
2867	(25*10^136303+161)/3	136304	Robert Price	09/2019
2868	35337^7196+7196^35337	136299	Hans Havermann	12/2020
2869	(182*10^136291+1)/3	136293	Robert Price	02/2020
2870	23*10^136225-7	136227	Robert Price	02/2020
2871	L(651821)	136223	Henri Lifchitz	09/2008
2872	2^452460+77701	136205	Enzo Doria	05/2016
2873	2^452440-114755	136199	Enzo Doria	04/2015
2874	32286^16489+16489^32286	136157	Hans Havermann	11/2020
2875	(47*10^136141+493)/9	136142	Robert Price	03/2019
2876	40392^2339+2339^40392	136082	Hans Havermann	12/2020
2877	2*10^136057-43	136058	Robert Price	04/2018
2878	(2^451956-5)/181	136051	Lelio R Paula	07/2015
2879	2^451947-22165	136050	Enzo Doria	07/2013
2880	2^451787-21805	136002	Enzo Doria	07/2013
2881	2^451734-112817	135986	Enzo Doria	06/2014
2882	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
2883	2^451705-21879	135977	Enzo Doria	07/2013
2884	2^451560-112349	135934	Enzo Doria	06/2014
2885	2^451530+45	135925	Lelio R Paula	08/2017
2886	31622^19875+19875^31622	135922	Hans Havermann	11/2020
2887	(25*10^135906-73)/3	135907	Robert Price	09/2019
2888	2^451450-21743	135900	Enzo Doria	07/2013
2889	35218^7199+7199^35218	135846	Hans Havermann	11/2020
2890	35661^6446+6446^35661	135844	Hans Havermann	11/2020
2891	31869^18248+18248^31869	135801	Hans Havermann	12/2020
2892	2^450805+65	135706	Lelio R Paula	08/2017
2893	30761^25728+25728^30761	135669	Hans Havermann	12/2020
2894	2*10^135663+69	135664	Robert Price	06/2020
2895	33962^9867+9867^33962	135651	Hans Havermann	11/2020
2896	34474^8605+8605^34474	135647	Hans Havermann	11/2020
2897	34501^8508+8508^34501	135583	Hans Havermann	12/2020
2898	35487^6614+6614^35487	135577	Hans Havermann	12/2020
2899	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
2900	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
2901	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
2902	(844*10^135527-7)/9	135529	Robert Price	05/2021
2903	40387^2260+2260^40387	135463	Hans Havermann	12/2020
2904	2^449944-113247	135447	Enzo Doria	07/2014
2905	2^449770-113247	135395	Enzo Doria	07/2014
2906	2^449637-21471	135355	Enzo Doria	07/2013
2907	2^449571-75	135335	Lelio R Paula	08/2017
2908	(14*10^135301-53)/3	135302	Robert Price	12/2018
2909	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
2910	(13*10^135279+437)/9	135280	Robert Price	04/2018
2911	2^449330-35	135262	Lelio R Paula	08/2017
2912	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2913	(13*10^135184-43)/3	135185	Robert Price	11/2018
2914	2^449049-115309	135178	Enzo Doria	07/2015
2915	(10^135174+191)/3	135174	Robert Price	02/2018
2916	2^449030-15	135172	Lelio R Paula	08/2017
2917	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
2918	(37*10^135099+251)/9	135100	Robert Price	09/2021
2919	32221^15586+15586^32221	135095	Hans Havermann	12/2020
2920	2^448762-351401	135091	Enzo Doria	07/2015
2921	2*10^135083-43	135084	Robert Price	04/2018
2922	31357^20278+20278^31357	135056	Hans Havermann	12/2020
2923	32242^15445+15445^32242	135055	Hans Havermann	12/2020
2924	k(198476)	135054	Robert Price	07/2020
2925	32461^14470+14470^32461	135053	Hans Havermann	12/2020
2926	31353^20288+20288^31353	135045	Hans Havermann	12/2020
2927	5*10^135019+77	135020	Robert Price	12/2018
2928	(10^135011+719)/9	135011	Serge Batalov	12/2014
2929	(197*10^134978+7)/3	134980	Robert Price	12/2020
2930	2^448386-2786261	134978	Enzo Doria	03/2016
2931	(73*10^134939+143)/9	134940	Robert Price	07/2019
2932	33957^9392+9392^33957	134903	Hans Havermann	12/2020
2933	2^448113-113949	134896	Enzo Doria	11/2014
2934	30958^22755+22755^30958	134887	Hans Havermann	12/2020
2935	2^447888-2786639	134828	Enzo Doria	03/2016
2936	2^447870-396765	134823	Enzo Doria	07/2013
2937	2^447766-21791	134791	Enzo Doria	07/2013
2938	(19*10^134786-49)/3	134787	Robert Price	05/2019
2939	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
2940	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
2941	2^447552-1019	134727	Yves Minet	02/2014
2942	(2*10^134720-41)/3	134720	Robert Price	02/2018
2943	(25*10^134695-97)/9	134696	Robert Price	01/2022
2944	2^447437-113569	134692	Enzo Doria	08/2014
2945	2^447426-65	134689	Lelio R Paula	08/2017
2946	2^447357-2797573	134668	Enzo Doria	04/2016
2947	2^447278+93	134645	Lelio R Paula	08/2017
2948	33193^11370+11370^33193	134623	Hans Havermann	12/2020
2949	30736^23979+23979^30736	134619	Hans Havermann	11/2020
2950	2^447094-113193	134589	Enzo Doria	07/2014
2951	3^282041-9934	134568	Enzo Doria	05/2014
2952	2^447019-109039	134567	Enzo Doria	04/2014
2953	31376^19437+19437^31376	134561	Hans Havermann	12/2020
2954	2^446990-22041	134558	Enzo Doria	07/2013
2955	123^64370+122	134528	Karsten Bonath	04/2018
2956	30100^29461+29461^30100	134525	Hans Havermann	11/2020
2957	31251^20158+20158^31251	134519	Hans Havermann	11/2020
2958	2^446782-39701	134495	Enzo Doria	09/2015
2959	31817^16858+16858^31817	134485	Hans Havermann	12/2020
2960	32448^13937+13937^32448	134471	Hans Havermann	12/2020
2961	2^446494-16485	134409	Enzo Doria	04/2013
2962	30042^29785+29785^30042	134408	Hans Havermann	12/2020
2963	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
2964	2^446441+65	134393	Lelio R Paula	08/2017
2965	(10^134385+719)/9	134385	Serge Batalov	12/2014
2966	30043^29688+29688^30043	134370	Hans Havermann	12/2020
2967	(2*10^134364+529)/9	134364	Robert Price	01/2018
2968	34657^7512+7512^34657	134323	Hans Havermann	11/2020
2969	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
2970	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
2971	42035^1564+1564^42035	134270	Hans Havermann	12/2020
2973	(2^446022-7)/339	134264	Lelio R Paula	07/2015
2972	30621^24248+24248^30621	134264	Hans Havermann	12/2020
2974	30341^26562+26562^30341	134237	Hans Havermann	11/2020
2975	10^134209+99867	134210	Patrick De Geest	05/2021
2976	10^134209-80000001	134209	Robert Price	04/2021
2977	10^134209-323283	134209	Patrick De Geest	05/2021
2978	29976^29953+29953^29976	134186	Hans Havermann	12/2020
2979	35038^6755+6755^35038	134183	Hans Havermann	12/2020
2980	63^74568+2	134174	Lelio R Paula	06/2017
2981	2^445671-22071	134161	Enzo Doria	07/2013
2982	532^49205+49205^532	134129	Norbert Schneider	02/2019
2983	36453^4780+4780^36453	134127	Hans Havermann	04/2021
2984	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
2985	2^445515-113859	134114	Enzo Doria	10/2014
2987	(22*10^134111-37)/3	134112	Robert Price	04/2019
2986	31083^20636+20636^31083	134112	Hans Havermann	04/2021
2988	31622^17379+17379^31622	134079	Hans Havermann	04/2021
2989	2^445328-216917	134058	Enzo Doria	05/2014
2990	2^445202+1874899	134020	Enzo Doria	06/2016
2991	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
2992	(35*10^133979-593)/9	133980	Robert Price	07/2018
2993	2*10^133955+51	133956	Robert Price	05/2018
2994	(49*10^133952+437)/9	133953	Robert Price	09/2021
2995	2^444964-113639	133948	Enzo Doria	08/2014
2996	31811^16240+16240^31811	133943	Hans Havermann	04/2021
2997	10^133902+167841	133903	Patrick De Geest	05/2021
2999	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
2998	10^133902-100001	133902	Robert Price	07/2020
3000	2^444784-113859	133894	Enzo Doria	10/2014

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Probable Primes Top 10000

(288949 PRPs in the top)