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	(203*10^140615-11)/3	140617	Robert Price	12/2020
2752	(85*10^140609+473)/9	140610	Robert Price	01/2020
2753	39231^3836+3836^39231	140600	Hans Havermann	06/2021
2754	2^466866-1840571	140541	Enzo Doria	06/2015
2755	2^466829-459523	140530	Enzo Doria	05/2015
2756	2^466692-113213	140489	Enzo Doria	07/2014
2757	23*10^140464-3	140466	Robert Price	10/2021
2758	31335^30364+30364^31335	140455	Hans Havermann	05/2021
2759	32795^19126+19126^32795	140416	Hans Havermann	05/2021
2760	(44*10^140410-503)/9	140411	Robert Price	12/2018
2761	153^64265-2	140400	Lelio R Paula	11/2017
2762	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2763	(29*10^140337-17)/3	140338	Robert Price	09/2019
2764	2^466181-112735	140335	Enzo Doria	07/2014
2765	(16*10^140290-37)/3	140291	Robert Price	05/2021
2766	(5*10^140281-119)/3	140282	Robert Price	03/2018
2767	34568^11415+11415^34568	140259	Hans Havermann	05/2021
2768	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2769	33632^14781+14781^33632	140236	Hans Havermann	05/2021
2770	31803^25670+25670^31803	140233	Hans Havermann	05/2021
2771	2^465803-114817	140221	Enzo Doria	05/2015
2772	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2773	2^465503-112735	140131	Enzo Doria	07/2014
2774	(16*10^140091+167)/3	140092	Robert Price	06/2019
2775	(8*10^140087-137)/3	140088	Robert Price	03/2022
2776	6^179964+179964^6-1	140040	Robert Price	04/2014
2777	(89*10^140008-179)/9	140009	Robert Price	12/2019
2778	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
2779	2^465072-344789	140001	Enzo Doria	07/2015
2780	34742^10683+10683^34742	139965	Hans Havermann	05/2021
2781	5*10^139945+81	139946	Robert Price	03/2019
2782	32648^19335+19335^32648	139941	Hans Havermann	05/2021
2783	2^464864-17	139939	Lelio R Paula	09/2017
2784	8*10^139920+51	139921	Robert Price	08/2019
2785	(85*10^139913-1)/3	139915	Robert Price	02/2020
2786	31203^30436+30436^31203	139896	Hans Havermann	04/2021
2787	4*10^139839-27	139840	Robert Price	08/2021
2788	33582^14573+14573^33582	139821	Hans Havermann	05/2021
2789	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
2791	2*10^139800-21	139801	Robert Price	09/2020
2790	32628^19261+19261^32628	139801	Hans Havermann	04/2021
2792	(13*10^139782+191)/3	139783	Robert Price	11/2018
2793	(64*10^139776+791)/9	139777	Robert Price	01/2022
2794	(695*10^139772+7)/9	139774	Robert Price	12/2021
2795	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
2796	(74*10^139723+133)/9	139724	Robert Price	06/2019
2797	3*10^139722+13	139723	Robert Price	07/2018
2798	31577^26592+26592^31577	139721	Hans Havermann	05/2021
2799	77*10^139692+3	139694	Robert Price	06/2020
2800	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
2801	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
2802	39640^3321+3321^39640	139584	Hans Havermann	05/2021
2803	36663^6410+6410^36663	139571	Hans Havermann	05/2021
2804	2^463633-2788423	139568	Enzo Doria	11/2015
2805	33659^13978+13978^33659	139532	Hans Havermann	05/2021
2806	31811^24318+24318^31811	139521	Hans Havermann	04/2021
2807	34149^12172+12172^34149	139512	Hans Havermann	04/2021
2808	(29*10^139476+313)/9	139477	Robert Price	04/2021
2809	31721^24940+24940^31721	139474	Hans Havermann	05/2021
2810	32833^17698+17698^32833	139473	Hans Havermann	05/2021
2811	2^463271-109501	139459	Enzo Doria	04/2014
2812	(5*10^139457+79)/3	139458	Robert Price	03/2018
2813	2^463237-99	139449	Lelio R Paula	09/2017
2814	(49*10^139442+383)/9	139443	Robert Price	04/2019
2815	31155^29902+29902^31155	139441	Hans Havermann	05/2021
2816	(7*10^139417-547)/9	139417	Robert Price	01/2018
2817	(10^139398+191)/3	139398	Robert Price	02/2018
2818	23*10^139386-3	139388	Robert Price	10/2021
2819	2^463019+79463	139383	Enzo Doria	06/2016
2820	3^292129-112756	139381	Enzo Doria	07/2014
2821	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
2822	31922^23205+23205^31922	139359	Hans Havermann	05/2021
2824	2^462855-1865707	139334	Enzo Doria	02/2016
2823	31237^28876+28876^31237	139334	Hans Havermann	05/2021
2825	(86*10^139315+121)/9	139316	Robert Price	08/2019
2826	2^462786-292043	139313	Enzo Doria	08/2015
2827	38915^3798+3798^38915	139299	Hans Havermann	05/2021
2828	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
2829	34065^12248+12248^34065	139260	Hans Havermann	05/2021
2830	36425^6654+6654^36425	139256	Hans Havermann	05/2021
2831	39252^3527+3527^39252	139243	Hans Havermann	05/2021
2832	(17*10^139239+67)/3	139240	Robert Price	01/2019
2833	31887^23248+23248^31887	139231	Hans Havermann	05/2021
2834	(25*10^139210-97)/9	139211	Robert Price	01/2022
2835	2^462238-935	139148	Yves Minet	02/2014
2836	(29*10^139134-119)/9	139135	Robert Price	12/2021
2837	(109*10^139100-7)/3	139102	Robert Price	03/2021
2838	38744^3885+3885^38744	139068	Hans Havermann	05/2021
2839	31112^29499+29499^31112	139065	Hans Havermann	05/2021
2840	2*10^139043-63	139044	Robert Price	01/2022
2841	36390^6613+6613^36390	139025	Hans Havermann	04/2021
2842	2*10^138975+33	138976	Robert Price	11/2021
2843	42437^1882+1882^42437	138966	Hans Havermann	05/2021
2844	32151^20990+20990^32151	138958	Hans Havermann	05/2021
2845	32154^20933+20933^32154	138933	Hans Havermann	04/2021
2846	31082^29499+29499^31082	138931	Hans Havermann	04/2021
2847	2^461228+1870441	138844	Enzo Doria	05/2016
2848	2^461204-113675	138837	Enzo Doria	08/2014
2849	(2^461139-7)/47	138815	Lelio R Paula	08/2015
2850	(17*10^138812-521)/9	138813	Robert Price	04/2018
2851	3*10^138811-11	138812	Robert Price	07/2018
2852	(28*10^138768+173)/3	138769	Robert Price	12/2019
2853	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
2854	(379*10^138737-1)/9	138739	Robert Price	02/2020
2855	(43*10^138648+101)/9	138649	Robert Price	11/2018
2856	2^460567-113541	138645	Enzo Doria	08/2014
2857	(10^138622+161)/9	138622	Robert Price	09/2021
2858	7*10^138604+3	138605	Robert Price	08/2015
2859	(133*10^138600+17)/3	138602	Robert Price	11/2021
2860	33912^12203+12203^33912	138581	Hans Havermann	05/2021
2861	2^460330+69	138574	Lelio R Paula	09/2017
2862	(17*10^138569-77)/3	138570	Robert Price	08/2019
2863	31186^27725+27725^31186	138556	Hans Havermann	05/2021
2864	(16*10^138545+89)/3	138546	Robert Price	03/2021
2865	39753^3056+3056^39753	138546	Hans Havermann	05/2021
2866	31282^26847+26847^31282	138545	Hans Havermann	05/2021
2867	6*10^138520-37	138521	Robert Price	02/2021
2869	2^460078-69581	138498	Enzo Doria	12/2015
2868	31830^22447+22447^31830	138498	Hans Havermann	05/2021
2870	37384^5065+5065^37384	138492	Hans Havermann	05/2021
2871	34774^9585+9585^34774	138456	Hans Havermann	05/2021
2872	10^138444-5001	138444	Robert Price	12/2021
2873	2^459768+1531	138404	Lelio R Paula	06/2012
2874	(266*10^138328-17)/3	138330	Robert Price	07/2020
2875	32963^15696+15696^32963	138306	Hans Havermann	05/2021
2876	2^459343-113611	138277	Enzo Doria	08/2014
2877	(28*10^138240+113)/3	138241	Robert Price	03/2020
2878	2^459199+1874393	138233	Enzo Doria	06/2016
2879	33339^14002+14002^33339	138230	Hans Havermann	05/2021
2880	2^459063-345307	138192	Enzo Doria	06/2015
2881	2*10^138162-43	138163	Robert Price	04/2018
2882	2^458927-112747	138151	Enzo Doria	06/2014
2883	2^458927-69217	138151	Enzo Doria	11/2015
2884	30907^29458+29458^30907	138130	Hans Havermann	05/2021
2885	32882^15837+15837^32882	138094	Hans Havermann	05/2021
2886	39252^3295+3295^39252	138083	Hans Havermann	05/2021
2887	33789^12190+12190^33789	138062	Hans Havermann	06/2021
2888	555555*2^458524+1513	138036	Darren Bedwell	08/2009
2889	30931^29002+29002^30931	138028	Hans Havermann	05/2021
2890	2^458465+2^32+1	138012	T. D. Noe	06/2007
2891	32206^19275+19275^32206	138003	Hans Havermann	05/2021
2892	2^458321-113053	137969	Enzo Doria	07/2014
2893	2^458298+79459	137962	Enzo Doria	06/2016
2894	2^458248-21815	137947	Enzo Doria	07/2013
2895	2^458194+1876549	137931	Enzo Doria	07/2016
2896	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
2897	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
2898	(793*10^137887+53)/9	137889	Robert Price	01/2022
2899	2^457937+57	137853	Lelio R Paula	09/2017
2900	(8*10^137845+13)/3	137846	Robert Price	06/2018
2901	2^457822+105	137819	Donovan Johnson	06/2006
2902	2^457754-113711	137798	Enzo Doria	09/2014
2903	11^132315-360	137792	Enzo Doria	09/2012
2904	32072^19689+19689^32072	137725	Hans Havermann	06/2021
2905	44592^1225+1225^44592	137707	Hans Havermann	05/2021
2906	2^457347-37	137676	Lelio R Paula	09/2017
2907	2^457322-2786393	137668	Enzo Doria	10/2015
2908	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
2909	34015^11134+11134^34015	137647	Hans Havermann	06/2021
2910	2^457240-59939	137643	Enzo Doria	10/2015
2911	(856*10^137633-1)/9	137635	Robert Price	03/2020
2912	36232^6289+6289^36232	137631	Hans Havermann	05/2021
2913	2^457120-21575	137607	Enzo Doria	07/2013
2914	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
2915	30963^27722+27722^30963	137564	Hans Havermann	04/2021
2916	33722^12003+12003^33722	137562	Hans Havermann	06/2021
2917	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
2918	41901^1918+1918^41901	137555	Hans Havermann	06/2021
2919	32930^15021+15021^32930	137539	Hans Havermann	05/2021
2920	31178^25785+25785^31178	137538	Hans Havermann	05/2021
2921	419^52446+52446^419	137525	Norbert Schneider	11/2020
2922	2^456796-113513	137510	Enzo Doria	08/2014
2923	31788^21137+21137^31788	137485	Hans Havermann	04/2021
2924	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
2925	2^456503-114361	137422	Enzo Doria	01/2015
2926	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
2927	36248^6147+6147^36248	137332	Hans Havermann	05/2021
2928	31986^19651+19651^31986	137329	Hans Havermann	05/2021
2929	31817^20656+20656^31817	137292	Hans Havermann	05/2021
2930	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
2931	2^455922+76249	137247	Enzo Doria	05/2016
2932	31310^24171+24171^31310	137241	Hans Havermann	05/2021
2933	14^119741-119741^14	137239	Serge Batalov	04/2016
2934	35014^8297+8297^35014	137218	Hans Havermann	05/2021
2935	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
2937	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
2936	124^65536+57^65536	137195	Serge Batalov	03/2018
2938	2^455689+72677	137177	Enzo Doria	04/2016
2939	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
2940	31287^24128+24128^31287	137116	Hans Havermann	05/2021
2941	(37^87421-1)/36	137093	Robert Price	03/2012
2942	36233^6070+6070^36233	137077	Hans Havermann	05/2021
2943	38418^3697+3697^38418	137070	Hans Havermann	04/2021
2944	2^455323-57	137066	Lelio R Paula	09/2017
2945	(56*10^137019+583)/9	137020	Robert Price	08/2021
2946	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
2947	2^455025-112723	136977	Enzo Doria	06/2014
2948	33876^11039+11039^33876	136959	Hans Havermann	05/2021
2949	35142^7873+7873^35142	136919	Hans Havermann	05/2021
2950	66*10^136894+7	136896	Robert Price	07/2020
2951	2^454675-1777	136871	Yves Minet	10/2011
2952	31676^20931+20931^31676	136866	Hans Havermann	05/2021
2953	3*10^136829+29	136830	Robert Price	05/2018
2954	4*10^136813-57	136814	Robert Price	10/2018
2955	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
2956	37359^4588+4588^37359	136795	Hans Havermann	05/2021
2957	2^454348-53	136773	Lelio R Paula	09/2017
2958	31^91680-2	136729	Lelio R Paula	05/2017
2959	2^454199-113697	136728	Enzo Doria	09/2014
2960	30785^27622+27622^30785	136725	Hans Havermann	05/2021
2961	32973^14014+14014^32973	136725	Hans Havermann	05/2021
2963	7*10^136716+69	136717	Robert Price	07/2019
2962	36002^6273+6273^36002	136717	Hans Havermann	05/2021
2964	6*10^136692+53	136693	Robert Price	05/2020
2965	(13*10^136687+47)/3	136688	Robert Price	10/2018
2966	2^453935-2791357	136649	Enzo Doria	01/2016
2967	2^453906-69131	136640	Enzo Doria	11/2015
2968	33232^12915+12915^33232	136620	Hans Havermann	05/2021
2969	2^453791+1873913	136605	Enzo Doria	06/2016
2970	34166^9951+9951^34166	136592	Hans Havermann	05/2021
2971	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
2972	31102^24635+24635^31102	136587	Hans Havermann	05/2021
2973	580^49413+49413^580	136550	Norbert Schneider	02/2019
2974	2^453503-2788297	136519	Enzo Doria	11/2015
2975	34989^7958+7958^34989	136486	Hans Havermann	12/2020
2976	(2*10^136484+187)/9	136484	Robert Price	06/2022
2977	31007^25158+25158^31007	136452	Hans Havermann	11/2020
2978	2^453267-113827	136447	Enzo Doria	09/2014
2979	32234^17085+17085^32234	136435	Hans Havermann	12/2020
2980	2^453102+1877629	136398	Enzo Doria	08/2016
2981	31016^24981+24981^31016	136397	Hans Havermann	12/2020
2982	(62*10^136384-791)/9	136385	Robert Price	06/2019
2983	34171^9798+9798^34171	136382	Hans Havermann	12/2020
2984	(17*10^136354-113)/3	136355	Robert Price	06/2021
2985	32756^14541+14541^32756	136350	Hans Havermann	11/2020
2986	32205^17086+17086^32205	136313	Hans Havermann	12/2020
2987	(25*10^136303+161)/3	136304	Robert Price	09/2019
2988	35337^7196+7196^35337	136299	Hans Havermann	12/2020
2989	(182*10^136291+1)/3	136293	Robert Price	02/2020
2990	(88*10^136234+83)/9	136235	Robert Price	03/2022
2991	23*10^136225-7	136227	Robert Price	02/2020
2992	L(651821)	136223	Henri Lifchitz	09/2008
2993	2^452460+77701	136205	Enzo Doria	05/2016
2994	2^452440-114755	136199	Enzo Doria	04/2015
2995	32286^16489+16489^32286	136157	Hans Havermann	11/2020
2996	(47*10^136141+493)/9	136142	Robert Price	03/2019
2997	40392^2339+2339^40392	136082	Hans Havermann	12/2020
2998	2*10^136057-43	136058	Robert Price	04/2018
2999	(2^451956-5)/181	136051	Lelio R Paula	07/2015
3000	2^451947-22165	136050	Enzo Doria	07/2013

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Probable Primes Top 10000

(290751 PRPs in the top)