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	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2752	2^481045-113215	144809	Enzo Doria	07/2014
2753	(64*10^144797+287)/9	144798	Robert Price	04/2019
2754	2^480859-113695	144753	Enzo Doria	09/2014
2755	(106*10^144744+17)/3	144746	Robert Price	04/2021
2756	7*10^144742-27	144743	Robert Price	11/2022
2757	2^480766-2787191	144725	Enzo Doria	11/2015
2758	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2759	2^480678+1874239	144699	Enzo Doria	06/2016
2760	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2761	L(692147)	144651	Henri Lifchitz	10/2008
2762	(76*10^144648+77)/9	144649	Robert Price	10/2019
2763	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2764	2^480417+35	144620	Robert Price	11/2015
2765	2^480296-59879	144584	Enzo Doria	10/2015
2766	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2767	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2768	2^479844+3	144448	Donovan Johnson	06/2006
2769	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2770	31892^32061-32061^31892	144393	Norbert Schneider	01/2023
2771	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2772	(56*10^144380+169)/9	144381	Robert Price	03/2022
2773	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2774	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2775	(56*10^144336+583)/9	144337	Robert Price	08/2021
2776	2^479348-2792219	144299	Enzo Doria	02/2016
2777	3^302389-6242	144277	Enzo Doria	05/2014
2778	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2779	2*10^144220-3	144221	Robert Price	07/2015
2780	2^478904-109109	144165	Enzo Doria	04/2014
2781	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2782	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2783	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2784	(772*10^144036-7)/9	144038	Robert Price	06/2022
2785	34295^15828+15828^34295	144020	Hans Havermann	01/2021
2786	2^478337-115333	143994	Enzo Doria	07/2015
2787	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2788	88^74047-87^74047	143984	Robert Price	05/2015
2789	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2790	(19*10^143963+467)/9	143964	Robert Price	02/2018
2791	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2792	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2793	(853*10^143931-7)/9	143933	Robert Price	07/2021
2794	2^478088+27	143919	Robert Price	11/2015
2795	(8*10^143898-137)/3	143899	Robert Price	03/2022
2796	7*10^143857-93	143858	Robert Price	08/2020
2797	3*10^143844+61	143845	Robert Price	09/2020
2798	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2799	2^477475-22071	143735	Enzo Doria	07/2013
2800	2^477417-22123	143717	Enzo Doria	07/2013
2801	2^477359-3577	143700	Yves Minet	03/2017
2802	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2803	(14*10^143662-71)/3	143663	Robert Price	12/2018
2804	6^184614+5	143658	Paul Bourdelais	01/2021
2805	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2806	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2807	2^476936-396765	143573	Enzo Doria	07/2013
2808	2^476888-2791229	143558	Enzo Doria	01/2016
2809	2^476868-1859939	143552	Enzo Doria	11/2015
2810	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2811	755^49878+49878^755	143547	Norbert Schneider	04/2019
2812	(19^112247-4^112247)/15	143536	Robert Price	03/2021
2813	35561^10872+10872^35561	143536	Hans Havermann	06/2021
2814	37637^6492+6492^37637	143487	Hans Havermann	05/2021
2815	61567^214+214^61567	143477	Hans Havermann	05/2021
2816	2^476558-113627	143459	Enzo Doria	08/2014
2817	2^476478-45	143435	Lelio R Paula	11/2017
2818	36380^8757+8757^36380	143423	Hans Havermann	06/2021
2819	32510^25707+25707^32510	143371	Hans Havermann	05/2021
2820	8*10^143361+17	143362	Robert Price	07/2021
2821	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2822	2^475813-113239	143234	Enzo Doria	07/2014
2823	(19*10^143212+137)/3	143213	Robert Price	03/2022
2824	32218^27849+27849^32218	143203	Hans Havermann	04/2021
2825	2^475624-114059	143178	Enzo Doria	11/2014
2826	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2827	2^475480-2786129	143134	Enzo Doria	10/2015
2828	33912^16621+16621^33912	143131	Hans Havermann	05/2021
2829	(19*10^143129-43)/3	143130	Robert Price	05/2019
2830	31830^31373+31373^31830	143126	Hans Havermann	05/2021
2831	6*10^143105-53	143106	Robert Price	05/2021
2832	(14*10^143097+73)/3	143098	Robert Price	12/2018
2833	2^475299-111937	143080	Enzo Doria	05/2014
2834	35488^10753+10753^35488	143071	Hans Havermann	04/2021
2835	2^475160-2797859	143038	Enzo Doria	04/2016
2836	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2837	2^475027-461437	142998	Enzo Doria	07/2015
2838	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2839	(8*10^142932+43)/3	142933	Robert Price	06/2018
2840	35055^11942+11942^35055	142922	Hans Havermann	05/2021
2841	37650^6239+6239^37650	142887	Hans Havermann	05/2021
2842	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2843	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2844	2^474417-59923	142814	Enzo Doria	10/2015
2845	4*10^142810-21	142811	Robert Price	09/2018
2846	32287^26494+26494^32287	142811	Hans Havermann	06/2021
2847	37162^6965+6965^37162	142811	Hans Havermann	06/2021
2848	(34*10^142805-601)/9	142806	Robert Price	07/2022
2849	37456^6493+6493^37456	142799	Hans Havermann	05/2021
2850	35141^11572+11572^35141	142793	Hans Havermann	05/2021
2851	32231^26908+26908^32231	142780	Hans Havermann	05/2021
2852	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2853	2^474053+2897	142705	Lelio R Paula	08/2012
2854	(10^142699+359)/9	142699	Serge Batalov	12/2014
2855	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2856	2^473740-1856639	142610	Enzo Doria	09/2015
2857	(25*10^142573-403)/9	142574	Robert Price	12/2020
2858	2^473617-114223	142573	Enzo Doria	12/2014
2859	36115^8856+8856^36115	142555	Hans Havermann	05/2021
2860	2^473257+1873217	142465	Enzo Doria	06/2016
2861	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2862	32750^22371+22371^32750	142453	Hans Havermann	06/2021
2863	(61*10^142446-1)/3	142448	Robert Price	01/2020
2864	(14*10^142440+61)/3	142441	Robert Price	12/2018
2865	(10^142425+359)/9	142425	Serge Batalov	12/2014
2866	2^473101+773027	142418	Enzo Doria	05/2016
2867	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2868	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2869	36915^7162+7162^36915	142309	Hans Havermann	05/2021
2870	2^472634-109511	142278	Enzo Doria	04/2014
2871	31870^28997+28997^31870	142216	Hans Havermann	06/2021
2872	(48^84589+1)/49	142213	Robert Price	01/2014
2873	7*10^142189+87	142190	Robert Price	07/2019
2874	2^472258+7	142164	Lelio R Paula	08/2015
2875	40135^3484+3484^40135	142162	Hans Havermann	05/2021
2876	(23*10^142105+91)/3	142106	Robert Price	08/2019
2877	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2878	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2879	(16*10^142058+197)/3	142059	Robert Price	04/2019
2880	9*10^142037+91	142038	Robert Price	10/2020
2881	(4*10^142034+17)/3	142035	Tyler Busby	01/2023
2882	2^471792+1880881	142024	Enzo Doria	11/2016
2883	(509*10^142018+31)/9	142020	Robert Price	08/2022
2884	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2885	(4*10^141926-79)/3	141927	Robert Price	02/2018
2886	2^471464-111546435	141925	Paul Bourdelais	10/2021
2887	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2888	(14*10^141853+37)/3	141854	Robert Price	12/2018
2889	(41*10^141836-59)/9	141837	Robert Price	10/2018
2890	4*5^202913-9	141831	Lelio R Paula	04/2015
2891	2*7^167812-3	141818	Lelio R Paula	12/2014
2892	2^471043+35	141799	Robert Price	11/2015
2893	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2894	43636^1773+1773^43636	141761	Hans Havermann	05/2021
2895	(2*10^141751-17)/3	141751	Serge Batalov	11/2022
2896	(53*10^141722-611)/9	141723	Robert Price	02/2022
2897	(11*10^141718-131)/3	141719	Robert Price	09/2018
2898	(61*10^141716+47)/9	141717	Robert Price	07/2022
2899	2^470692+76771	141693	Enzo Doria	05/2016
2900	50160^667+667^50160	141659	Hans Havermann	05/2021
2901	31522^31181+31181^31522	141657	Hans Havermann	05/2021
2902	33076^19135+19135^33076	141626	Hans Havermann	04/2021
2903	(91*10^141610+71)/9	141612	Robert Price	01/2022
2904	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2905	(5*10^141594-23)/9	141594	Serge Batalov	11/2022
2906	31932^27155+27155^31932	141582	Hans Havermann	05/2021
2907	36449^7660+7660^36449	141577	Hans Havermann	05/2021
2908	2^470305-459373	141576	Enzo Doria	05/2015
2909	32195^24936+24936^32195	141556	Hans Havermann	05/2021
2910	2^470183+72623	141540	Enzo Doria	04/2016
2911	2^470173-16465	141537	Enzo Doria	04/2013
2912	37297^6234+6234^37297	141534	Hans Havermann	05/2021
2913	(509*10^141479+13)/9	141481	Robert Price	05/2022
2914	44*10^141476+9	141478	Robert Price	10/2020
2915	2^469974-1841	141477	Enzo Doria	05/2014
2916	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2917	2*10^141448+63	141449	Robert Price	05/2018
2918	2^469824+43	141432	Lelio R Paula	09/2017
2919	2*10^141407-27	141408	Robert Price	05/2018
2920	(214*10^141385-1)/3	141387	Robert Price	01/2021
2921	2^469630-59711	141373	Enzo Doria	10/2015
2922	35277^10172+10172^35277	141370	Hans Havermann	04/2021
2923	33397^17100+17100^33397	141370	Hans Havermann	04/2021
2924	(25*10^141366-331)/9	141367	Robert Price	08/2018
2925	36986^6639+6639^36986	141365	Hans Havermann	06/2021
2926	34572^12271+12271^34572	141361	Hans Havermann	06/2021
2927	37179^6338+6338^37179	141353	Hans Havermann	05/2021
2928	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2929	197^61601+2	141342	Lelio R Paula	08/2017
2930	33420^16951+16951^33420	141340	Hans Havermann	05/2021
2931	31623^29458+29458^31623	141330	Hans Havermann	05/2021
2932	48112^865+865^48112	141306	Hans Havermann	05/2021
2933	2^469372-112949	141296	Enzo Doria	07/2014
2934	5*10^141294-63	141295	Robert Price	04/2021
2935	3^296115+4	141283	Tyler NeSmith	01/2021
2936	(64*10^141256+161)/9	141257	Robert Price	08/2022
2937	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2938	143^65536+106^65536	141253	Serge Batalov	03/2018
2939	(11*10^141243-23)/3	141244	Robert Price	09/2021
2941	2^469198+782569	141243	Enzo Doria	10/2016
2940	38129^5062+5062^38129	141243	Hans Havermann	05/2021
2942	2^469076-2786939	141206	Enzo Doria	11/2015
2943	38630^4521+4521^38630	141202	Hans Havermann	05/2021
2944	31755^27836+27836^31755	141139	Hans Havermann	05/2021
2945	35554^9325+9325^35554	141137	Hans Havermann	05/2021
2946	2^468804+1874941	141125	Enzo Doria	06/2016
2947	2^468787+81353	141119	Enzo Doria	08/2016
2948	2^468595-350407	141062	Enzo Doria	06/2015
2949	2^468564+87855	141052	Lelio R Paula	01/2016
2950	2^468551-21987	141048	Enzo Doria	07/2013
2951	2^468523-7	141040	Lelio R Paula	08/2015
2952	(25*10^141019-13)/3	141020	Robert Price	09/2019
2953	2^468405+87855	141004	Lelio R Paula	01/2016
2954	39338^3831+3831^39338	140961	Hans Havermann	05/2021
2955	31458^30239+30239^31458	140950	Hans Havermann	05/2021
2956	8*10^140932+29	140933	Robert Price	11/2021
2957	33166^17691+17691^33166	140881	Hans Havermann	06/2021
2958	2^467978-113051	140876	Enzo Doria	07/2014
2959	2^467780-344429	140816	Enzo Doria	07/2015
2960	9*10^140802-89	140803	Robert Price	04/2020
2961	2^467605-1855603	140764	Enzo Doria	09/2015
2962	5*10^140744-7	140745	Robert Price	09/2015
2963	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
2964	2^467401-1850023	140702	Enzo Doria	08/2015
2965	(266*10^140681-17)/3	140683	Robert Price	07/2020
2966	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
2967	32138^23781+23781^32138	140644	Hans Havermann	05/2021
2968	31654^27735+27735^31654	140640	Hans Havermann	05/2021
2969	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
2970	2^467166-1854941	140631	Enzo Doria	09/2015
2971	(203*10^140615-11)/3	140617	Robert Price	12/2020
2972	(85*10^140609+473)/9	140610	Robert Price	01/2020
2973	39231^3836+3836^39231	140600	Hans Havermann	06/2021
2974	2^466866-1840571	140541	Enzo Doria	06/2015
2975	2^466829-459523	140530	Enzo Doria	05/2015
2976	2^466692-113213	140489	Enzo Doria	07/2014
2977	23*10^140464-3	140466	Robert Price	10/2021
2978	(2*10^140461-17)/3	140461	Serge Batalov	11/2022
2979	31335^30364+30364^31335	140455	Hans Havermann	05/2021
2980	32795^19126+19126^32795	140416	Hans Havermann	05/2021
2981	(44*10^140410-503)/9	140411	Robert Price	12/2018
2982	153^64265-2	140400	Lelio R Paula	11/2017
2983	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
2984	(29*10^140337-17)/3	140338	Robert Price	09/2019
2985	2^466181-112735	140335	Enzo Doria	07/2014
2986	(16*10^140290-37)/3	140291	Robert Price	05/2021
2987	(5*10^140281-119)/3	140282	Robert Price	03/2018
2988	34568^11415+11415^34568	140259	Hans Havermann	05/2021
2989	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
2990	33632^14781+14781^33632	140236	Hans Havermann	05/2021
2991	31803^25670+25670^31803	140233	Hans Havermann	05/2021
2992	2^465803-114817	140221	Enzo Doria	05/2015
2993	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
2994	2^465503-112735	140131	Enzo Doria	07/2014
2995	(16*10^140091+167)/3	140092	Robert Price	06/2019
2996	(8*10^140087-137)/3	140088	Robert Price	03/2022
2997	6^179964+179964^6-1	140040	Robert Price	04/2014
2998	(89*10^140008-179)/9	140009	Robert Price	12/2019
2999	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
3000	2^465072-344789	140001	Enzo Doria	07/2015

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PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)