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	70^78989-69^78989	145743	Robert Price	01/2014
2752	51^85334+2	145714	Robert Price	07/2015
2753	2^483886-1857101	145665	Enzo Doria	10/2015
2754	33350^23307+23307^33350	145656	Hans Havermann	01/2021
2755	(19*10^145585+131)/3	145586	Robert Price	06/2020
2756	2^483563-1863457	145567	Enzo Doria	12/2015
2757	4*10^145563-69	145564	Robert Price	01/2022
2758	2^483516-1861409	145553	Enzo Doria	11/2015
2759	2^483384-115019	145514	Enzo Doria	06/2015
2760	(259*10^145501-1)/3	145503	Robert Price	12/2020
2761	(19*10^145499-61)/3	145500	Robert Price	05/2019
2762	2^483302-3221	145489	Lelio R Paula	12/2012
2763	(23*10^145463+61)/3	145464	Robert Price	01/2022
2764	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2765	2^483046+1874029	145412	Enzo Doria	06/2016
2766	2^482991-2789317	145395	Enzo Doria	12/2015
2767	2^482978-2789711	145391	Enzo Doria	12/2015
2768	2^482966-2789711	145388	Enzo Doria	12/2015
2769	2^482817-1858843	145343	Enzo Doria	10/2015
2770	2^482751-113635	145323	Enzo Doria	08/2014
2771	2^482705-459763	145309	Enzo Doria	05/2015
2772	(4^241306+11)/3	145281	Robert Price	03/2017
2773	(238*10^145276-1)/3	145278	Robert Price	04/2020
2774	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2775	53^84239-52^84239	145252	Robert Price	01/2013
2776	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2777	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2778	2^482087+72623	145123	Enzo Doria	04/2016
2779	2^482016-286565	145102	Enzo Doria	07/2015
2780	(19*10^145093+101)/3	145094	Robert Price	09/2019
2781	2^481956+121	145084	Stefano Morozzi	04/2021
2782	2^481840+15	145049	Robert Price	09/2015
2783	2^481801-481801	145037	Henri Lifchitz	03/2005
2784	2^481775+1869083	145029	Enzo Doria	05/2016
2785	29^99167+2	145022	Ray Chandler	08/2011
2786	2^481663+1875653	144996	Enzo Doria	07/2016
2787	8*10^144977+27	144978	Robert Price	09/2021
2788	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2789	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2790	2^481149-459073	144841	Enzo Doria	05/2015
2791	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2792	2^481045-113215	144809	Enzo Doria	07/2014
2793	(64*10^144797+287)/9	144798	Robert Price	04/2019
2794	2^480859-113695	144753	Enzo Doria	09/2014
2795	(106*10^144744+17)/3	144746	Robert Price	04/2021
2796	7*10^144742-27	144743	Robert Price	11/2022
2797	2^480766-2787191	144725	Enzo Doria	11/2015
2798	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2799	2^480678+1874239	144699	Enzo Doria	06/2016
2800	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2801	L(692147)	144651	Henri Lifchitz	10/2008
2802	(76*10^144648+77)/9	144649	Robert Price	10/2019
2803	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2804	2^480417+35	144620	Robert Price	11/2015
2805	2^480296-59879	144584	Enzo Doria	10/2015
2806	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2807	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2808	2^479844+3	144448	Donovan Johnson	06/2006
2809	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2810	31892^32061-32061^31892	144393	Norbert Schneider	01/2023
2811	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2812	(56*10^144380+169)/9	144381	Robert Price	03/2022
2813	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2814	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2815	(56*10^144336+583)/9	144337	Robert Price	08/2021
2816	2^479348-2792219	144299	Enzo Doria	02/2016
2817	3^302389-6242	144277	Enzo Doria	05/2014
2818	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2819	2*10^144220-3	144221	Robert Price	07/2015
2820	2^478904-109109	144165	Enzo Doria	04/2014
2821	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2822	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2823	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2824	(772*10^144036-7)/9	144038	Robert Price	06/2022
2825	34295^15828+15828^34295	144020	Hans Havermann	01/2021
2826	2^478337-115333	143994	Enzo Doria	07/2015
2827	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2828	88^74047-87^74047	143984	Robert Price	05/2015
2829	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2830	(19*10^143963+467)/9	143964	Robert Price	02/2018
2831	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2832	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2833	(853*10^143931-7)/9	143933	Robert Price	07/2021
2834	2^478088+27	143919	Robert Price	11/2015
2835	(8*10^143898-137)/3	143899	Robert Price	03/2022
2836	7*10^143857-93	143858	Robert Price	08/2020
2837	3*10^143844+61	143845	Robert Price	09/2020
2838	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2839	2^477475-22071	143735	Enzo Doria	07/2013
2840	2^477417-22123	143717	Enzo Doria	07/2013
2841	2^477359-3577	143700	Yves Minet	03/2017
2842	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2843	(14*10^143662-71)/3	143663	Robert Price	12/2018
2844	6^184614+5	143658	Paul Bourdelais	01/2021
2845	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2846	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2847	2^476936-396765	143573	Enzo Doria	07/2013
2848	2^476888-2791229	143558	Enzo Doria	01/2016
2849	2^476868-1859939	143552	Enzo Doria	11/2015
2850	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2851	755^49878+49878^755	143547	Norbert Schneider	04/2019
2852	(19^112247-4^112247)/15	143536	Robert Price	03/2021
2853	35561^10872+10872^35561	143536	Hans Havermann	06/2021
2854	37637^6492+6492^37637	143487	Hans Havermann	05/2021
2855	61567^214+214^61567	143477	Hans Havermann	05/2021
2856	2^476558-113627	143459	Enzo Doria	08/2014
2857	2^476478-45	143435	Lelio R Paula	11/2017
2858	36380^8757+8757^36380	143423	Hans Havermann	06/2021
2859	32510^25707+25707^32510	143371	Hans Havermann	05/2021
2860	8*10^143361+17	143362	Robert Price	07/2021
2861	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2862	2^475813-113239	143234	Enzo Doria	07/2014
2863	(19*10^143212+137)/3	143213	Robert Price	03/2022
2864	32218^27849+27849^32218	143203	Hans Havermann	04/2021
2865	2^475624-114059	143178	Enzo Doria	11/2014
2866	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2867	2^475480-2786129	143134	Enzo Doria	10/2015
2868	33912^16621+16621^33912	143131	Hans Havermann	05/2021
2869	(19*10^143129-43)/3	143130	Robert Price	05/2019
2870	31830^31373+31373^31830	143126	Hans Havermann	05/2021
2871	6*10^143105-53	143106	Robert Price	05/2021
2872	(14*10^143097+73)/3	143098	Robert Price	12/2018
2873	2^475299-111937	143080	Enzo Doria	05/2014
2874	35488^10753+10753^35488	143071	Hans Havermann	04/2021
2875	2^475160-2797859	143038	Enzo Doria	04/2016
2876	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2877	2^475027-461437	142998	Enzo Doria	07/2015
2878	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2879	(8*10^142932+43)/3	142933	Robert Price	06/2018
2880	35055^11942+11942^35055	142922	Hans Havermann	05/2021
2881	37650^6239+6239^37650	142887	Hans Havermann	05/2021
2882	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2883	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2884	2^474417-59923	142814	Enzo Doria	10/2015
2885	4*10^142810-21	142811	Robert Price	09/2018
2886	32287^26494+26494^32287	142811	Hans Havermann	06/2021
2887	37162^6965+6965^37162	142811	Hans Havermann	06/2021
2888	(34*10^142805-601)/9	142806	Robert Price	07/2022
2889	37456^6493+6493^37456	142799	Hans Havermann	05/2021
2890	35141^11572+11572^35141	142793	Hans Havermann	05/2021
2891	32231^26908+26908^32231	142780	Hans Havermann	05/2021
2892	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2893	2^474053+2897	142705	Lelio R Paula	08/2012
2894	(10^142699+359)/9	142699	Serge Batalov	12/2014
2895	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2896	2^473740-1856639	142610	Enzo Doria	09/2015
2897	(25*10^142573-403)/9	142574	Robert Price	12/2020
2898	2^473617-114223	142573	Enzo Doria	12/2014
2899	36115^8856+8856^36115	142555	Hans Havermann	05/2021
2900	2^473257+1873217	142465	Enzo Doria	06/2016
2901	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2902	32750^22371+22371^32750	142453	Hans Havermann	06/2021
2903	(61*10^142446-1)/3	142448	Robert Price	01/2020
2904	(14*10^142440+61)/3	142441	Robert Price	12/2018
2905	(10^142425+359)/9	142425	Serge Batalov	12/2014
2906	2^473101+773027	142418	Enzo Doria	05/2016
2907	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2908	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2909	36915^7162+7162^36915	142309	Hans Havermann	05/2021
2910	2^472634-109511	142278	Enzo Doria	04/2014
2911	31870^28997+28997^31870	142216	Hans Havermann	06/2021
2912	(48^84589+1)/49	142213	Robert Price	01/2014
2913	7*10^142189+87	142190	Robert Price	07/2019
2914	2^472258+7	142164	Lelio R Paula	08/2015
2915	40135^3484+3484^40135	142162	Hans Havermann	05/2021
2916	(23*10^142105+91)/3	142106	Robert Price	08/2019
2917	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2918	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2919	(16*10^142058+197)/3	142059	Robert Price	04/2019
2920	9*10^142037+91	142038	Robert Price	10/2020
2921	(4*10^142034+17)/3	142035	Tyler Busby	01/2023
2922	2^471792+1880881	142024	Enzo Doria	11/2016
2923	(509*10^142018+31)/9	142020	Robert Price	08/2022
2924	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2925	(4*10^141926-79)/3	141927	Robert Price	02/2018
2926	2^471464-111546435	141925	Paul Bourdelais	10/2021
2927	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2928	(14*10^141853+37)/3	141854	Robert Price	12/2018
2929	(41*10^141836-59)/9	141837	Robert Price	10/2018
2930	4*5^202913-9	141831	Lelio R Paula	04/2015
2931	2*7^167812-3	141818	Lelio R Paula	12/2014
2932	2^471043+35	141799	Robert Price	11/2015
2933	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
2934	43636^1773+1773^43636	141761	Hans Havermann	05/2021
2935	(2*10^141751-17)/3	141751	Serge Batalov	11/2022
2936	(53*10^141722-611)/9	141723	Robert Price	02/2022
2937	(11*10^141718-131)/3	141719	Robert Price	09/2018
2938	(61*10^141716+47)/9	141717	Robert Price	07/2022
2939	2^470692+76771	141693	Enzo Doria	05/2016
2940	50160^667+667^50160	141659	Hans Havermann	05/2021
2941	31522^31181+31181^31522	141657	Hans Havermann	05/2021
2942	33076^19135+19135^33076	141626	Hans Havermann	04/2021
2943	(91*10^141610+71)/9	141612	Robert Price	01/2022
2944	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
2945	(5*10^141594-23)/9	141594	Serge Batalov	11/2022
2946	31932^27155+27155^31932	141582	Hans Havermann	05/2021
2947	36449^7660+7660^36449	141577	Hans Havermann	05/2021
2948	2^470305-459373	141576	Enzo Doria	05/2015
2949	32195^24936+24936^32195	141556	Hans Havermann	05/2021
2950	2^470183+72623	141540	Enzo Doria	04/2016
2951	2^470173-16465	141537	Enzo Doria	04/2013
2952	37297^6234+6234^37297	141534	Hans Havermann	05/2021
2953	(509*10^141479+13)/9	141481	Robert Price	05/2022
2954	44*10^141476+9	141478	Robert Price	10/2020
2955	2^469974-1841	141477	Enzo Doria	05/2014
2956	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
2957	2*10^141448+63	141449	Robert Price	05/2018
2958	2^469824+43	141432	Lelio R Paula	09/2017
2959	2*10^141407-27	141408	Robert Price	05/2018
2960	(214*10^141385-1)/3	141387	Robert Price	01/2021
2961	2^469630-59711	141373	Enzo Doria	10/2015
2962	35277^10172+10172^35277	141370	Hans Havermann	04/2021
2963	33397^17100+17100^33397	141370	Hans Havermann	04/2021
2964	(25*10^141366-331)/9	141367	Robert Price	08/2018
2965	36986^6639+6639^36986	141365	Hans Havermann	06/2021
2966	34572^12271+12271^34572	141361	Hans Havermann	06/2021
2967	37179^6338+6338^37179	141353	Hans Havermann	05/2021
2968	(2^469564-3)/611	141351	Lelio R Paula	08/2015
2969	197^61601+2	141342	Lelio R Paula	08/2017
2970	33420^16951+16951^33420	141340	Hans Havermann	05/2021
2971	31623^29458+29458^31623	141330	Hans Havermann	05/2021
2972	48112^865+865^48112	141306	Hans Havermann	05/2021
2973	2^469372-112949	141296	Enzo Doria	07/2014
2974	5*10^141294-63	141295	Robert Price	04/2021
2975	3^296115+4	141283	Tyler NeSmith	01/2021
2976	(64*10^141256+161)/9	141257	Robert Price	08/2022
2977	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
2978	143^65536+106^65536	141253	Serge Batalov	03/2018
2979	(11*10^141243-23)/3	141244	Robert Price	09/2021
2981	2^469198+782569	141243	Enzo Doria	10/2016
2980	38129^5062+5062^38129	141243	Hans Havermann	05/2021
2982	2^469076-2786939	141206	Enzo Doria	11/2015
2983	38630^4521+4521^38630	141202	Hans Havermann	05/2021
2984	31755^27836+27836^31755	141139	Hans Havermann	05/2021
2985	35554^9325+9325^35554	141137	Hans Havermann	05/2021
2986	2^468804+1874941	141125	Enzo Doria	06/2016
2987	2^468787+81353	141119	Enzo Doria	08/2016
2988	2^468595-350407	141062	Enzo Doria	06/2015
2989	2^468564+87855	141052	Lelio R Paula	01/2016
2990	2^468551-21987	141048	Enzo Doria	07/2013
2991	2^468523-7	141040	Lelio R Paula	08/2015
2992	(25*10^141019-13)/3	141020	Robert Price	09/2019
2993	2^468405+87855	141004	Lelio R Paula	01/2016
2994	39338^3831+3831^39338	140961	Hans Havermann	05/2021
2995	31458^30239+30239^31458	140950	Hans Havermann	05/2021
2996	8*10^140932+29	140933	Robert Price	11/2021
2997	33166^17691+17691^33166	140881	Hans Havermann	06/2021
2998	2^467978-113051	140876	Enzo Doria	07/2014
2999	2^467780-344429	140816	Enzo Doria	07/2015
3000	9*10^140802-89	140803	Robert Price	04/2020

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Probable Primes Top 10000

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