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	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2752	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2753	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
2754	2^416641-2*416641+1	125422	Robert Price	05/2018
2755	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2756	2^416530+1870429	125389	Enzo Doria	05/2016
2757	(56*10^125385+691)/9	125386	Robert Price	05/2019
2758	2^416490+1875109	125376	Enzo Doria	09/2016
2759	2^416416-114929	125354	Enzo Doria	05/2015
2760	(77*10^125330-293)/9	125331	Robert Price	09/2019
2761	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2762	2^416134+1865899	125269	Enzo Doria	03/2016
2763	153^57337-152	125264	Norbert Schneider	12/2018
2764	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2765	(23^91943-1)/22	125201	Robert Price	01/2012
2766	43125^27010-106	125185	Enzo Doria	08/2012
2767	(38*10^125166+349)/9	125167	Robert Price	10/2018
2768	2^415765-112603	125158	Enzo Doria	06/2014
2769	8*10^125088-13	125089	Robert Price	08/2019
2770	(25*10^125076-13)/3	125077	Robert Price	09/2019
2771	(29*10^125021-113)/3	125022	Robert Price	10/2019
2772	2^415290-113591	125015	Enzo Doria	08/2014
2773	2^415276-460919	125011	Enzo Doria	06/2015
2774	2^415259+77243	125006	Enzo Doria	05/2016
2775	2^415144-3683	124971	Yves Minet	10/2011
2776	2^414874+79	124890	Lelio R Paula	01/2015
2777	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2778	2^414618+79459	124813	Enzo Doria	06/2016
2779	(61*10^124809-1)/3	124811	Robert Price	01/2020
2780	2^414432-1846709	124757	Enzo Doria	07/2015
2781	2*10^124751-51	124752	Robert Price	04/2018
2782	(56*10^124735+367)/9	124736	Robert Price	06/2019
2783	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2784	56*10^124656-3	124658	Robert Price	03/2020
2785	(7*10^124648+197)/3	124649	Robert Price	07/2018
2787	2^414032-5	124637	Henri Lifchitz	07/2006
2786	2^414032+1872331	124637	Enzo Doria	05/2016
2788	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2789	(85*10^124485-49)/9	124486	Robert Price	12/2020
2790	64^68909-63^68909	124463	Robert Price	07/2013
2791	2^413387+76253	124442	Enzo Doria	04/2016
2792	2^413352+524287	124432	Paul Underwood	09/2018
2793	287117#+391613	124424	Nicolas PALAU	01/2017
2794	(4*10^124420+83)/3	124421	Robert Price	02/2018
2795	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2796	(41*10^124335-383)/9	124336	Robert Price	11/2018
2797	(304*10^124329-43)/9	124331	Robert Price	02/2020
2798	2^412868-120599	124286	Paul Bourdelais	02/2012
2799	10^124248-1000001	124248	Robert Price	08/2020
2800	45^75145-2	124231	Lelio R Paula	08/2015
2801	2^412645-112213	124219	Enzo Doria	06/2014
2802	2^412248+74611	124100	Enzo Doria	04/2016
2803	(22*10^124096-13)/9	124097	Robert Price	06/2018
2804	2^412192-3329	124083	Yves Minet	12/2014
2805	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
2806	(25*10^124076-67)/3	124077	Robert Price	06/2019
2807	F(593689)	124074	Henri Lifchitz	01/2005
2808	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
2809	(266*10^124022-11)/3	124024	Robert Price	04/2020
2810	2^411884-113279	123990	Enzo Doria	07/2014
2811	(2^411832+1)/257	123972	Lelio R Paula	05/2014
2812	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
2813	(26*10^123970-89)/9	123971	Robert Price	06/2018
2814	2^411790-1853531	123962	Enzo Doria	08/2015
2815	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
2816	2^411711-113257	123938	Enzo Doria	07/2014
2817	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
2818	(11*10^123899-179)/3	123900	Robert Price	09/2018
2819	2^411325-351103	123822	Enzo Doria	06/2015
2820	2^411052+1872481	123739	Enzo Doria	05/2016
2821	2^410997+39	123723	Lelio R Paula	05/2014
2822	(649^43987-1)/648	123700	Michael Stocker	05/2020
2823	(148*10^123688-1)/3	123690	Robert Price	03/2020
2824	8*10^123657+87	123658	Robert Price	10/2019
2825	155^56438+154	123618	Norbert Schneider	01/2019
2826	2^410596-39	123602	Lelio R Paula	05/2014
2827	2^410540-115079	123585	Enzo Doria	06/2015
2828	(7*10^123563+107)/3	123564	Robert Price	02/2018
2829	9*10^123549+89	123550	Robert Price	11/2019
2830	(197*10^123545+7)/3	123547	Robert Price	12/2020
2831	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
2832	2^410206-113081	123485	Enzo Doria	07/2014
2833	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
2834	2^409909-189	123395	Enzo Doria	05/2014
2835	2^409896-109043	123391	Enzo Doria	04/2014
2836	2^409890+75409	123390	Enzo Doria	04/2016
2837	133^58076-2	123345	Lelio R Paula	10/2017
2838	F(590041)	123311	Henri Lifchitz	01/2005
2839	2^409566-113501	123292	Enzo Doria	08/2014
2840	2^409533+77747	123282	Enzo Doria	05/2016
2841	2^409436-112799	123253	Enzo Doria	06/2014
2842	2^409225+1873787	123189	Enzo Doria	06/2016
2843	2^409174+73009	123174	Enzo Doria	04/2016
2844	2^409058-112685	123139	Enzo Doria	06/2014
2845	(13*10^123137-61)/3	123138	Robert Price	11/2018
2846	4*10^123113+21	123114	Robert Price	12/2018
2847	2^408778+77689	123055	Enzo Doria	05/2016
2848	2^408690-75	123028	Lelio R Paula	11/2013
2849	(29*10^122996+673)/9	122997	Robert Price	12/2018
2850	2^408574-2787341	122994	Enzo Doria	03/2016
2851	3*10^122977+37	122978	Robert Price	08/2018
2852	Phi(157825,10)	122961	Maksym Voznyy	06/2015
2853	(68*10^122933-419)/9	122934	Robert Price	07/2019
2854	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
2855	(266*10^122872-17)/3	122874	Robert Price	07/2020
2856	(16*10^122871+77)/3	122872	Robert Price	03/2019
2857	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
2858	(19*10^122836-43)/3	122837	Robert Price	05/2019
2859	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
2860	(32*10^122733-77)/9	122734	Robert Price	06/2018
2861	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
2862	(22*10^122681+161)/3	122682	Robert Price	05/2019
2863	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
2864	(26*10^122625-131)/3	122626	Robert Price	10/2019
2865	(73*10^122592-1)/9	122593	Robert Price	01/2015
2866	(5*10^122592+91)/3	122593	Robert Price	04/2018
2867	(85*10^122585-1)/3	122587	Robert Price	02/2020
2868	2^407179-112075	122574	Enzo Doria	06/2014
2869	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
2870	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
2871	2^407008-1867919	122522	Enzo Doria	04/2016
2872	11^117642-300	122512	Enzo Doria	10/2012
2873	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
2874	2^406949+72197	122504	Enzo Doria	04/2016
2875	(19*10^122501+149)/3	122502	Robert Price	05/2019
2876	2^406826-65	122467	Lelio R Paula	11/2013
2877	2^406821-2797363	122466	Enzo Doria	04/2016
2878	2^406758-17	122447	Lelio R Paula	11/2013
2879	(30^82883-1)/29	122427	Robert Price	12/2011
2880	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
2881	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
2882	4*10^122377+19	122378	Robert Price	10/2018
2883	Phi(246362,10)	122365	Makoto Kamada	09/2019
2884	3*10^122345-97	122346	Robert Price	07/2018
2885	97^61575-2	122336	Lelio R Paula	12/2014
2886	208^52765+52765^208	122313	Norbert Schneider	11/2020
2887	2^406298+2799109	122308	Enzo Doria	04/2016
2888	7*10^122294+57	122295	Robert Price	06/2019
2889	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
2890	2^406229-1849993	122288	Enzo Doria	08/2015
2891	3*10^122274+7	122275	Robert Price	07/2015
2892	2^406117+1876577	122254	Enzo Doria	07/2016
2893	3^256199-2^256199	122238	Mike Oakes	06/2005
2894	2^405992-78557	122216	Jorge Menendez	03/2018
2895	(8*10^122203+43)/3	122204	Robert Price	06/2018
2896	(58*10^122170+329)/9	122171	Robert Price	05/2019
2897	2^405774+179149	122151	Enzo Doria	06/2016
2898	34*10^122082-9	122084	Robert Price	06/2020
2899	5*10^122082+41	122083	Robert Price	03/2019
2900	2^405514-3311	122072	Yves Minet	12/2014
2901	2^405514-115511	122072	Enzo Doria	07/2015
2902	23*10^122070-7	122072	Robert Price	02/2020
2903	2^405422-113261	122045	Enzo Doria	07/2014
2904	2^405173+71237	121970	Enzo Doria	04/2016
2905	(2^405016+1)/257	121920	Lelio R Paula	04/2014
2906	2^404858+71329	121875	Enzo Doria	04/2016
2907	2^404813-114703	121861	Enzo Doria	04/2015
2908	2^404764+77791	121847	Enzo Doria	05/2016
2909	317^48694+48694^317	121787	Norbert Schneider	08/2015
2910	2^404536-115259	121778	Enzo Doria	06/2015
2911	2^404501-631	121767	Yves Minet	07/2012
2912	63^67620+2	121672	Lelio R Paula	08/2015
2913	(16*10^121633+167)/3	121634	Robert Price	06/2019
2914	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
2915	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
2916	(10^121543-79)/3	121543	Robert Price	01/2018
2917	2^403676+76831	121519	Enzo Doria	05/2016
2918	(7*10^121487+143)/3	121488	Robert Price	03/2018
2919	2^403363-113635	121425	Enzo Doria	08/2014
2920	2^403336-1861469	121417	Enzo Doria	03/2016
2921	p(24442)#/2-64	121381	Robert Price	04/2017
2922	11^116555-720	121380	Enzo Doria	11/2012
2923	2^403100-461267	121346	Enzo Doria	07/2015
2924	2^403093-112213	121344	Enzo Doria	06/2014
2925	(316^48539+1)/317	121330	Eric Chen	10/2017
2926	(23*10^121320-71)/3	121321	Robert Price	07/2020
2927	2^403004+1866361	121317	Enzo Doria	03/2016
2928	2^402953+89	121301	Lelio R Paula	10/2013
2929	2^402944-2788319	121299	Enzo Doria	03/2016
2930	(44*10^121297-719)/9	121298	Robert Price	12/2018
2931	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
2932	2^402828-113183	121264	Enzo Doria	07/2014
2933	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
2934	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
2935	2^402715+1874223	121230	Enzo Doria	06/2016
2936	(35*10^121229-593)/9	121230	Robert Price	07/2018
2937	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
2938	7*10^121144+9	121145	Robert Price	09/2015
2939	2^401725-113251	120932	Enzo Doria	07/2014
2940	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
2941	2^401652+73711	120910	Enzo Doria	04/2016
2942	(2^401632+3)/79	120902	Lelio R Paula	04/2014
2943	40450^973+973^40450	120870	Hans Havermann	01/2021
2944	10^120841+88417	120842	Patrick De Geest	04/2020
2945	10^120841-123456789	120841	Robert Price	02/2020
2946	10^120841-176853	120841	Patrick De Geest	04/2020
2947	2^401406-2791331	120836	Enzo Doria	03/2016
2948	(28^83497+1)/29	120832	Robert Price	07/2013
2949	(22*10^120828+161)/3	120829	Robert Price	05/2019
2950	2^401369+1867367	120825	Enzo Doria	03/2016
2951	(10^120782+29)/3	120782	Serge Batalov	12/2014
2952	2^401215-1657	120778	Yves Minet	07/2014
2953	2^401159+53	120761	Lelio R Paula	10/2013
2954	27782^22179+22179^27782	120739	Hans Havermann	01/2021
2955	2^401031-113047	120723	Enzo Doria	07/2014
2956	(71*10^120703-287)/9	120704	Robert Price	09/2019
2957	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
2958	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
2959	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
2960	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
2961	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
2962	2^400571-15	120584	Lelio R Paula	10/2013
2963	(10^120574+359)/9	120574	Serge Batalov	12/2014
2964	2^400424-216413	120540	Enzo Doria	04/2013
2965	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
2966	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
2968	2^400166+1874899	120462	Enzo Doria	06/2016
2967	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
2969	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
2970	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
2971	2^399966+73759	120402	Enzo Doria	04/2016
2972	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
2973	2^399918-95	120388	Lelio R Paula	04/2013
2974	(28*10^120381-67)/3	120382	Robert Price	10/2020
2975	(49*10^120380-139)/9	120381	Robert Price	03/2019
2976	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
2977	2^399792-1849259	120350	Enzo Doria	08/2015
2978	9*10^120342-7	120343	Robert Price	09/2015
2979	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
2980	(13*10^120306-37)/3	120307	Robert Price	01/2019
2981	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
2982	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
2983	2^399526-1861721	120270	Enzo Doria	11/2015
2984	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
2985	2^399322-2798111	120208	Enzo Doria	04/2016
2986	72^64693-71^64693	120157	Robert Price	03/2014
2987	2^399111-28489	120145	Enzo Doria	08/2015
2989	2^398877+105	120074	Donovan Johnson	01/2006
2988	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
2990	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
2991	2^398710+57	120024	Lelio R Paula	04/2013
2992	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
2993	2^398691-115057	120018	Enzo Doria	06/2015
2994	L(574219)	120005	Renaud Lifchitz	03/2004
2995	2^398571+60413	119982	Yves Minet	03/2011
2996	p(24179)#/2-64	119949	Robert Price	04/2017
2997	2^398448+1872001	119945	Enzo Doria	05/2016
2998	634^42803+42803^634	119938	Norbert Schneider	07/2019
2999	(68*10^119931-11)/3	119933	Robert Price	01/2020
3000	8*10^119930-3	119931	Ray Chandler	04/2011

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Probable Primes Top 10000

(277054 PRPs in the top)