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	11^123594-240	128710	Enzo Doria	09/2012
2752	2^427504-21503	128692	Enzo Doria	07/2013
2753	2^427420+91	128667	Lelio R Paula	05/2017
2754	(68*10^128645-257)/9	128646	Robert Price	07/2019
2755	2^427269-113635	128621	Enzo Doria	08/2014
2756	2^427130+1877569	128579	Enzo Doria	08/2016
2757	2^427016-115349	128545	Enzo Doria	07/2015
2758	(4*10^128510+137)/3	128511	Robert Price	03/2018
2759	2^426889-112879	128507	Enzo Doria	06/2014
2760	2^426804+1869931	128481	Enzo Doria	05/2016
2761	2^426750+77635	128465	Enzo Doria	05/2016
2762	36988^2969+2969^36988	128445	Hans Havermann	03/2021
2763	36664^3185+3185^36664	128439	Hans Havermann	03/2021
2764	2^426425-91	128367	Lelio R Paula	05/2017
2765	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
2767	2^426352+74971	128345	Enzo Doria	04/2016
2766	(199*10^128343-7)/3	128345	Robert Price	05/2020
2768	4*10^128343-21	128344	Robert Price	09/2018
2769	2^426300-1863689	128330	Enzo Doria	03/2016
2770	2^426293+1881017	128327	Enzo Doria	11/2016
2771	(88*10^128324-637)/9	128325	Robert Price	11/2020
2772	39103^1908+1908^39103	128281	Hans Havermann	04/2021
2773	2^426043+35	128252	Robert Price	11/2015
2774	(4*10^128244-19)/3	128245	Robert Price	03/2018
2775	(305*10^128198+1)/9	128200	Robert Price	02/2020
2776	2^425808-459959	128181	Enzo Doria	06/2015
2777	30632^15291+15291^30632	128178	Hans Havermann	04/2021
2778	35981^3648+3648^35981	128167	Hans Havermann	04/2021
2779	2^425627-113605	128127	Enzo Doria	08/2014
2780	(22*10^128094+53)/3	128095	Robert Price	07/2019
2781	(86*10^128086-221)/9	128087	Robert Price	09/2019
2782	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
2783	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
2784	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
2785	2^425205+4911	128000	Marek Hubal	02/2017
2786	29241^23836+23836^29241	127995	Hans Havermann	04/2021
2787	2^425118-113663	127974	Enzo Doria	08/2014
2788	(86*10^127967-329)/9	127968	Robert Price	01/2020
2789	2^425061+1869761	127957	Enzo Doria	05/2016
2790	746^44541+44541^746	127955	Norbert Schneider	07/2019
2791	30236^17043+17043^30236	127946	Hans Havermann	03/2021
2792	2^424918-21141	127914	Enzo Doria	07/2013
2793	2^424864-29489	127897	Enzo Doria	08/2015
2794	30438^15893+15893^30438	127877	Hans Havermann	02/2021
2795	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
2796	28929^26258+26258^28929	127845	Hans Havermann	03/2021
2797	30563^15220+15220^30563	127828	Hans Havermann	03/2021
2798	2^424632-2786639	127827	Enzo Doria	03/2016
2799	2^424577-113755	127811	Enzo Doria	09/2014
2800	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
2801	(56*10^127752+691)/9	127753	Robert Price	05/2019
2802	11^122629-720	127705	Enzo Doria	11/2012
2803	22*10^127645+3	127647	Robert Price	01/2020
2804	28715^27844+27844^28715	127631	Hans Havermann	03/2021
2805	(5*36^81995+821)/7	127609	Eric Chen	01/2021
2806	4*10^127562-39	127563	Robert Price	09/2020
2807	32595^8186+8186^32595	127547	Hans Havermann	03/2021
2808	2^423696-21429	127546	Enzo Doria	07/2013
2809	2^423664-1864559	127536	Enzo Doria	03/2016
2810	37889^2322+2322^37889	127530	Hans Havermann	03/2021
2811	37668^2429+2429^37668	127523	Hans Havermann	03/2021
2812	3^267267-4	127519	Henri Lifchitz	10/2014
2813	(103*10^127491+17)/3	127493	Robert Price	08/2020
2814	29376^21869+21869^29376	127487	Hans Havermann	03/2021
2815	31186^12241+12241^31186	127483	Hans Havermann	02/2021
2816	(19^99689+5^99689)/24	127477	Robert Price	09/2013
2817	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
2818	30594^14645+14645^30594	127446	Hans Havermann	03/2021
2819	2^423328-21537	127435	Enzo Doria	07/2013
2820	(67*10^127413-7)/3	127415	Robert Price	01/2020
2821	(2*10^127407+73)/3	127407	Robert Price	09/2020
2822	(2^423165-7)/25	127384	Lelio R Paula	05/2015
2823	29512^20647+20647^29512	127341	Hans Havermann	03/2021
2824	(112*10^127324+17)/3	127326	Robert Price	03/2020
2825	29565^20252+20252^29565	127321	Hans Havermann	03/2021
2826	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
2827	(16*10^127259+197)/3	127260	Robert Price	04/2019
2828	(26*10^127240+61)/3	127241	Robert Price	10/2019
2829	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
2830	2^422515-114997	127190	Enzo Doria	06/2015
2831	5*10^127179-3	127180	Robert Price	07/2015
2832	31678^10343+10343^31678	127176	Hans Havermann	03/2021
2833	(44*10^127169-233)/9	127170	Robert Price	01/2019
2834	34947^4352+4352^34947	127162	Hans Havermann	03/2021
2835	30469^14902+14902^30469	127155	Hans Havermann	03/2021
2836	5*10^127153+77	127154	Robert Price	12/2018
2837	29941^17620+17620^29941	127130	Hans Havermann	02/2021
2838	31607^10516+10516^31607	127119	Hans Havermann	03/2021
2839	736^44335+44335^736	127104	Norbert Schneider	07/2019
2840	33040^7023+7023^33040	127090	Hans Havermann	03/2021
2841	29748^18661+18661^29748	127052	Hans Havermann	03/2021
2842	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
2843	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
2844	31436^10965+10965^31436	127002	Hans Havermann	03/2021
2845	28905^24758+24758^28905	127001	Hans Havermann	03/2021
2846	2^421860-113285	126993	Enzo Doria	07/2014
2847	(2^421827-7)/11	126982	Lelio R Paula	05/2015
2848	11^121910-840	126957	Enzo Doria	12/2012
2849	28915^24538+24538^28915	126933	Hans Havermann	03/2021
2850	(29*10^126928-77)/3	126929	Robert Price	02/2020
2851	(259*10^126919-1)/3	126921	Robert Price	12/2020
2852	10^126919-100001	126919	Robert Price	07/2020
2853	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
2854	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
2855	(5*10^126871-119)/3	126872	Robert Price	03/2018
2856	331^50339-10004	126846	Enzo Doria	07/2012
2857	2^421363-2790757	126843	Enzo Doria	03/2016
2858	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
2859	37938^2203+2203^37938	126828	Hans Havermann	03/2021
2860	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
2861	(14*10^126784-83)/3	126785	Robert Price	12/2018
2862	2^421161-286183	126783	Enzo Doria	06/2015
2863	30718^13347+13347^30718	126724	Hans Havermann	03/2021
2864	2^420939-113935	126716	Enzo Doria	10/2014
2865	177^56363-2	126703	Lelio R Paula	10/2017
2866	2^420741-113659	126656	Enzo Doria	08/2014
2867	2^420694-21	126642	Lelio R Paula	05/2017
2868	(13*10^126638+437)/9	126639	Robert Price	04/2018
2869	(167*10^126637-17)/3	126639	Robert Price	03/2020
2870	4*10^126625+87	126626	Robert Price	08/2018
2872	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
2871	7*10^126600-99	126601	Robert Price	06/2019
2873	2^420424-59189	126561	Enzo Doria	10/2015
2874	28717^25534+25534^28717	126560	Hans Havermann	03/2021
2875	28922^23655+23655^28922	126503	Hans Havermann	03/2021
2876	2^420126+71893	126471	Enzo Doria	04/2016
2877	(43*10^126441+47)/9	126442	Robert Price	12/2018
2878	2^419866+1877059	126393	Enzo Doria	07/2016
2879	29315^20484+20484^29315	126390	Hans Havermann	03/2021
2880	29433^19676+19676^29433	126384	Hans Havermann	03/2021
2881	F(604711)	126377	Henri Lifchitz	02/2005
2882	2^419757+72707	126360	Enzo Doria	04/2016
2883	2^419720-21569	126349	Enzo Doria	07/2013
2884	2^419637+29	126324	Henri Lifchitz	02/2006
2885	31004^11865+11865^31004	126319	Hans Havermann	03/2021
2886	2^419612+1876741	126316	Enzo Doria	07/2016
2887	2^419520+2793271	126289	Enzo Doria	03/2016
2888	(2^419447-5)/369	126264	Lelio R Paula	05/2014
2889	2^419328-1859939	126231	Enzo Doria	03/2016
2890	2^419282-1851507	126217	Enzo Doria	08/2015
2891	2^419251+1866143	126208	Enzo Doria	03/2016
2892	11^121185+2	126202	Robert Price	05/2014
2893	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
2894	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
2895	2^418851+23	126087	Robert Price	09/2015
2896	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
2897	2^418829+167	126081	Lelio R Paula	01/2012
2898	31037^11530+11530^31037	126067	Hans Havermann	03/2021
2899	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
2900	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
2901	33016^6551+6551^33016	126000	Hans Havermann	03/2021
2902	34736^4227+4227^34736	125954	Hans Havermann	03/2021
2903	2^418319-109501	125927	Enzo Doria	04/2014
2904	2^418316-112373	125926	Enzo Doria	06/2014
2905	40398^1309+1309^40398	125919	Hans Havermann	03/2021
2906	(8*10^125894-29)/3	125895	Robert Price	07/2018
2907	(26*10^125886-413)/9	125887	Robert Price	05/2018
2908	2^417968+1869811	125821	Enzo Doria	06/2016
2909	2^417902+63	125802	Lelio R Paula	09/2015
2910	(10^125792-91)/9	125792	Serge Batalov	12/2014
2911	30438^13573+13573^30438	125791	Hans Havermann	03/2021
2912	32867^6714+6714^32867	125782	Hans Havermann	03/2021
2913	31155^10892+10892^31155	125777	Hans Havermann	03/2021
2914	(35*10^125754-593)/9	125755	Robert Price	07/2018
2915	30455^13464+13464^30455	125754	Hans Havermann	03/2021
2916	(32*10^125751-77)/9	125752	Robert Price	06/2018
2917	2^417704+77011	125742	Enzo Doria	05/2016
2918	29755^16816+16816^29755	125737	Hans Havermann	03/2021
2919	29918^15915+15915^29918	125710	Hans Havermann	03/2021
2920	(10^125706+149)/3	125706	Serge Batalov	12/2014
2921	28531^25368+25368^28531	125659	Hans Havermann	03/2021
2922	2^417419-115309	125656	Enzo Doria	07/2015
2923	2^417300+77281	125620	Enzo Doria	05/2016
2924	30638^12537+12537^30638	125561	Hans Havermann	03/2021
2925	2^417095-1657	125559	Yves Minet	07/2014
2926	30162^14525+14525^30162	125538	Hans Havermann	03/2021
2927	(88*10^125492-637)/9	125493	Robert Price	11/2020
2928	28958^21525+21525^28958	125474	Hans Havermann	02/2021
2929	2^416773-25	125462	Lelio R Paula	09/2015
2930	33889^5032+5032^33889	125449	Hans Havermann	03/2021
2931	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
2932	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
2933	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
2934	2^416641-2*416641+1	125422	Robert Price	05/2018
2935	33392^5697+5697^33392	125409	Hans Havermann	03/2021
2936	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
2937	2^416530+1870429	125389	Enzo Doria	05/2016
2938	(56*10^125385+691)/9	125386	Robert Price	05/2019
2939	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
2940	31074^10837+10837^31074	125381	Hans Havermann	03/2021
2941	33745^5194+5194^33745	125380	Hans Havermann	03/2021
2942	2^416490+1875109	125376	Enzo Doria	09/2016
2943	28360^26331+26331^28360	125365	Hans Havermann	03/2021
2944	2^416416-114929	125354	Enzo Doria	05/2015
2945	(77*10^125330-293)/9	125331	Robert Price	09/2019
2946	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
2947	2^416134+1865899	125269	Enzo Doria	03/2016
2948	153^57337-152	125264	Norbert Schneider	12/2018
2949	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
2950	30054^14657+14657^30054	125207	Hans Havermann	03/2021
2951	(23^91943-1)/22	125201	Robert Price	01/2012
2952	43125^27010-106	125185	Enzo Doria	08/2012
2953	(38*10^125166+349)/9	125167	Robert Price	10/2018
2954	2^415765-112603	125158	Enzo Doria	06/2014
2955	8*10^125088-13	125089	Robert Price	08/2019
2956	(25*10^125076-13)/3	125077	Robert Price	09/2019
2957	(29*10^125021-113)/3	125022	Robert Price	10/2019
2958	2^415290-113591	125015	Enzo Doria	08/2014
2959	2^415276-460919	125011	Enzo Doria	06/2015
2960	2^415259+77243	125006	Enzo Doria	05/2016
2961	2^415144-3683	124971	Yves Minet	10/2011
2962	31936^8173+8173^31936	124946	Hans Havermann	03/2021
2963	29767^15700+15700^29767	124900	Hans Havermann	03/2021
2964	2^414874+79	124890	Lelio R Paula	01/2015
2965	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
2966	2^414618+79459	124813	Enzo Doria	06/2016
2967	(61*10^124809-1)/3	124811	Robert Price	01/2020
2968	2^414432-1846709	124757	Enzo Doria	07/2015
2969	2*10^124751-51	124752	Robert Price	04/2018
2970	(56*10^124735+367)/9	124736	Robert Price	06/2019
2971	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
2972	56*10^124656-3	124658	Robert Price	03/2020
2973	(7*10^124648+197)/3	124649	Robert Price	07/2018
2975	2^414032-5	124637	Henri Lifchitz	07/2006
2974	2^414032+1872331	124637	Enzo Doria	05/2016
2976	37373^2158+2158^37373	124604	Hans Havermann	03/2021
2977	29811^15112+15112^29811	124590	Hans Havermann	03/2021
2978	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
2979	29757^15296+15296^29757	124521	Hans Havermann	03/2021
2980	35056^3561+3561^35056	124504	Hans Havermann	03/2021
2981	40588^1167+1167^40588	124487	Hans Havermann	02/2021
2982	(85*10^124485-49)/9	124486	Robert Price	12/2020
2983	64^68909-63^68909	124463	Robert Price	07/2013
2984	35016^3581+3581^35016	124448	Hans Havermann	03/2021
2985	2^413387+76253	124442	Enzo Doria	04/2016
2986	28749^21298+21298^28749	124436	Hans Havermann	03/2021
2987	2^413352+524287	124432	Paul Underwood	09/2018
2988	287117#+391613	124424	Nicolas PALAU	01/2017
2990	(4*10^124420+83)/3	124421	Robert Price	02/2018
2989	34578^3965+3965^34578	124421	Hans Havermann	03/2021
2991	(68*10^124392-329)/9	124393	Robert Price	03/2021
2992	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
2993	10^124383-8000001	124383	Robert Price	04/2021
2994	(41*10^124335-383)/9	124336	Robert Price	11/2018
2995	(304*10^124329-43)/9	124331	Robert Price	02/2020
2996	34716^3811+3811^34716	124320	Hans Havermann	03/2021
2997	2^412868-120599	124286	Paul Bourdelais	02/2012
2998	10^124248-1000001	124248	Robert Price	08/2020
2999	45^75145-2	124231	Lelio R Paula	08/2015
3000	29901^14272+14272^29901	124224	Hans Havermann	03/2021

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