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 ?
2501	(91*10^160249+11)/3	160251	Robert Price	02/2020
2502	(772*10^160239-7)/9	160241	Robert Price	06/2022
2503	(2*10^160226+187)/9	160226	Robert Price	06/2022
2504	2^532253+1868417	160225	Enzo Doria	04/2016
2505	2^532108-291989	160181	Enzo Doria	07/2015
2506	(28*10^160171-79)/3	160172	Robert Price	02/2021
2507	(26*10^160166-131)/3	160167	Robert Price	10/2019
2508	55*10^160145+9	160147	Robert Price	03/2022
2509	(17*10^160143+67)/3	160144	Robert Price	01/2019
2510	(394^61637-1)/393	159977	Jinyuan Wang	04/2023
2511	(19*10^159921-49)/3	159922	Robert Price	05/2019
2512	2^531110-1853771	159881	Enzo Doria	09/2015
2513	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
2514	2^530992-1845299	159845	Enzo Doria	07/2015
2515	2^530810+25	159790	Stefano Morozzi	04/2021
2516	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
2517	2^530417-113833	159672	Enzo Doria	09/2014
2518	2^530406-69701	159669	Enzo Doria	02/2016
2519	5*10^159656+41	159657	Robert Price	03/2019
2520	8*10^159614+29	159615	Robert Price	11/2021
2521	7^188858-188858^7	159604	Norbert Schneider	05/2018
2522	7*10^159553-27	159554	Robert Price	11/2022
2523	3^334409-5*2^334409	159554	Jon Grantham	08/2023
2524	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
2525	(17*10^159438-377)/9	159439	Robert Price	03/2018
2526	(203*10^159381+1)/3	159383	Robert Price	03/2020
2527	89*10^159258-9	159260	Robert Price	05/2020
2528	2^528944-461315	159229	Enzo Doria	07/2015
2529	(13*10^159147+161)/3	159148	Robert Price	11/2018
2530	2^528620-113879	159131	Enzo Doria	10/2014
2531	(47*10^159083+259)/9	159084	Robert Price	03/2022
2532	2^528000-23307	158944	Enzo Doria	08/2013
2533	(29*10^158909+61)/9	158910	Robert Price	08/2018
2534	2^527817+1876817	158889	Enzo Doria	07/2016
2535	2^527774-49451	158876	Enzo Doria	10/2015
2536	2^527745-291553	158868	Enzo Doria	07/2015
2537	(91*10^158862+11)/3	158864	Robert Price	02/2020
2538	2^527644-1856999	158837	Enzo Doria	10/2015
2539	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
2540	(17*10^158819+7)/3	158820	Robert Price	06/2023
2541	2^527573-1863253	158816	Enzo Doria	12/2015
2542	2^527553-23401	158810	Enzo Doria	08/2013
2543	(49*10^158783+437)/9	158784	Robert Price	09/2021
2544	10^158755+310207	158756	Patrick De Geest	08/2021
2545	10^158755-50001	158755	Robert Price	08/2020
2546	(61*10^158748-619)/9	158749	Robert Price	03/2022
2547	11^152420-210	158730	Enzo Doria	09/2012
2548	(13*10^158694+401)/9	158695	Robert Price	01/2018
2549	2^527052-69059	158659	Enzo Doria	11/2015
2550	2^526849-113233	158598	Enzo Doria	07/2014
2551	24286^36161+36161^24286	158579	Norbert Schneider	08/2023
2552	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
2553	(299*10^158544-17)/3	158546	Robert Price	04/2020
2554	2^526658-3551	158540	Yves Minet	03/2017
2555	7*10^158465-11	158466	Robert Price	06/2019
2556	(7^187507-3^187507)/4	158462	Jon Grantham	08/2023
2557	2^526375-23115	158455	Enzo Doria	08/2013
2558	(77*10^158407-293)/9	158408	Robert Price	09/2019
2559	2^526028-112793	158351	Enzo Doria	07/2014
2560	(229*10^158339-1)/3	158341	Robert Price	07/2020
2561	2^525690-9221	158249	Lelio R Paula	01/2013
2562	2*10^158242-7	158243	Robert Price	10/2015
2563	2^525667-525667^2	158242	Henri Lifchitz	12/2017
2564	(56*10^158230+187)/9	158231	Robert Price	10/2021
2565	10^158209-7000000001	158209	Robert Price	12/2021
2566	2^525186-1857431	158097	Enzo Doria	10/2015
2567	2^524515-23245	157895	Enzo Doria	08/2013
2568	2^524499-109087	157890	Enzo Doria	04/2014
2569	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
2570	2^524288+189093	157827	Makoto Morimoto	01/2016
2571	2^524288-164073	157827	Matthias Baur	03/2020
2572	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
2573	(10^157792+359)/9	157792	Serge Batalov	12/2014
2574	2^524154+25	157787	Stefano Morozzi	04/2021
2575	2^523924+1876591	157717	Enzo Doria	07/2016
2576	(17*10^157705+67)/3	157706	Robert Price	01/2019
2577	(46^94841+1)/47	157696	Robert Price	01/2014
2578	2^523774+77839	157672	Enzo Doria	05/2016
2579	2^523587+2799143	157616	Enzo Doria	04/2016
2580	2^523371+1872113	157551	Enzo Doria	05/2016
2581	8*10^157477+27	157478	Robert Price	09/2021
2582	(8*10^157368+49)/3	157369	Robert Price	05/2020
2583	(82*10^157319+449)/9	157320	Robert Price	11/2019
2584	2^522535-351457	157299	Enzo Doria	07/2015
2585	2^522226+2799079	157206	Enzo Doria	04/2016
2586	(134*10^157191-11)/3	157193	Robert Price	01/2022
2587	2^522134-1849451	157178	Enzo Doria	08/2015
2588	9*10^157152+71	157153	Robert Price	08/2020
2589	4*10^157150+93	157151	Robert Price	08/2018
2590	fibonacci(751442)-2	157042	Jon Grantham	08/2023
2591	2^521401-29593	156958	Enzo Doria	08/2015
2592	7*10^156956+87	156957	Robert Price	07/2019
2593	2^521348-23397	156942	Enzo Doria	08/2013
2594	10^156902+34509	156903	Patrick De Geest	08/2021
2596	10^156902-80000001	156902	Robert Price	04/2021
2595	10^156902-69789	156902	Patrick De Geest	08/2021
2597	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
2598	65^86522+64	156857	Lelio R Paula	04/2016
2599	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
2600	2^520977-1858183	156830	Enzo Doria	10/2015
2601	(8*10^156718-101)/3	156719	Robert Price	08/2018
2602	(10^156640+7)/53	156639	Alfred Reich	07/2021
2603	2^520314-1849481	156631	Enzo Doria	08/2015
2604	(16*10^156563-637)/9	156564	Robert Price	09/2022
2605	(13*10^156522+89)/3	156523	Robert Price	09/2018
2607	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
2606	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
2608	(4*10^156501+119)/3	156502	Robert Price	12/2021
2609	(83*10^156476-101)/9	156477	Robert Price	08/2021
2610	3*10^156435-97	156436	Robert Price	07/2018
2611	(8*10^156371-77)/3	156372	Robert Price	07/2018
2612	53^90679-52^90679	156356	Robert Price	01/2013
2613	(418*10^156309-31)/9	156311	Robert Price	05/2022
2614	2^519106-59141	156267	Enzo Doria	10/2015
2615	2^519053+6077	156251	Enzo Doria	02/2016
2616	2^518968-1860989	156225	Enzo Doria	11/2015
2617	(25*10^156221-7)/9	156222	Robert Price	05/2018
2618	2^518931-2782297	156214	Enzo Doria	09/2015
2619	2^518608-2939	156117	Yves Minet	09/2014
2620	10*27^109005+697	156027	Curtis Bright	05/2015
2621	(49*10^155933-319)/9	155934	Robert Price	10/2021
2622	2^517967-113485	155924	Enzo Doria	08/2014
2623	(103*10^155904+17)/3	155906	Robert Price	08/2020
2624	(8*10^155887-719)/9	155887	Robert Price	03/2021
2625	4*10^155853-39	155854	Robert Price	09/2020
2626	2^517698+4429	155843	Lelio R Paula	01/2013
2627	2^517543-113257	155796	Enzo Doria	07/2014
2628	(14*10^155740-143)/3	155741	Robert Price	11/2018
2629	31^104309-30^104309	155563	Henri Lifchitz	08/2013
2630	2^516742-39851	155555	Enzo Doria	09/2015
2631	(22*10^155543+47)/3	155544	Robert Price	06/2021
2632	(19*10^155504+131)/3	155505	Robert Price	06/2020
2633	7*10^155496+61	155497	Robert Price	08/2019
2634	2^516440+1878421	155464	Enzo Doria	08/2016
2635	2^515863-1867237	155291	Enzo Doria	03/2016
2636	2^515786-461861	155268	Enzo Doria	07/2015
2637	2^515644-113247	155225	Enzo Doria	07/2014
2638	(7*10^155203+107)/3	155204	Robert Price	02/2018
2639	10^155163+206871	155164	Patrick De Geest	05/2021
2640	10^155163-40001	155163	Robert Price	01/2021
2641	(17*10^155133-89)/9	155134	Robert Price	07/2018
2642	2^515227-114997	155099	Enzo Doria	06/2015
2644	EPrime(155025)	155025	Eric W. Weisstein	10/2010
2643	(14*10^155024-221)/9	155025	Robert Price	04/2018
2645	(4*10^155022+173)/3	155023	Robert Price	02/2018
2646	(266*10^154897+1)/3	154899	Robert Price	04/2020
2647	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
2648	(86*10^154853-221)/9	154854	Robert Price	09/2019
2649	2^514361+78167	154839	Enzo Doria	05/2016
2650	2^514281-115033	154815	Enzo Doria	06/2015
2651	2^514194-3311	154788	Yves Minet	12/2014
2652	(14*10^154773+37)/3	154774	Robert Price	12/2018
2653	(16*10^154748+131)/3	154749	Robert Price	03/2022
2654	6*10^154742-31	154743	Robert Price	07/2020
2655	(14*10^154645+139)/9	154646	Robert Price	11/2021
2656	5*10^154618-79	154619	Robert Price	03/2021
2657	(167*10^154595+1)/3	154597	Robert Price	04/2021
2658	2^513437+1879337	154560	Enzo Doria	09/2016
2659	2^513306-113201	154521	Enzo Doria	07/2014
2660	(10^154494-13)/3	154494	Robert Price	12/2017
2661	23462^35343+35343^23462	154462	Norbert Schneider	04/2023
2662	2^513042-113787	154442	Enzo Doria	09/2014
2663	(151*10^154434-7)/9	154436	Robert Price	01/2020
2664	(118*10^154428+11)/3	154430	Robert Price	03/2022
2665	(14*10^154413+139)/9	154414	Robert Price	11/2021
2666	(77*10^154389-149)/9	154390	Robert Price	03/2022
2667	10^154359+49	154360	Robert Price	02/2023
2668	2^512628-114053	154317	Enzo Doria	11/2014
2669	2^512529-49783	154287	Enzo Doria	10/2015
2670	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
2671	2^512315-115297	154223	Enzo Doria	06/2015
2672	(47*10^154221+241)/9	154222	Robert Price	06/2022
2673	(7*10^154211+173)/9	154211	Robert Price	01/2022
2674	2^512243+22703	154201	Enzo Doria	09/2023
2675	2^512168+79561	154178	Enzo Doria	06/2016
2676	(77*10^154175+67)/9	154176	Robert Price	12/2021
2677	(5*10^154158-311)/9	154158	Robert Price	12/2021
2678	(89*10^154103-737)/9	154104	Robert Price	01/2022
2679	4*10^154078-57	154079	Robert Price	10/2018
2680	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
2681	7*10^154038-57	154039	Robert Price	06/2020
2682	2^511658-114371	154025	Enzo Doria	02/2015
2683	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2684	2^511580-1846679	154001	Enzo Doria	07/2015
2685	(259*10^153998-1)/3	154000	Robert Price	12/2020
2686	2^511541-113713	153990	Enzo Doria	09/2014
2687	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2688	10^153935+970801	153936	Patrick De Geest	05/2021
2689	10^153935-1000001	153935	Robert Price	08/2020
2690	(16*10^153868-73)/3	153869	Robert Price	07/2020
2691	9*10^153851-67	153852	Robert Price	11/2020
2692	2^511077-112723	153850	Enzo Doria	06/2014
2693	69^83653-68^83653	153826	Robert Price	12/2013
2694	2^510963-113707	153816	Enzo Doria	09/2014
2695	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2696	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2697	2*10^153746-3	153747	Robert Price	07/2015
2698	2^510626+1179379	153714	Enzo Doria	05/2016
2699	(7*10^153664+113)/3	153665	Robert Price	02/2018
2700	2^510420+81121	153652	Enzo Doria	07/2016
2701	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2702	2^509894-459161	153494	Enzo Doria	05/2015
2703	(74*10^153489+673)/9	153490	Robert Price	02/2022
2704	(49*10^153484-211)/9	153485	Robert Price	06/2022
2705	2^509841+71657	153478	Enzo Doria	04/2016
2706	9*10^153446+41	153447	Robert Price	08/2020
2707	2^509533-1846723	153385	Enzo Doria	07/2015
2708	2^509468-39989	153366	Enzo Doria	09/2015
2709	70^83117-69^83117	153360	Robert Price	01/2014
2710	(209246*34^99997-81)/11	153148	Eric Chen	08/2023
2711	(7*10^153116-1)/3	153117	Robert Price	08/2022
2712	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
2713	(19*10^153010+131)/3	153011	Robert Price	06/2020
2714	2^508174-1855151	152976	Enzo Doria	09/2015
2715	181^67757-2	152974	Lelio R Paula	12/2017
2716	2^508160-1864829	152972	Enzo Doria	01/2016
2717	10^152960+412563	152961	Patrick De Geest	05/2021
2718	10^152960-50000000001	152960	Robert Price	12/2020
2719	10^152960-423749	152960	Patrick De Geest	05/2021
2720	(71*10^152933-143)/9	152934	Robert Price	10/2021
2721	2^507857-1848199	152881	Enzo Doria	07/2015
2722	2^507638-115361	152815	Enzo Doria	07/2015
2723	2^507551-114025	152789	Enzo Doria	11/2014
2724	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
2725	(22*10^152670-13)/9	152671	Robert Price	06/2018
2726	2^506451-22339	152457	Enzo Doria	07/2013
2727	2^505995-113185	152320	Enzo Doria	07/2014
2728	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
2729	(4*10^152253+149)/9	152253	Robert Price	04/2018
2730	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
2731	2^505431-505431	152150	Henri Lifchitz	04/2005
2732	(203*10^152143+1)/3	152145	Robert Price	03/2020
2733	2^505053+73097	152037	Enzo Doria	04/2016
2734	22*10^151998+3	152000	Robert Price	01/2020
2735	(238*10^151979-1)/3	151981	Robert Price	04/2020
2736	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
2737	350377#+797581	151937	Nicolas PALAU	08/2017
2738	(79*10^151906-529)/9	151907	Robert Price	01/2022
2739	2^504618-343991	151906	Enzo Doria	07/2015
2740	2^504259+211193	151798	Enzo Doria	08/2023
2741	2^504212-461939	151783	Enzo Doria	07/2015
2742	7*10^151772-41	151773	Robert Price	08/2021
2743	2^504054-2231	151736	Yves Minet	10/2011
2744	(28*10^151682+191)/3	151683	Robert Price	02/2020
2745	2^503475-933075	151562	Paul Bourdelais	06/2021
2746	2^503361-39883	151527	Enzo Doria	09/2015
2747	2^503225+382667	151486	Enzo Doria	10/2016
2748	(206*10^151483-11)/3	151485	Robert Price	02/2022
2749	(844*10^151396-7)/9	151398	Robert Price	05/2021
2750	(26*10^151391-503)/9	151392	Robert Price	07/2018

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PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)