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	(49*10^153484-211)/9	153485	Robert Price	06/2022
2502	2^509841+71657	153478	Enzo Doria	04/2016
2503	9*10^153446+41	153447	Robert Price	08/2020
2504	2^509533-1846723	153385	Enzo Doria	07/2015
2505	2^509468-39989	153366	Enzo Doria	09/2015
2506	70^83117-69^83117	153360	Robert Price	01/2014
2507	(7*10^153116-1)/3	153117	Robert Price	08/2022
2508	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
2509	(19*10^153010+131)/3	153011	Robert Price	06/2020
2510	2^508174-1855151	152976	Enzo Doria	09/2015
2511	181^67757-2	152974	Lelio R Paula	12/2017
2512	2^508160-1864829	152972	Enzo Doria	01/2016
2513	10^152960+412563	152961	Patrick De Geest	05/2021
2514	10^152960-50000000001	152960	Robert Price	12/2020
2515	10^152960-423749	152960	Patrick De Geest	05/2021
2516	(71*10^152933-143)/9	152934	Robert Price	10/2021
2517	2^507857-1848199	152881	Enzo Doria	07/2015
2518	2^507638-115361	152815	Enzo Doria	07/2015
2519	2^507551-114025	152789	Enzo Doria	11/2014
2520	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
2521	(22*10^152670-13)/9	152671	Robert Price	06/2018
2522	2^506451-22339	152457	Enzo Doria	07/2013
2523	2^505995-113185	152320	Enzo Doria	07/2014
2524	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
2525	(4*10^152253+149)/9	152253	Robert Price	04/2018
2526	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
2527	2^505431-505431	152150	Henri Lifchitz	04/2005
2528	(203*10^152143+1)/3	152145	Robert Price	03/2020
2529	2^505053+73097	152037	Enzo Doria	04/2016
2530	22*10^151998+3	152000	Robert Price	01/2020
2531	(238*10^151979-1)/3	151981	Robert Price	04/2020
2532	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
2533	350377#+797581	151937	Nicolas PALAU	08/2017
2534	(79*10^151906-529)/9	151907	Robert Price	01/2022
2535	2^504618-343991	151906	Enzo Doria	07/2015
2536	2^504212-461939	151783	Enzo Doria	07/2015
2537	7*10^151772-41	151773	Robert Price	08/2021
2538	2^504054-2231	151736	Yves Minet	10/2011
2539	(28*10^151682+191)/3	151683	Robert Price	02/2020
2540	2^503475-933075	151562	Paul Bourdelais	06/2021
2541	2^503361-39883	151527	Enzo Doria	09/2015
2542	2^503225+382667	151486	Enzo Doria	10/2016
2543	(206*10^151483-11)/3	151485	Robert Price	02/2022
2544	(844*10^151396-7)/9	151398	Robert Price	05/2021
2545	(26*10^151391-503)/9	151392	Robert Price	07/2018
2546	2^502769+1877567	151349	Enzo Doria	08/2016
2547	2^502576-4019	151291	Yves Minet	10/2011
2548	5*10^151257+41	151258	Robert Price	03/2019
2549	2^502290-2792501	151205	Enzo Doria	02/2016
2550	2^502181+1868417	151172	Enzo Doria	04/2016
2551	6*10^151063-77	151064	Robert Price	09/2021
2552	2^501781-1850503	151052	Enzo Doria	08/2015
2553	(5*10^151007+37)/3	151008	Robert Price	03/2018
2554	2^501627-991	151005	Yves Minet	02/2014
2555	2^501577-115333	150990	Enzo Doria	07/2015
2556	8*10^150975+3	150976	Robert Price	08/2015
2557	2^501512-113669	150971	Enzo Doria	09/2014
2558	(83*10^150908+493)/9	150909	Robert Price	12/2021
2559	2*10^150818+83	150819	Robert Price	12/2021
2560	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
2561	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
2562	2^500899-500899	150786	Henri Lifchitz	04/2005
2563	2^500832+1876801	150766	Enzo Doria	07/2016
2564	(23*10^150763-59)/9	150764	Robert Price	05/2018
2565	2^500699+1884953	150726	Enzo Doria	02/2017
2566	(13*10^150675-37)/3	150676	Robert Price	01/2019
2567	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
2568	2^500337-71101	150617	Enzo Doria	04/2016
2569	(74*10^150616+133)/9	150617	Robert Price	06/2019
2570	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
2571	4*10^150577+91	150578	Robert Price	08/2018
2572	2^500160+80071	150564	Enzo Doria	06/2016
2573	(2^500120+5)/9	150551	Lelio R Paula	12/2017
2574	(43*10^150515-421)/9	150516	Robert Price	01/2019
2575	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
2576	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
2577	2^499861-29503	150474	Enzo Doria	08/2015
2578	2^499653-113533	150411	Enzo Doria	08/2014
2579	(14*10^150391-191)/3	150392	Robert Price	10/2020
2580	2^499534-221	150375	Yves Minet	06/2012
2581	(28*10^150294+41)/3	150295	Robert Price	07/2021
2582	2^499225+49727	150282	Enzo Doria	09/2016
2583	(695*10^150274+7)/9	150276	Robert Price	12/2021
2584	2^499054-29261	150231	Enzo Doria	07/2015
2585	(844*10^150196-7)/9	150198	Robert Price	05/2021
2586	2^498907-933075	150186	Paul Bourdelais	06/2021
2587	(2^498898-7)/9	150183	Lelio R Paula	10/2015
2588	3*10^150182+17	150183	Robert Price	07/2018
2589	5*10^150175+63	150176	Robert Price	09/2020
2590	32363^33292+33292^32363	150149	Norbert Schneider	07/2022
2591	(77*10^150128+67)/9	150129	Robert Price	12/2021
2592	2^498623+1866983	150101	Enzo Doria	03/2016
2593	(25*10^150050-403)/9	150051	Robert Price	12/2020
2594	numbpart(18140942830)	150033	Serge Batalov	04/2017
2595	10^150029+4381	150030	Patrick De Geest	05/2016
2596	10^150029-41	150029	Serge Batalov	12/2014
2597	10^150000+1158603	150001	Patrick De Geest	09/2018
2598	10^150000-245703	150000	Patrick De Geest	09/2018
2599	(38*10^149999+691)/9	150000	Robert Price	10/2018
2600	2043563126843649194^8192+2043563126843649185^8192	150000	Youcef Lemsafer	01/2023
2601	(2043563126843649232^8192+2043563126843649201^8192)/147457	149994	Youcef Lemsafer	01/2023
2602	2^498238-53	149985	Lelio R Paula	12/2017
2603	45728^1905+1905^45728	149984	Hans Havermann	10/2020
2604	5*10^149907+23	149908	Robert Price	03/2019
2605	39347^6442+6442^39347	149874	Hans Havermann	09/2020
2606	2^497850+81049	149868	Enzo Doria	07/2016
2607	37228^10575+10575^37228	149816	Hans Havermann	10/2020
2608	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
2609	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
2610	(2*10^149803-143)/3	149803	Robert Price	03/2018
2611	33845^26604+26604^33845	149763	Hans Havermann	09/2020
2612	2^497434-2784191	149743	Enzo Doria	10/2015
2613	(865*10^149737-1)/9	149739	Robert Price	04/2020
2614	10^149695-7000001	149695	Robert Price	06/2021
2615	38237^8214+8214^38237	149681	Hans Havermann	09/2020
2616	(23*10^149655+19)/3	149656	Robert Price	07/2019
2617	2^497068-113579	149633	Enzo Doria	08/2014
2618	2^497037+73727	149624	Enzo Doria	04/2016
2619	11*10^149618+3	149620	Robert Price	07/2021
2620	34942^19067+19067^34942	149562	Hans Havermann	09/2020
2621	33696^27449+27449^33696	149561	Hans Havermann	09/2020
2622	2^496773+77747	149544	Enzo Doria	05/2016
2623	(7*10^149483-493)/9	149483	Robert Price	04/2021
2624	(206*10^149459+7)/3	149461	Robert Price	07/2020
2625	34589^20940+20940^34589	149459	Hans Havermann	09/2020
2626	2^496477-113485	149455	Enzo Doria	08/2014
2627	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
2628	2^496270-49451	149393	Enzo Doria	10/2015
2629	2^496238-1865081	149383	Enzo Doria	01/2016
2630	33831^26030+26030^33831	149380	Hans Havermann	09/2020
2631	34131^23780+23780^34131	149365	Hans Havermann	09/2020
2632	(5*10^149335-53)/3	149336	Robert Price	09/2020
2633	2^495968-1853699	149302	Enzo Doria	09/2015
2634	2^495935-4117	149292	Yves Minet	02/2018
2635	35816^14709+14709^35816	149267	Hans Havermann	09/2020
2636	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
2637	10^149240-40000001	149240	Robert Price	07/2022
2638	2^495712-396765	149225	Enzo Doria	07/2013
2639	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
2640	2^495420+1880701	149137	Enzo Doria	10/2016
2641	2^495337-1847293	149112	Enzo Doria	07/2015
2642	(2^495193-7)/5	149068	Lelio R Paula	10/2015
2643	2^495163+111546435	149059	Paul Bourdelais	10/2021
2644	33282^30097+30097^33282	149055	Hans Havermann	09/2020
2645	37384^9705+9705^37384	149050	Hans Havermann	09/2020
2646	34808^19143+19143^34808	149049	Hans Havermann	09/2020
2647	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
2648	47^89113-46^89113	149006	Robert Price	10/2012
2649	2^494916+87855	148985	Lelio R Paula	01/2016
2650	6*10^148982+73	148983	Robert Price	04/2019
2651	3^312155-4	148936	Anonymous	02/2023
2652	10^148934+1530019	148935	Patrick De Geest	02/2021
2653	10^148934-1000000001	148934	Robert Price	11/2020
2654	10^148934-512057	148934	Patrick De Geest	02/2021
2655	39000^6571+6571^39000	148888	Hans Havermann	10/2020
2656	2^494586-2791991	148886	Enzo Doria	02/2016
2657	8*10^148860-3	148861	Ray Chandler	04/2011
2658	38262^7769+7769^38262	148854	Hans Havermann	10/2020
2659	10^148816-500001	148816	Robert Price	03/2022
2660	(53*10^148811-287)/9	148812	Robert Price	02/2022
2661	2^494333-286183	148810	Enzo Doria	06/2015
2662	2^494144-264119	148753	Enzo Doria	05/2014
2663	6*10^148734+47	148735	Robert Price	06/2022
2664	36502^11823+11823^36502	148663	Hans Havermann	11/2020
2665	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
2666	64239^206+206^64239	148641	Hans Havermann	10/2020
2667	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
2668	(23*10^148627-137)/3	148628	Robert Price	08/2021
2669	(151*10^148601-1)/3	148603	Robert Price	03/2020
2670	2^493636+82081	148600	Enzo Doria	09/2016
2671	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
2672	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
2673	(2*10^148460-23)/3	148460	Robert Price	04/2018
2674	(28*10^148445+101)/3	148446	Robert Price	09/2020
2675	36203^12556+12556^36203	148391	Hans Havermann	10/2020
2676	33912^23749+23749^33912	148387	Hans Havermann	10/2020
2677	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
2678	34294^21117+21117^34294	148309	Hans Havermann	10/2020
2679	(71*10^148306-539)/9	148307	Robert Price	07/2019
2680	38042^7875+7875^38042	148222	Hans Havermann	10/2020
2681	5^211959-12874	148153	Enzo Doria	05/2014
2682	34142^21831+21831^34142	148145	Hans Havermann	10/2020
2683	10^148112+34059	148113	Patrick De Geest	05/2021
2684	10^148112-70000001	148112	Robert Price	03/2021
2685	10^148112-106593	148112	Patrick De Geest	05/2021
2686	36303^12016+12016^36303	148108	Hans Havermann	10/2020
2687	(77*10^148089-149)/9	148090	Robert Price	03/2022
2688	(16*10^148071+41)/3	148072	Robert Price	03/2019
2689	187^65175-2	148068	Lelio R Paula	11/2017
2690	2^491851+1871453	148062	Enzo Doria	05/2016
2691	(68*10^148060-257)/9	148061	Robert Price	07/2019
2692	(151*10^148020-1)/3	148022	Robert Price	03/2020
2693	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2694	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2695	(26*10^147973-23)/3	147974	Robert Price	12/2019
2696	2^491521-1865323	147963	Enzo Doria	02/2016
2697	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2698	2*10^147928+47	147929	Robert Price	12/2021
2699	2^491391-7807	147924	Lelio R Paula	01/2013
2700	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2701	2^491370-113297	147918	Enzo Doria	07/2014
2702	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2703	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2704	(17*10^147890+79)/3	147891	Robert Price	04/2019
2705	94*10^147871-3	147873	Robert Price	05/2020
2706	10^147843+620967	147844	Patrick De Geest	05/2021
2707	10^147843-50000000001	147843	Robert Price	12/2020
2708	10^147843-182891	147843	Patrick De Geest	05/2021
2709	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2710	2^490672+255255	147707	Paul Bourdelais	10/2021
2711	2^490660-17	147704	Lelio R Paula	12/2017
2712	(229*10^147699-1)/3	147701	Robert Price	07/2020
2713	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2714	2^490550+1179439	147671	Enzo Doria	06/2016
2715	(23*10^147649-59)/9	147650	Robert Price	05/2018
2716	2^490303+2793653	147596	Enzo Doria	03/2016
2717	2^490266+255255	147585	Paul Bourdelais	10/2021
2718	199^64181-2	147543	Lelio R Paula	11/2017
2719	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2720	2^489871-286987	147466	Enzo Doria	07/2015
2721	2^489864-351899	147464	Enzo Doria	07/2015
2722	175^65724-2	147422	Lelio R Paula	11/2017
2723	2^489712+1874851	147419	Enzo Doria	06/2016
2724	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2725	63^81896-2	147359	Lelio R Paula	10/2017
2726	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2727	(11*10^147313-107)/3	147314	Robert Price	09/2018
2728	(397*10^147310+17)/9	147312	Robert Price	03/2022
2729	2^489305-59815	147296	Enzo Doria	10/2015
2730	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2731	2*10^147264-61	147265	Robert Price	10/2021
2732	2*10^147260+29	147261	Robert Price	02/2021
2733	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2734	2^489125+80357	147242	Enzo Doria	06/2016
2735	10^147240-40000001	147240	Robert Price	07/2022
2736	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2737	(19*10^147213-97)/3	147214	Robert Price	10/2021
2738	(148*10^147139-1)/3	147141	Robert Price	03/2020
2739	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2740	2^488648-112799	147098	Enzo Doria	07/2014
2741	2^488627-350317	147092	Enzo Doria	06/2015
2742	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2743	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2744	2^488280-2165	146987	Yves Minet	07/2014
2745	2^488278+45	146987	Lelio R Paula	12/2017
2746	2^487927-39	146881	Lelio R Paula	12/2017
2747	(7*10^146860-13)/3	146861	Robert Price	07/2018
2748	(26*10^146856-77)/3	146857	Robert Price	11/2019
2749	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2750	42596^2799+2799^42596	146829	Hans Havermann	12/2020

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