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	(8*10^180725-629)/9	180725	Robert Price	01/2022
2502	(79*10^180710-1)/3	180712	Robert Price	02/2020
2503	2^600300-1852559	180709	Enzo Doria	08/2015
2504	(2*10^180706-77)/3	180706	Robert Price	02/2021
2505	(156^82393-1)/155	180696	Anonymous	06/2024
2506	(10^180689+71)/9	180689	Serge Batalov	07/2015
2507	2^600209+76487	180681	Enzo Doria	05/2016
2508	2^599999+378461	180618	Norman Luhn	09/2023
2509	(8*10^180536-269)/9	180536	Robert Price	09/2021
2510	2^599702-369885	180529	Enzo Doria	11/2013
2511	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
2512	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
2513	(29*10^180432-17)/3	180433	Robert Price	09/2019
2514	4*10^180360+93	180361	Robert Price	08/2018
2515	2^599035+219323	180328	Enzo Doria	03/2024
2516	2^598942+80779	180300	Enzo Doria	07/2016
2517	(38*10^180296+403)/9	180297	Robert Price	10/2018
2518	(85*10^180241+77)/9	180242	Robert Price	07/2022
2519	2^598591-1844797	180194	Enzo Doria	06/2015
2520	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
2521	2^598301+28517	180107	Enzo Doria	01/2024
2522	(29*10^180072+691)/9	180073	Robert Price	08/2021
2523	(59*10^180038+157)/9	180039	Robert Price	12/2021
2524	95*10^180019-9	180021	Robert Price	01/2022
2525	6*10^179970+91	179971	Robert Price	05/2019
2526	(4*10^179963-79)/3	179964	Robert Price	02/2018
2527	(403*10^179944-43)/9	179946	Robert Price	06/2021
2528	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
2529	2^597424-1859729	179843	Enzo Doria	11/2015
2530	Phi(180683,10)	179760	Maksym Voznyy	09/2015
2531	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
2532	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
2533	(29*10^179697+223)/9	179698	Robert Price	09/2018
2534	U(1289697)	179687	Serge Batalov	07/2024
2536	2^596884+73	179680	Stefano Morozzi	04/2021
2535	(11*10^179679+13)/3	179680	Robert Price	03/2022
2537	(68*10^179656+7)/3	179658	Robert Price	01/2020
2538	(10^179643+173)/3	179643	Robert Price	05/2021
2539	2^596690-461261	179622	Enzo Doria	07/2015
2540	2^596684-113939	179620	Enzo Doria	10/2014
2541	2^596642+39	179608	Jon Grantham	08/2023
2542	2*10^179602+63	179603	Robert Price	05/2018
2543	32262^39815-39815^32262	179514	Frank Doornink	02/2024
2544	(25*10^179488-403)/9	179489	Robert Price	01/2021
2545	7*10^179460+99	179461	Robert Price	05/2021
2546	2^596127+74333	179453	Enzo Doria	07/2023
2547	3^375887-112696	179344	Enzo Doria	07/2014
2548	4*10^179265-71	179266	Robert Price	12/2018
2549	2*10^179193+83	179194	Robert Price	12/2021
2550	2^595144-1850429	179157	Enzo Doria	08/2015
2551	2^595122-5	179150	Stefano Morozzi	07/2022
2552	3*10^179138+89	179139	Robert Price	10/2018
2553	(52*10^179062-133)/9	179063	Robert Price	09/2021
2554	2^594531+82253	178972	Enzo Doria	09/2016
2555	(664*10^178939-61)/9	178941	Robert Price	09/2021
2556	2^594260-2787899	178891	Enzo Doria	11/2015
2557	(14*10^178822+67)/9	178823	Robert Price	05/2022
2558	(29*10^178732-119)/9	178733	Robert Price	12/2021
2559	2^593631+101381	178701	Jorge Menendez	04/2018
2560	10^178695+136719	178696	Patrick De Geest	05/2016
2561	10^178695-71	178695	Serge Batalov	12/2014
2562	(2*10^178649-161)/3	178649	Robert Price	12/2020
2563	(691^62903-1)/690	178609	Michael Stocker	05/2020
2564	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
2565	2^593242+28309	178584	Enzo Doria	01/2024
2566	2^593222-14145	178578	Jorge Menendez	10/2017
2567	7*10^178566+33	178567	Robert Price	06/2020
2568	2^593178+1867219	178565	Enzo Doria	03/2016
2569	2^593152+22441	178557	Enzo Doria	09/2023
2570	(38*10^178456+151)/9	178457	Robert Price	03/2022
2571	(302*10^178369+13)/9	178371	Robert Price	02/2020
2572	(26*10^178296-113)/3	178297	Robert Price	06/2020
2573	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
2574	(13*10^178233+137)/3	178234	Robert Price	06/2021
2575	(5*10^178206+91)/3	178207	Robert Price	04/2018
2576	2^591872-291929	178172	Enzo Doria	07/2015
2577	2^591682-286871	178115	Enzo Doria	07/2015
2578	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
2579	4*10^178091+9	178092	Robert Price	05/2015
2580	410747#+478483	178007	Makoto Morimoto	02/2016
2581	3*10^177872+73	177873	Robert Price	08/2018
2582	2^590762-396765	177838	Enzo Doria	08/2013
2583	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
2584	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
2585	Smr(37765)	177719	Eric W. Weisstein	12/2021
2586	(266*10^177577-11)/3	177579	Robert Price	04/2020
2587	(11*10^177466-113)/3	177467	Robert Price	10/2018
2588	3*10^177373-97	177374	Robert Price	07/2018
2589	2^589204+1881151	177369	Enzo Doria	11/2016
2590	2^589132-69479	177347	Enzo Doria	01/2016
2591	(101*10^177302-17)/3	177304	Robert Price	02/2020
2592	2^588912-113519	177281	Enzo Doria	08/2014
2593	(682*10^177266-7)/9	177268	Robert Price	08/2021
2594	15^150706+2	177245	Robert Price	06/2015
2595	(31208^39601-1)/(31208^199-1)	177084	Ryan Propper	11/2023
2596	2^588194-1861001	177065	Enzo Doria	11/2015
2597	5*10^177016-37	177017	Robert Price	11/2021
2598	fibonacci(846926)-4	176997	Jon Grantham	08/2023
2599	(23*10^176964-47)/3	176965	Robert Price	09/2019
2600	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
2601	(19*10^176932+521)/9	176933	Robert Price	05/2018
2602	(8*10^176908+43)/3	176909	Robert Price	06/2018
2603	(85*10^176900+203)/9	176901	Robert Price	09/2020
2604	2^587560-113699	176874	Enzo Doria	09/2014
2605	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
2606	(101*10^176815-17)/3	176817	Robert Price	02/2020
2607	(25*10^176715-37)/3	176716	Robert Price	10/2019
2608	5^252763-12862	176674	Enzo Doria	05/2014
2609	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
2610	2^586829+23961	176654	Enzo Doria	10/2023
2611	2^586804+81721	176646	Enzo Doria	08/2016
2612	(10^176584+77)/3	176584	Robert Price	01/2018
2613	2^586570+1874419	176576	Enzo Doria	06/2016
2614	(157*10^176482-1)/3	176484	Robert Price	01/2022
2615	5*2^586202+3	176466	Jon Grantham	07/2023
2616	27122^39799-39799^27122	176442	Frank Doornink	01/2024
2617	2^585994-3311	176402	Yves Minet	12/2014
2618	8*10^176383-81	176384	Robert Price	02/2021
2619	(23*10^176357+61)/3	176358	Robert Price	01/2022
2620	2^585832-112799	176354	Enzo Doria	07/2014
2621	fibonacci(843383)+4	176257	Jon Grantham	08/2023
2622	(29*10^176240+49)/3	176241	Robert Price	09/2021
2623	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
2624	2^585336-461039	176204	Enzo Doria	06/2015
2625	(25*10^176164+143)/3	176165	Robert Price	08/2020
2626	2^585095-1848127	176132	Enzo Doria	08/2015
2627	(5*10^176101-311)/9	176101	Robert Price	12/2021
2628	6*10^176092+77	176093	Robert Price	06/2020
2629	2^584950-115451	176088	Enzo Doria	07/2015
2630	(646*10^176044+11)/9	176046	Robert Price	10/2021
2631	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
2632	2^584671-3697	176004	Yves Minet	03/2017
2633	(13*10^175965-37)/3	175966	Robert Price	01/2019
2634	31728^39089-39089^31728	175957	Frank Doornink	01/2024
2635	2*10^175860-87	175861	Robert Price	04/2018
2636	27009^39670-39670^27009	175798	Frank Doornink	01/2024
2637	(86*10^175774-221)/9	175775	Robert Price	09/2019
2638	2^583614+216037	175686	Enzo Doria	11/2023
2639	9*10^175654+47	175655	Robert Price	01/2022
2640	25430^39869-39869^25430	175637	Frank Doornink	01/2024
2641	10^175608+2971	175609	Mike Oakes	05/2010
2642	10^175608-55829	175608	Patrick De Geest	09/2013
2643	2^583051+1879793	175516	Enzo Doria	09/2016
2644	(76*10^175514+491)/9	175515	Robert Price	10/2021
2646	2^582860-23829	175459	Enzo Doria	08/2013
2645	(200^76253-1)/199	175459	Anonymous	06/2024
2647	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
2648	(28*10^175417-67)/3	175418	Robert Price	10/2020
2649	2^582670-23913	175402	Enzo Doria	08/2013
2650	2^582573-29563	175372	Enzo Doria	08/2015
2651	2^582435-1862767	175331	Enzo Doria	12/2015
2652	10^175295-40000001	175295	Robert Price	07/2022
2653	31093^39018-39018^31093	175295	Frank Doornink	01/2024
2654	(11*10^175250-149)/3	175251	Robert Price	09/2018
2655	(29*10^175236+31)/3	175237	Robert Price	04/2021
2656	2^582072-1848599	175222	Enzo Doria	08/2015
2657	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
2658	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
2659	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
2660	(5*10^175117-311)/9	175117	Robert Price	12/2021
2661	31193^38966-38966^31193	175116	Frank Doornink	01/2024
2662	2^581695+225893	175108	Enzo Doria	08/2024
2663	10^175093-89	175093	Riley Fisher	10/2023
2664	(220221^32768+1)/2	175075	Serge Batalov	03/2018
2665	2^581560+1874911	175068	Enzo Doria	06/2016
2666	(25*10^174987-97)/9	174988	Robert Price	01/2022
2667	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
2668	26446^39555-39555^26446	174927	Frank Doornink	03/2024
2669	31522^38883-38883^31522	174920	Frank Doornink	01/2024
2670	(27398^39601-1)/(27398^199-1)	174855	Ryan Propper	11/2023
2671	(861^59557-1)/860	174798	Jinyuan Wang	11/2023
2672	31492^38859-38859^31492	174796	Frank Doornink	01/2024
2673	(47*10^174790+493)/9	174791	Robert Price	03/2019
2674	2^580528-114035	174757	Enzo Doria	11/2014
2675	(19*10^174754+737)/9	174755	Robert Price	07/2018
2676	V(1045270)/4181081/12543241/81333115129561	174730	Serge Batalov	07/2024
2677	(35*10^174704-377)/9	174705	Robert Price	07/2018
2679	(49*10^174681+293)/9	174682	Robert Price	03/2021
2678	6*10^174681+11	174682	Robert Price	07/2022
2680	3*10^174665-97	174666	Robert Price	07/2018
2681	2^580046-459161	174612	Enzo Doria	05/2015
2682	2^579992-39779	174595	Enzo Doria	09/2015
2683	25613^39582-39582^25613	174496	Frank Doornink	02/2024
2684	(29*10^174481-149)/3	174482	Robert Price	08/2022
2685	(4*10^174423+101)/3	174424	Robert Price	11/2021
2686	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
2687	(2*10^174301-71)/3	174301	Robert Price	12/2017
2688	14^152048+3	174267	Paul Bourdelais	12/2020
2689	(2^578696+1)/257	174203	Lelio R Paula	09/2015
2690	2^578656-1851809	174193	Enzo Doria	08/2015
2691	2^578583-113917	174171	Enzo Doria	10/2014
2692	2^578434-83	174126	Yves Minet	07/2017
2693	15^148048-2	174118	Robert Price	06/2015
2694	5*10^174101+81	174102	Robert Price	03/2019
2695	2^578346+2794249	174100	Enzo Doria	03/2016
2696	10^173947+1372429	173948	Patrick De Geest	08/2021
2698	10^173947-500000001	173947	Robert Price	12/2020
2697	10^173947-286391	173947	Patrick De Geest	08/2021
2699	5*10^173904-13	173905	Robert Price	01/2019
2700	(8*10^173862-59)/3	173863	Robert Price	08/2021
2701	(71*10^173854-287)/9	173855	Robert Price	09/2019
2702	(43*10^173826+101)/9	173827	Robert Price	11/2018
2703	2*10^173809-87	173810	Robert Price	04/2018
2704	(2^577372-23)/7	173806	Stefano Morozzi	08/2022
2705	(L!41532)/2	173772	Serge Batalov	07/2017
2706	2^577146-49877	173739	Enzo Doria	10/2015
2707	2^576889+49727	173661	Enzo Doria	09/2016
2708	(167*10^173571-17)/3	173573	Robert Price	03/2020
2709	37803^37916+37916^37803	173562	Norbert Schneider	06/2022
2710	5*10^173534+29	173535	Robert Price	12/2020
2711	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
2712	4*10^173509+99	173510	Robert Price	12/2020
2713	(13*10^173467-37)/3	173468	Robert Price	01/2019
2714	2^576016-113919	173399	Enzo Doria	11/2014
2715	2^575911-1849387	173367	Enzo Doria	08/2015
2716	2^575879+215843	173357	Enzo Doria	11/2023
2717	2^575871+28733	173355	Enzo Doria	01/2024
2718	515^63898+63898^515	173280	Norbert Schneider	12/2022
2719	2^575614+9	173278	Stefano Morozzi	04/2021
2720	2^575606-219533	173275	Enzo Doria	03/2024
2721	(16*10^173251+107)/3	173252	Robert Price	03/2019
2722	26618^39149-39149^26618	173242	Frank Doornink	03/2024
2723	2^575196-114053	173152	Enzo Doria	11/2014
2724	7*10^173135-53	173136	Robert Price	06/2020
2725	(301*10^173047+23)/9	173049	Robert Price	06/2021
2726	2^574591-115387	172970	Enzo Doria	07/2015
2727	25210^39297-39297^25210	172969	Frank Doornink	12/2023
2728	(202*10^172940-13)/9	172942	Robert Price	01/2020
2729	45^104608+104608^45	172940	Norbert Schneider	06/2021
2730	2^574328+81121	172890	Enzo Doria	07/2016
2731	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
2732	3*10^172812+13	172813	Robert Price	07/2018
2733	4*5^247217-9	172798	Lelio R Paula	10/2015
2734	6*10^172772-31	172773	Robert Price	07/2020
2735	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
2736	(34*10^172693-547)/9	172694	Robert Price	03/2021
2737	5*10^172692+57	172693	Robert Price	12/2018
2738	2^573668-2782319	172692	Enzo Doria	09/2015
2739	2^573444-1855109	172624	Enzo Doria	09/2015
2740	25500^39173-39173^25500	172618	Frank Doornink	02/2024
2741	27180^38917-38917^27180	172568	Frank Doornink	01/2024
2742	(14*10^172532-29)/3	172533	Robert Price	09/2021
2743	3^361608+2	172531	Robert Price	08/2014
2744	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
2745	2^572592-114893	172368	Enzo Doria	05/2015
2746	4*10^172354-39	172355	Robert Price	09/2020
2747	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
2748	(11*10^172322-119)/9	172323	Robert Price	11/2021
2749	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
2750	(38^109037-1)/37	172254	Paul Bourdelais	10/2017

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