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	2*10^179193+83	179194	Robert Price	12/2021
2502	2^595144-1850429	179157	Enzo Doria	08/2015
2503	2^595122-5	179150	Stefano Morozzi	07/2022
2504	3*10^179138+89	179139	Robert Price	10/2018
2505	(52*10^179062-133)/9	179063	Robert Price	09/2021
2506	2^594531+82253	178972	Enzo Doria	09/2016
2507	(664*10^178939-61)/9	178941	Robert Price	09/2021
2508	2^594260-2787899	178891	Enzo Doria	11/2015
2509	(14*10^178822+67)/9	178823	Robert Price	05/2022
2510	(29*10^178732-119)/9	178733	Robert Price	12/2021
2511	2^593631+101381	178701	Jorge Menendez	04/2018
2512	10^178695+136719	178696	Patrick De Geest	05/2016
2513	10^178695-71	178695	Serge Batalov	12/2014
2514	(2*10^178649-161)/3	178649	Robert Price	12/2020
2515	(691^62903-1)/690	178609	Michael Stocker	05/2020
2516	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
2517	2^593242+28309	178584	Enzo Doria	01/2024
2518	2^593222-14145	178578	Jorge Menendez	10/2017
2519	7*10^178566+33	178567	Robert Price	06/2020
2520	2^593178+1867219	178565	Enzo Doria	03/2016
2521	2^593152+22441	178557	Enzo Doria	09/2023
2522	(38*10^178456+151)/9	178457	Robert Price	03/2022
2523	(302*10^178369+13)/9	178371	Robert Price	02/2020
2524	(26*10^178296-113)/3	178297	Robert Price	06/2020
2525	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
2526	(13*10^178233+137)/3	178234	Robert Price	06/2021
2527	(5*10^178206+91)/3	178207	Robert Price	04/2018
2528	2^591872-291929	178172	Enzo Doria	07/2015
2529	2^591682-286871	178115	Enzo Doria	07/2015
2530	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
2531	4*10^178091+9	178092	Robert Price	05/2015
2532	410747#+478483	178007	Makoto Morimoto	02/2016
2533	3*10^177872+73	177873	Robert Price	08/2018
2534	2^590762-396765	177838	Enzo Doria	08/2013
2535	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
2536	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
2537	Smr(37765)	177719	Eric W. Weisstein	12/2021
2538	(266*10^177577-11)/3	177579	Robert Price	04/2020
2539	(11*10^177466-113)/3	177467	Robert Price	10/2018
2540	3*10^177373-97	177374	Robert Price	07/2018
2541	2^589204+1881151	177369	Enzo Doria	11/2016
2542	2^589132-69479	177347	Enzo Doria	01/2016
2543	(101*10^177302-17)/3	177304	Robert Price	02/2020
2544	2^588912-113519	177281	Enzo Doria	08/2014
2545	(682*10^177266-7)/9	177268	Robert Price	08/2021
2546	15^150706+2	177245	Robert Price	06/2015
2547	(31208^39601-1)/(31208^199-1)	177084	Ryan Propper	11/2023
2548	2^588194-1861001	177065	Enzo Doria	11/2015
2549	5*10^177016-37	177017	Robert Price	11/2021
2550	fibonacci(846926)-4	176997	Jon Grantham	08/2023
2551	(23*10^176964-47)/3	176965	Robert Price	09/2019
2552	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
2553	(19*10^176932+521)/9	176933	Robert Price	05/2018
2554	(8*10^176908+43)/3	176909	Robert Price	06/2018
2555	(85*10^176900+203)/9	176901	Robert Price	09/2020
2556	2^587560-113699	176874	Enzo Doria	09/2014
2557	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
2558	(101*10^176815-17)/3	176817	Robert Price	02/2020
2559	(25*10^176715-37)/3	176716	Robert Price	10/2019
2560	5^252763-12862	176674	Enzo Doria	05/2014
2561	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
2562	2^586829+23961	176654	Enzo Doria	10/2023
2563	2^586804+81721	176646	Enzo Doria	08/2016
2564	(10^176584+77)/3	176584	Robert Price	01/2018
2565	2^586570+1874419	176576	Enzo Doria	06/2016
2566	(157*10^176482-1)/3	176484	Robert Price	01/2022
2567	5*2^586202+3	176466	Jon Grantham	07/2023
2568	27122^39799-39799^27122	176442	Frank Doornink	01/2024
2569	2^585994-3311	176402	Yves Minet	12/2014
2570	8*10^176383-81	176384	Robert Price	02/2021
2571	(23*10^176357+61)/3	176358	Robert Price	01/2022
2572	2^585832-112799	176354	Enzo Doria	07/2014
2573	fibonacci(843383)+4	176257	Jon Grantham	08/2023
2574	(29*10^176240+49)/3	176241	Robert Price	09/2021
2575	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
2576	2^585336-461039	176204	Enzo Doria	06/2015
2577	(25*10^176164+143)/3	176165	Robert Price	08/2020
2578	2^585095-1848127	176132	Enzo Doria	08/2015
2579	(5*10^176101-311)/9	176101	Robert Price	12/2021
2580	6*10^176092+77	176093	Robert Price	06/2020
2581	2^584950-115451	176088	Enzo Doria	07/2015
2582	(646*10^176044+11)/9	176046	Robert Price	10/2021
2583	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
2584	2^584671-3697	176004	Yves Minet	03/2017
2585	(13*10^175965-37)/3	175966	Robert Price	01/2019
2586	31728^39089-39089^31728	175957	Frank Doornink	01/2024
2587	2*10^175860-87	175861	Robert Price	04/2018
2588	27009^39670-39670^27009	175798	Frank Doornink	01/2024
2589	(86*10^175774-221)/9	175775	Robert Price	09/2019
2590	2^583614+216037	175686	Enzo Doria	11/2023
2591	9*10^175654+47	175655	Robert Price	01/2022
2592	25430^39869-39869^25430	175637	Frank Doornink	01/2024
2593	10^175608+2971	175609	Mike Oakes	05/2010
2594	10^175608-55829	175608	Patrick De Geest	09/2013
2595	2^583051+1879793	175516	Enzo Doria	09/2016
2596	(76*10^175514+491)/9	175515	Robert Price	10/2021
2598	2^582860-23829	175459	Enzo Doria	08/2013
2597	(200^76253-1)/199	175459	Anonymous	06/2024
2599	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
2600	(28*10^175417-67)/3	175418	Robert Price	10/2020
2601	2^582670-23913	175402	Enzo Doria	08/2013
2602	2^582573-29563	175372	Enzo Doria	08/2015
2603	2^582435-1862767	175331	Enzo Doria	12/2015
2604	10^175295-40000001	175295	Robert Price	07/2022
2605	31093^39018-39018^31093	175295	Frank Doornink	01/2024
2606	(11*10^175250-149)/3	175251	Robert Price	09/2018
2607	(29*10^175236+31)/3	175237	Robert Price	04/2021
2608	2^582072-1848599	175222	Enzo Doria	08/2015
2609	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
2610	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
2611	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
2612	(5*10^175117-311)/9	175117	Robert Price	12/2021
2613	31193^38966-38966^31193	175116	Frank Doornink	01/2024
2614	10^175093-89	175093	Riley Fisher	10/2023
2615	(220221^32768+1)/2	175075	Serge Batalov	03/2018
2616	2^581560+1874911	175068	Enzo Doria	06/2016
2617	(25*10^174987-97)/9	174988	Robert Price	01/2022
2618	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
2619	26446^39555-39555^26446	174927	Frank Doornink	03/2024
2620	31522^38883-38883^31522	174920	Frank Doornink	01/2024
2621	(27398^39601-1)/(27398^199-1)	174855	Ryan Propper	11/2023
2622	(861^59557-1)/860	174798	Jinyuan Wang	11/2023
2623	31492^38859-38859^31492	174796	Frank Doornink	01/2024
2624	(47*10^174790+493)/9	174791	Robert Price	03/2019
2625	2^580528-114035	174757	Enzo Doria	11/2014
2626	(19*10^174754+737)/9	174755	Robert Price	07/2018
2627	(35*10^174704-377)/9	174705	Robert Price	07/2018
2629	(49*10^174681+293)/9	174682	Robert Price	03/2021
2628	6*10^174681+11	174682	Robert Price	07/2022
2630	3*10^174665-97	174666	Robert Price	07/2018
2631	2^580046-459161	174612	Enzo Doria	05/2015
2632	2^579992-39779	174595	Enzo Doria	09/2015
2633	25613^39582-39582^25613	174496	Frank Doornink	02/2024
2634	(29*10^174481-149)/3	174482	Robert Price	08/2022
2635	(4*10^174423+101)/3	174424	Robert Price	11/2021
2636	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
2637	(2*10^174301-71)/3	174301	Robert Price	12/2017
2638	14^152048+3	174267	Paul Bourdelais	12/2020
2639	(2^578696+1)/257	174203	Lelio R Paula	09/2015
2640	2^578656-1851809	174193	Enzo Doria	08/2015
2641	2^578583-113917	174171	Enzo Doria	10/2014
2642	2^578434-83	174126	Yves Minet	07/2017
2643	15^148048-2	174118	Robert Price	06/2015
2644	5*10^174101+81	174102	Robert Price	03/2019
2645	2^578346+2794249	174100	Enzo Doria	03/2016
2646	10^173947+1372429	173948	Patrick De Geest	08/2021
2648	10^173947-500000001	173947	Robert Price	12/2020
2647	10^173947-286391	173947	Patrick De Geest	08/2021
2649	5*10^173904-13	173905	Robert Price	01/2019
2650	(8*10^173862-59)/3	173863	Robert Price	08/2021
2651	(71*10^173854-287)/9	173855	Robert Price	09/2019
2652	(43*10^173826+101)/9	173827	Robert Price	11/2018
2653	2*10^173809-87	173810	Robert Price	04/2018
2654	(2^577372-23)/7	173806	Stefano Morozzi	08/2022
2655	(L!41532)/2	173772	Serge Batalov	07/2017
2656	2^577146-49877	173739	Enzo Doria	10/2015
2657	2^576889+49727	173661	Enzo Doria	09/2016
2658	(167*10^173571-17)/3	173573	Robert Price	03/2020
2659	37803^37916+37916^37803	173562	Norbert Schneider	06/2022
2660	5*10^173534+29	173535	Robert Price	12/2020
2661	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
2662	4*10^173509+99	173510	Robert Price	12/2020
2663	(13*10^173467-37)/3	173468	Robert Price	01/2019
2664	2^576016-113919	173399	Enzo Doria	11/2014
2665	2^575911-1849387	173367	Enzo Doria	08/2015
2666	2^575879+215843	173357	Enzo Doria	11/2023
2667	2^575871+28733	173355	Enzo Doria	01/2024
2668	515^63898+63898^515	173280	Norbert Schneider	12/2022
2669	2^575614+9	173278	Stefano Morozzi	04/2021
2670	2^575606-219533	173275	Enzo Doria	03/2024
2671	(16*10^173251+107)/3	173252	Robert Price	03/2019
2672	26618^39149-39149^26618	173242	Frank Doornink	03/2024
2673	2^575196-114053	173152	Enzo Doria	11/2014
2674	7*10^173135-53	173136	Robert Price	06/2020
2675	(301*10^173047+23)/9	173049	Robert Price	06/2021
2676	2^574591-115387	172970	Enzo Doria	07/2015
2677	25210^39297-39297^25210	172969	Frank Doornink	12/2023
2678	(202*10^172940-13)/9	172942	Robert Price	01/2020
2679	45^104608+104608^45	172940	Norbert Schneider	06/2021
2680	2^574328+81121	172890	Enzo Doria	07/2016
2681	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
2682	3*10^172812+13	172813	Robert Price	07/2018
2683	4*5^247217-9	172798	Lelio R Paula	10/2015
2684	6*10^172772-31	172773	Robert Price	07/2020
2685	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
2686	(34*10^172693-547)/9	172694	Robert Price	03/2021
2687	5*10^172692+57	172693	Robert Price	12/2018
2688	2^573668-2782319	172692	Enzo Doria	09/2015
2689	2^573444-1855109	172624	Enzo Doria	09/2015
2690	25500^39173-39173^25500	172618	Frank Doornink	02/2024
2691	27180^38917-38917^27180	172568	Frank Doornink	01/2024
2692	(14*10^172532-29)/3	172533	Robert Price	09/2021
2693	3^361608+2	172531	Robert Price	08/2014
2694	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
2695	2^572592-114893	172368	Enzo Doria	05/2015
2696	4*10^172354-39	172355	Robert Price	09/2020
2697	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
2698	(11*10^172322-119)/9	172323	Robert Price	11/2021
2699	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
2700	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
2701	(4*10^172241+89)/3	172242	Robert Price	08/2021
2702	3*10^172219+73	172220	Robert Price	08/2018
2703	2^571810+28549	172132	Enzo Doria	01/2024
2704	A352736(15)	172032	Kellen Shenton	05/2022
2705	32298^38149-38149^32298	172021	Frank Doornink	02/2024
2706	2^571300+25861	171979	Enzo Doria	11/2023
2707	(36^110503+1)/37	171975	Lelio R Paula	04/2017
2708	8*10^171934+71	171935	Robert Price	05/2022
2709	(11*10^171933+601)/9	171934	Robert Price	02/2022
2710	(22*10^171929-73)/3	171930	Robert Price	04/2019
2711	(49*10^171892-319)/9	171893	Robert Price	10/2021
2712	4*10^171891-63	171892	Robert Price	10/2018
2713	67*10^171882-9	171884	Robert Price	03/2021
2714	2^570980-2782289	171883	Enzo Doria	09/2015
2715	(25*10^171849-37)/3	171850	Robert Price	10/2019
2716	10^171832+387909	171833	Patrick De Geest	08/2021
2717	10^171832-10001	171832	Robert Price	02/2021
2719	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
2718	(2^570769-9)/7	171818	Stefano Morozzi	08/2022
2720	(74*10^171651-29)/9	171652	Robert Price	06/2022
2721	(536*10^171601-23)/9	171603	Robert Price	02/2020
2722	7*10^171535-99	171536	Robert Price	06/2019
2723	(28*10^171534+101)/3	171535	Robert Price	09/2020
2724	2^569563-1854607	171456	Enzo Doria	09/2015
2725	32133^38042-38042^32133	171454	Frank Doornink	02/2024
2726	3*10^171391+59	171392	Robert Price	08/2018
2727	(13*10^171306-37)/3	171307	Robert Price	01/2019
2728	8*10^171296+87	171297	Robert Price	10/2019
2729	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
2730	(29*10^171275+67)/3	171276	Robert Price	12/2019
2731	(457*10^171248-7)/9	171250	Robert Price	09/2022
2732	(194*10^171193+1)/3	171195	Robert Price	01/2022
2733	2^568642+1876129	171179	Enzo Doria	07/2016
2734	4*10^171146-47	171147	Robert Price	10/2021
2735	(19*10^170970+131)/3	170971	Robert Price	06/2020
2736	(46*10^170932+143)/9	170933	Robert Price	01/2019
2737	(79*10^170901-1)/3	170903	Robert Price	02/2020
2738	(58*10^170842+221)/9	170843	Robert Price	02/2017
2739	(29*10^170830+583)/9	170831	Robert Price	06/2021
2740	3*10^170800+73	170801	Robert Price	08/2018
2741	(29*10^170799-119)/9	170800	Robert Price	12/2021
2742	11^164009-270	170798	Enzo Doria	10/2012
2743	2*10^170767+41	170768	Robert Price	05/2018
2744	3^357706-112358	170670	Enzo Doria	07/2014
2745	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
2746	2^566871+1876163	170646	Enzo Doria	07/2016
2747	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
2748	2^566496+7	170533	Donovan Johnson	07/2006
2749	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
2750	32150^37807-37807^32150	170403	Frank Doornink	02/2024

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