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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^610356-1849019	183736	Enzo Doria	08/2015
2502	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
2503	23*10^183710-7	183712	Robert Price	02/2020
2504	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
2505	(4*10^183659+149)/9	183659	Robert Price	04/2018
2506	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
2507	7*10^183596+39	183597	Robert Price	01/2023
2508	2^609846-1834251	183582	Enzo Doria	07/2015
2509	10^183546+1547323	183547	Patrick De Geest	02/2021
2511	10^183546-800000001	183546	Robert Price	09/2020
2510	10^183546-584297	183546	Patrick De Geest	02/2021
2512	7*10^183511+39	183512	Robert Price	01/2023
2513	(23*10^183477-71)/3	183478	Robert Price	07/2020
2514	11^176176-240	183469	Enzo Doria	11/2012
2515	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
2516	6*10^183429+53	183430	Robert Price	05/2020
2517	(28*10^183403+191)/3	183404	Robert Price	02/2020
2518	U(1096855)	183383	Serge Batalov	07/2024
2519	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
2520	2^608965-113989	183317	Enzo Doria	10/2014
2521	A005165(43592)	183312	Serge Batalov	07/2017
2522	(61*10^183294+119)/9	183295	Robert Price	05/2019
2523	2^608814-461261	183272	Enzo Doria	06/2015
2524	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
2525	2^608541-608541^2	183190	Henri Lifchitz	02/2018
2526	2^608293+143807	183115	Enzo Doria	10/2016
2527	2^608164-462419	183076	Enzo Doria	08/2015
2528	2^607950-1862303	183012	Enzo Doria	12/2015
2529	5*3^383376+2^383376	182918	Jon Grantham	08/2023
2530	(46*10^182896+683)/9	182897	Robert Price	03/2019
2531	(2*10^182787+73)/3	182787	Robert Price	09/2020
2532	2^607101+1871987	182756	Enzo Doria	05/2016
2533	2^606869-69175	182686	Enzo Doria	11/2015
2534	8*10^182671+71	182672	Robert Price	05/2022
2535	(23*10^182666-71)/3	182667	Robert Price	07/2020
2536	3*10^182614-11	182615	Robert Price	07/2018
2537	2^606560-357	182593	Enzo Doria	05/2014
2538	66*10^182420+7	182422	Robert Price	07/2020
2539	2^605687+1866983	182330	Enzo Doria	03/2016
2540	2^605655-114445	182321	Enzo Doria	02/2015
2541	94*10^182291-3	182293	Robert Price	05/2020
2542	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
2543	(14*10^182177-221)/9	182178	Robert Price	04/2018
2544	2^605174-112751	182176	Enzo Doria	06/2014
2545	(905^61609-1)/904	182154	Anonymous	05/2024
2546	2^604761+1874507	182052	Enzo Doria	06/2016
2547	2^604705+1871957	182035	Enzo Doria	05/2016
2548	(14*10^182000+229)/9	182001	Robert Price	03/2018
2549	(10^181996+41)/3	181996	Robert Price	12/2017
2550	(17*10^181979+91)/9	181980	Robert Price	02/2022
2551	(5*10^181950-101)/3	181951	Robert Price	04/2018
2552	2^603915+75233	181797	Enzo Doria	04/2016
2553	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
2554	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
2555	7*10^181594-57	181595	Robert Price	06/2020
2556	8*10^181580+29	181581	Robert Price	11/2021
2557	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
2558	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
2559	3*10^181445+23	181446	Robert Price	03/2022
2560	(194*10^181369-11)/3	181371	Robert Price	09/2020
2561	11^174145-360	181354	Enzo Doria	10/2012
2562	2^602351-396765	181326	Enzo Doria	08/2013
2563	6*10^181306+17	181307	Robert Price	04/2019
2564	(353^71143-1)/352	181254	Anonymous	04/2024
2565	(286*10^181220-1)/3	181222	Robert Price	11/2020
2566	2^601957-113833	181208	Enzo Doria	09/2014
2567	66^99581-65^99581	181193	Robert Price	09/2013
2568	10^181182+383973	181183	Patrick De Geest	04/2016
2569	10^181182-21	181182	Serge Batalov	12/2014
2570	(797*10^181171-41)/9	181173	Robert Price	04/2022
2571	2^601722+74209	181137	Enzo Doria	08/2023
2572	(5*10^181127-29)/3	181128	Robert Price	03/2018
2573	2^601521-29143	181076	Enzo Doria	07/2015
2574	2^601442-2797811	181053	Enzo Doria	04/2016
2575	44*10^181029+3	181031	Robert Price	04/2020
2576	5*10^180992-9	180993	Robert Price	05/2015
2577	10^180979+79477	180980	Patrick De Geest	04/2016
2578	10^180979+107739	180980	Patrick De Geest	04/2016
2579	10^180979-11	180979	Serge Batalov	12/2014
2580	2^601023-113851	180926	Enzo Doria	10/2014
2581	(23*10^180862-143)/3	180863	Robert Price	12/2019
2582	3*10^180852+29	180853	Robert Price	05/2018
2583	(277*10^180782-7)/9	180784	Robert Price	02/2022
2584	2^600412+29851	180743	Enzo Doria	03/2024
2585	(8*10^180725-629)/9	180725	Robert Price	01/2022
2586	(79*10^180710-1)/3	180712	Robert Price	02/2020
2587	2^600300-1852559	180709	Enzo Doria	08/2015
2588	(2*10^180706-77)/3	180706	Robert Price	02/2021
2589	(156^82393-1)/155	180696	Anonymous	06/2024
2590	(10^180689+71)/9	180689	Serge Batalov	07/2015
2591	2^600209+76487	180681	Enzo Doria	05/2016
2592	2^599999+378461	180618	Norman Luhn	09/2023
2593	(8*10^180536-269)/9	180536	Robert Price	09/2021
2594	2^599702-369885	180529	Enzo Doria	11/2013
2595	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
2596	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
2597	(29*10^180432-17)/3	180433	Robert Price	09/2019
2598	4*10^180360+93	180361	Robert Price	08/2018
2599	2^599035+219323	180328	Enzo Doria	03/2024
2600	2^598942+80779	180300	Enzo Doria	07/2016
2601	(38*10^180296+403)/9	180297	Robert Price	10/2018
2602	(85*10^180241+77)/9	180242	Robert Price	07/2022
2603	2^598591-1844797	180194	Enzo Doria	06/2015
2604	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
2605	2^598301+28517	180107	Enzo Doria	01/2024
2606	(29*10^180072+691)/9	180073	Robert Price	08/2021
2607	(59*10^180038+157)/9	180039	Robert Price	12/2021
2608	95*10^180019-9	180021	Robert Price	01/2022
2609	6*10^179970+91	179971	Robert Price	05/2019
2610	(4*10^179963-79)/3	179964	Robert Price	02/2018
2611	(403*10^179944-43)/9	179946	Robert Price	06/2021
2612	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
2613	2^597424-1859729	179843	Enzo Doria	11/2015
2614	Phi(180683,10)	179760	Maksym Voznyy	09/2015
2615	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
2616	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
2617	(29*10^179697+223)/9	179698	Robert Price	09/2018
2618	U(1289697)	179687	Serge Batalov	07/2024
2620	2^596884+73	179680	Stefano Morozzi	04/2021
2619	(11*10^179679+13)/3	179680	Robert Price	03/2022
2621	(68*10^179656+7)/3	179658	Robert Price	01/2020
2622	(10^179643+173)/3	179643	Robert Price	05/2021
2623	2^596690-461261	179622	Enzo Doria	07/2015
2624	2^596684-113939	179620	Enzo Doria	10/2014
2625	2^596642+39	179608	Jon Grantham	08/2023
2626	2*10^179602+63	179603	Robert Price	05/2018
2627	32262^39815-39815^32262	179514	Frank Doornink	02/2024
2628	(25*10^179488-403)/9	179489	Robert Price	01/2021
2629	7*10^179460+99	179461	Robert Price	05/2021
2630	2^596127+74333	179453	Enzo Doria	07/2023
2631	3^375887-112696	179344	Enzo Doria	07/2014
2632	4*10^179265-71	179266	Robert Price	12/2018
2633	2*10^179193+83	179194	Robert Price	12/2021
2634	2^595144-1850429	179157	Enzo Doria	08/2015
2635	2^595122-5	179150	Stefano Morozzi	07/2022
2636	3*10^179138+89	179139	Robert Price	10/2018
2637	(52*10^179062-133)/9	179063	Robert Price	09/2021
2638	2^594531+82253	178972	Enzo Doria	09/2016
2639	(664*10^178939-61)/9	178941	Robert Price	09/2021
2640	2^594260-2787899	178891	Enzo Doria	11/2015
2641	(14*10^178822+67)/9	178823	Robert Price	05/2022
2642	(29*10^178732-119)/9	178733	Robert Price	12/2021
2643	2^593631+101381	178701	Jorge Menendez	04/2018
2644	10^178695+136719	178696	Patrick De Geest	05/2016
2645	10^178695-71	178695	Serge Batalov	12/2014
2646	(2*10^178649-161)/3	178649	Robert Price	12/2020
2647	(691^62903-1)/690	178609	Michael Stocker	05/2020
2648	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
2649	2^593242+28309	178584	Enzo Doria	01/2024
2650	2^593222-14145	178578	Jorge Menendez	10/2017
2651	7*10^178566+33	178567	Robert Price	06/2020
2652	2^593178+1867219	178565	Enzo Doria	03/2016
2653	2^593152+22441	178557	Enzo Doria	09/2023
2654	(38*10^178456+151)/9	178457	Robert Price	03/2022
2655	(302*10^178369+13)/9	178371	Robert Price	02/2020
2656	(26*10^178296-113)/3	178297	Robert Price	06/2020
2657	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
2658	(13*10^178233+137)/3	178234	Robert Price	06/2021
2659	(5*10^178206+91)/3	178207	Robert Price	04/2018
2660	2^591872-291929	178172	Enzo Doria	07/2015
2661	2^591682-286871	178115	Enzo Doria	07/2015
2662	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
2663	4*10^178091+9	178092	Robert Price	05/2015
2664	2^591435+335931	178040	Enzo Doria	09/2024
2665	410747#+478483	178007	Makoto Morimoto	02/2016
2666	3*10^177872+73	177873	Robert Price	08/2018
2667	2^590762-396765	177838	Enzo Doria	08/2013
2668	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
2669	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
2670	Smr(37765)	177719	Eric W. Weisstein	12/2021
2671	(266*10^177577-11)/3	177579	Robert Price	04/2020
2672	(11*10^177466-113)/3	177467	Robert Price	10/2018
2673	3*10^177373-97	177374	Robert Price	07/2018
2674	2^589204+1881151	177369	Enzo Doria	11/2016
2675	2^589132-69479	177347	Enzo Doria	01/2016
2676	(101*10^177302-17)/3	177304	Robert Price	02/2020
2677	2^588912-113519	177281	Enzo Doria	08/2014
2678	(682*10^177266-7)/9	177268	Robert Price	08/2021
2679	15^150706+2	177245	Robert Price	06/2015
2680	2^588403+335931	177127	Enzo Doria	09/2024
2681	(31208^39601-1)/(31208^199-1)	177084	Ryan Propper	11/2023
2682	2^588194-1861001	177065	Enzo Doria	11/2015
2683	5*10^177016-37	177017	Robert Price	11/2021
2684	fibonacci(846926)-4	176997	Jon Grantham	08/2023
2685	(23*10^176964-47)/3	176965	Robert Price	09/2019
2686	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
2687	(19*10^176932+521)/9	176933	Robert Price	05/2018
2688	(8*10^176908+43)/3	176909	Robert Price	06/2018
2689	(85*10^176900+203)/9	176901	Robert Price	09/2020
2690	2^587560-113699	176874	Enzo Doria	09/2014
2691	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
2692	(101*10^176815-17)/3	176817	Robert Price	02/2020
2693	(25*10^176715-37)/3	176716	Robert Price	10/2019
2694	5^252763-12862	176674	Enzo Doria	05/2014
2695	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
2696	2^586829+23961	176654	Enzo Doria	10/2023
2697	2^586804+81721	176646	Enzo Doria	08/2016
2698	(10^176584+77)/3	176584	Robert Price	01/2018
2699	2^586570+1874419	176576	Enzo Doria	06/2016
2700	(157*10^176482-1)/3	176484	Robert Price	01/2022
2701	5*2^586202+3	176466	Jon Grantham	07/2023
2702	27122^39799-39799^27122	176442	Frank Doornink	01/2024
2703	2^585994-3311	176402	Yves Minet	12/2014
2704	8*10^176383-81	176384	Robert Price	02/2021
2705	(23*10^176357+61)/3	176358	Robert Price	01/2022
2706	2^585832-112799	176354	Enzo Doria	07/2014
2707	fibonacci(843383)+4	176257	Jon Grantham	08/2023
2708	(29*10^176240+49)/3	176241	Robert Price	09/2021
2709	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
2710	2^585336-461039	176204	Enzo Doria	06/2015
2711	(25*10^176164+143)/3	176165	Robert Price	08/2020
2712	2^585095-1848127	176132	Enzo Doria	08/2015
2713	(5*10^176101-311)/9	176101	Robert Price	12/2021
2714	6*10^176092+77	176093	Robert Price	06/2020
2715	2^584950-115451	176088	Enzo Doria	07/2015
2716	(646*10^176044+11)/9	176046	Robert Price	10/2021
2717	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
2718	2^584671-3697	176004	Yves Minet	03/2017
2719	(13*10^175965-37)/3	175966	Robert Price	01/2019
2720	31728^39089-39089^31728	175957	Frank Doornink	01/2024
2721	2*10^175860-87	175861	Robert Price	04/2018
2722	27009^39670-39670^27009	175798	Frank Doornink	01/2024
2723	(86*10^175774-221)/9	175775	Robert Price	09/2019
2724	2^583614+216037	175686	Enzo Doria	11/2023
2725	9*10^175654+47	175655	Robert Price	01/2022
2726	25430^39869-39869^25430	175637	Frank Doornink	01/2024
2727	10^175608+2971	175609	Mike Oakes	05/2010
2728	10^175608-55829	175608	Patrick De Geest	09/2013
2729	2^583051+1879793	175516	Enzo Doria	09/2016
2730	(76*10^175514+491)/9	175515	Robert Price	10/2021
2732	2^582860-23829	175459	Enzo Doria	08/2013
2731	(200^76253-1)/199	175459	Anonymous	06/2024
2733	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
2734	(28*10^175417-67)/3	175418	Robert Price	10/2020
2735	2^582670-23913	175402	Enzo Doria	08/2013
2736	2^582573-29563	175372	Enzo Doria	08/2015
2737	2^582435-1862767	175331	Enzo Doria	12/2015
2738	10^175295-40000001	175295	Robert Price	07/2022
2739	31093^39018-39018^31093	175295	Frank Doornink	01/2024
2740	(11*10^175250-149)/3	175251	Robert Price	09/2018
2741	(29*10^175236+31)/3	175237	Robert Price	04/2021
2742	2^582072-1848599	175222	Enzo Doria	08/2015
2743	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
2744	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
2745	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
2746	(5*10^175117-311)/9	175117	Robert Price	12/2021
2747	31193^38966-38966^31193	175116	Frank Doornink	01/2024
2748	2^581695+225893	175108	Enzo Doria	08/2024
2749	10^175093-89	175093	Riley Fisher	10/2023
2750	(220221^32768+1)/2	175075	Serge Batalov	03/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(300560 PRPs in the top)