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 ?
2251	(47^140983-1)/2792206142311142462	235719	Paul Vanderveen	06/2025
2252	2^782821+37577	235653	Enzo Doria	10/2024
2253	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
2254	2^782634-113981	235597	Enzo Doria	11/2014
2255	2^782423+1879733	235533	Enzo Doria	09/2016
2256	(10^(2117707+1)+1210^117707-1)/3	235415	Robert Price	10/2023
2257	(2^781970)/(781970^2)	235385	Henri Lifchitz	06/2025
2258	2^781682-2789543	235310	Enzo Doria	12/2015
2259	2^780481+21489	234949	Enzo Doria	05/2024
2260	2^780408-113453	234927	Enzo Doria	08/2014
2261	7*10^234915+9	234916	Robert Price	04/2023
2262	2^780368-1864829	234915	Enzo Doria	01/2016
2263	2^780284+7	234889	Jon Grantham	08/2023
2264	2^779593-1836559	234681	Enzo Doria	05/2015
2265	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
2266	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
2267	2^778788+22201	234439	Enzo Doria	09/2023
2268	2^778395-113617	234321	Enzo Doria	08/2014
2269	5*2^778090+3	234230	Jon Grantham	07/2023
2270	(21430^54289-1)/(21430^233-1)	234118	Ryan Propper	11/2023
2271	(5*10^234054-101)/3	234055	Robert Price	08/2023
2272	23*10^234025-7	234027	Robert Price	10/2022
2273	2^777170+21489	233952	Enzo Doria	05/2024
2274	Phi(78125,5517)	233857	Anonymous	09/2022
2275	5^334359-3^334359-1	233707	Jon Grantham	08/2023
2276	2^776245-2792353	233674	Enzo Doria	02/2016
2277	49748^49748+49735^49735	233656	Henri Lifchitz	11/2024
2278	2^776060-114029	233618	Enzo Doria	11/2014
2279	2^775987-2789557	233596	Enzo Doria	12/2015
2280	2*10^233564-91	233565	Robert Price	02/2023
2281	2^775865+21489	233559	Enzo Doria	05/2024
2282	2^775672+1866721	233501	Enzo Doria	03/2016
2283	2^775238+57	233370	Stefano Morozzi	05/2021
2284	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
2285	U(1302049)	233238	Serge Batalov	07/2024
2286	2^774118+1885789	233033	Enzo Doria	04/2017
2287	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
2288	2^773723+217523	232914	Enzo Doria	01/2024
2289	2^773679-113425	232901	Enzo Doria	08/2014
2290	11*17^189085+232	232661	Eric Chen	01/2026
2291	(7*10^232620+23)/3	232621	Robert Price	05/2023
2292	10^232599+192489	232600	Patrick De Geest	12/2013
2293	10^232599-3	232599	Markus Tervooren	10/2010
2294	2^772552-458879	232562	Enzo Doria	04/2015
2295	2^772214+1874899	232460	Enzo Doria	06/2016
2296	2^771994-1862771	232394	Enzo Doria	12/2015
2297	2^771889+1876037	232362	Enzo Doria	07/2016
2298	2^771660+1866511	232293	Enzo Doria	02/2016
2299	5^332150-18188	232163	Enzo Doria	06/2014
2300	2^771227+61121	232163	Boyan Hu	05/2024
2301	2^770623+212543	231981	Enzo Doria	09/2023
2302	3^485977-2^485977	231870	Mike Oakes	09/2009
2303	2^770082-114161	231818	Enzo Doria	01/2015
2304	2^769791+25523	231731	Enzo Doria	11/2023
2305	7^274120-2	231659	Paul Bourdelais	08/2023
2306	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
2307	2^769011+81	231496	Henri Lifchitz	01/2025
2308	(71^125029-1)/105024430	231453	Paul Vanderveen	06/2025
2309	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
2310	2^768205+22217	231253	Enzo Doria	09/2023
2311	8^256065+256065	231250	Anonymous	08/2026
2312	49262^49262-49247^49247	231163	Henri Lifchitz	11/2024
2313	2^767622-9221	231078	Lelio R Paula	01/2016
2314	2^767344+1880311	230994	Enzo Doria	09/2016
2315	8*10^230921-13	230922	Robert Price	08/2023
2316	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
2317	(10^230706+179)/9	230706	Serge Batalov	12/2014
2318	2^766309+1875257	230682	Enzo Doria	06/2016
2319	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
2320	2^765635+1879883	230480	Enzo Doria	09/2016
2321	43^141090+141090	230467	Kellen Shenton	06/2023
2322	(26*10^230394-119)/3	230395	Robert Price	07/2023
2323	2^764348-113697	230092	Enzo Doria	09/2014
2324	2^764131+78863	230027	Enzo Doria	05/2016
2325	2^763701+60197	229897	Enzo Doria	03/2016
2326	4*10^229836+21	229837	Robert Price	12/2022
2327	2^763362+27799	229795	Enzo Doria	01/2024
2328	2^762841-25905	229639	Enzo Doria	10/2013
2329	2^762659+212633	229584	Enzo Doria	09/2023
2330	77*10^229211+3	229213	Robert Price	11/2023
2331	2^761117-113569	229120	Enzo Doria	08/2014
2332	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
2333	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
2334	5*3^479067-2^479067	228574	Jon Grantham	08/2023
2335	2^758645+216011	228375	Enzo Doria	12/2023
2336	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
2337	10^228208+111	228209	Boyan Hu	10/2024
2338	(298*10^228177-7)/3	228179	Robert Price	02/2023
2339	2^757985-2790013	228177	Enzo Doria	12/2015
2340	34*10^228129-9	228131	Robert Price	05/2023
2341	2^757038-1862081	227892	Enzo Doria	12/2015
2342	2^756839+95849	227832	Makoto Morimoto	10/2013
2344	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
2343	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
2345	2^756773-112723	227812	Enzo Doria	07/2014
2346	(710^(2113887+1)+9*10^113887-7)/9	227775	Robert Price	08/2024
2347	729^79563+728	227768	Alfred Reich	04/2026
2348	(10^227542)/(227542^10)	227489	Henri Lifchitz	05/2025
2349	524309#+616367	227431	Makoto Morimoto	02/2016
2350	2^755404+226575	227400	Enzo Doria	09/2024
2351	2^755116+81	227313	Henri Lifchitz	11/2024
2352	2^755097-114193	227307	Enzo Doria	12/2014
2353	7*10^227178+39	227179	Robert Price	01/2023
2354	9*10^227153-89	227154	Robert Price	02/2023
2355	2^754473-2791513	227120	Enzo Doria	01/2016
2356	2^754376+25	227090	Stefano Morozzi	05/2021
2357	2^754138+213289	227019	Enzo Doria	09/2023
2358	2^754038+25	226989	Stefano Morozzi	05/2021
2359	2^753263+217133	226755	Enzo Doria	12/2023
2360	7*10^226479-9	226480	Robert Price	02/2023
2361	(10^226381+1)/14973418875371	226368	Alfred Reich	06/2025
2362	2^751655+33893	226271	Enzo Doria	06/2024
2363	2^751426-764321	226202	Enzo Doria	12/2013
2364	(18^180181-1)/17	226176	Andy Steward	04/2007
2365	2^750740-3	225996	Paul Bourdelais	03/2012
2366	2^750725+60227	225991	Enzo Doria	02/2016
2367	2^750525-113743	225931	Enzo Doria	09/2014
2368	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
2369	2^749444-1861889	225606	Enzo Doria	12/2015
2370	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
2371	(3^472721+1)/9422189991086734893916	225524	Paul Vanderveen	06/2025
2372	2^749096+1876861	225501	Enzo Doria	07/2016
2373	2^748895+26213	225440	Enzo Doria	12/2023
2374	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
2375	2^748657+79607	225369	Enzo Doria	06/2016
2376	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
2377	2^746653-291583	224765	Enzo Doria	07/2015
2378	2^746461-114043	224708	Enzo Doria	11/2014
2379	2^746302+25	224660	Stefano Morozzi	05/2021
2380	(202*10^224545-1)/3	224547	Robert Price	06/2023
2381	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
2382	2^745674+213949	224471	Enzo Doria	10/2023
2383	2^745098-350471	224297	Enzo Doria	06/2015
2384	2^745039-4897	224280	Yves Minet	03/2021
2385	23*10^224232-7	224234	Robert Price	10/2022
2386	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
2387	2^744211-1845787	224030	Enzo Doria	07/2015
2388	2^743773+37757	223898	Enzo Doria	10/2024
2389	2^743592-134579	223844	Hans Havermann	10/2018
2390	2^742452+3	223501	Paul Bourdelais	06/2019
2391	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
2392	47747^47747-2512^2512	223406	Henri Lifchitz	10/2024
2393	2^741651-461197	223260	Enzo Doria	07/2015
2394	10^223236-1001	223236	Robert Price	10/2022
2395	2^741362-1845251	223173	Enzo Doria	07/2015
2396	3^467546-5*2^467546	223077	Jon Grantham	08/2023
2397	2^740455-1863877	222900	Enzo Doria	12/2015
2398	2^740274+217519	222845	Enzo Doria	01/2024
2399	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
2400	2^739636-2792219	222653	Enzo Doria	02/2016
2401	11^213654-180	222498	Enzo Doria	01/2013
2402	2^738957-1859743	222449	Enzo Doria	11/2015
2403	4*10^222253-21	222254	Robert Price	12/2022
2404	2^737825+57	222108	Stefano Morozzi	05/2021
2405	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
2406	3^232689+1^232689+4^232689+1^232689+5^232689+9^232689	222042	Henri Lifchitz	03/2025
2407	2^737166+220099	221910	Enzo Doria	03/2024
2408	394^85431+393	221736	Alfred Reich	03/2026
2409	(10^221654+179)/9	221654	Serge Batalov	12/2014
2410	2^736281+79817	221643	Enzo Doria	06/2016
2411	10^221631+247617	221632	Patrick De Geest	10/2013
2412	10^221631-9	221631	Alexander Gramolin	02/2011
2413	10^221628+7	221629	Alfred Reich	04/2021
2414	2^735970-1839821	221550	Enzo Doria	06/2015
2415	2^735367+60293	221368	Enzo Doria	03/2016
2416	77*10^221343+3	221345	Robert Price	11/2023
2417	299^299^299-582	221328	Henri Lifchitz	03/2025
2418	(241^92821-1)/240	221099	Anonymous	04/2024
2419	(202*10^221092-1)/3	221094	Robert Price	06/2023
2420	(5^316297-1)/220142716	221074	Paul Vanderveen	05/2025
2421	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
2422	2^734228+24751	221025	Enzo Doria	10/2023
2423	(28*10^220800+173)/3	220801	Robert Price	07/2024
2424	2^733264-2784089	220735	Enzo Doria	10/2015
2425	2^733114-24555	220690	Enzo Doria	09/2013
2426	2^731891-636259	220322	Enzo Doria	12/2013
2427	98*10^220185-9	220187	Robert Price	05/2023
2428	418319^39164+418318	220161	Alfred Reich	11/2023
2429	2^4^182829+182829^4^2	220149	Henri Lifchitz	03/2025
2430	2^731124-25539	220091	Enzo Doria	09/2013
2431	2^730972-462029	220045	Enzo Doria	07/2015
2432	2^730833+1868627	220003	Enzo Doria	04/2016
2433	2^730645-2787133	219947	Enzo Doria	11/2015
2434	2^730547-25581	219917	Enzo Doria	09/2013
2435	(113*13^197420-5)/12	219916	Anonymous	11/2022
2436	(13^197420*113-5)/12	219916	Eric Chen	10/2023
2437	2^730460+82291	219891	Enzo Doria	09/2016
2438	(5*10^219847-101)/3	219848	Robert Price	08/2023
2439	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
2440	L(1051849)	219824	Renaud Lifchitz	03/2009
2441	3*2^730149+5	219798	Jon Grantham	07/2023
2442	8*10^219740-3	219741	Serge Batalov	01/2023
2443	11^210961-240	219694	Enzo Doria	01/2013
2444	(26*10^219639-77)/3	219640	Robert Price	03/2023
2445	2^729611-113437	219635	Enzo Doria	08/2014
2446	7^259710-2	219481	Paul Bourdelais	01/2021
2447	F(1049897)	219416	Henri Lifchitz	10/2008
2448	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
2449	2^728604+1879321	219332	Enzo Doria	10/2016
2450	33^144412+2	219292	Robert Price	04/2015
2451	2^728277-183313	219234	Hans Havermann	10/2018
2452	2^727998-1862711	219150	Enzo Doria	12/2015
2453	(29*10^219124+91)/3	219125	Robert Price	12/2022
2454	2^727729-114073	219069	Enzo Doria	12/2014
2455	2^727496-1851809	218999	Enzo Doria	08/2015
2456	2^727025+25907	218857	Enzo Doria	12/2023
2457	2^726591+2793143	218726	Enzo Doria	02/2016
2458	(7*10^218644+17)/3	218645	Robert Price	06/2023
2459	2^725534-2791931	218408	Enzo Doria	02/2016
2460	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
2461	2^722184+1877821	217400	Enzo Doria	08/2016
2462	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
2463	2^721721-4453	217260	Yves Minet	03/2021
2464	10^216950+49	216951	Robert Price	02/2023
2465	281*499979#/46410-2702372	216849	Robert Smith	08/2016
2466	281*499979#/46410+2400766	216849	Robert Smith	08/2016
2467	Phi(83733,-13#)	216643	Henri Lifchitz	02/2026
2468	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
2469	2^718756-114107	216368	Enzo Doria	12/2014
2470	2^717672+121	216041	Stefano Morozzi	05/2021
2471	2^717305+80327	215931	Enzo Doria	07/2016
2472	Phi(358640,2^5)	215875	Henri Lifchitz	12/2025
2473	2^717069-59773	215860	Enzo Doria	10/2015
2474	10^215802+33	215803	Robert Price	08/2023
2475	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
2476	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
2477	2^716428+215011	215667	Enzo Doria	11/2023
2478	(13*10^215592-43)/3	215593	Robert Price	08/2023
2479	p(41292)#+p(41292+1)	215450	Henri Lifchitz	11/2024
2480	(29^147319-1)/466757843690852	215425	Paul Vanderveen	06/2025
2481	227^91413-40	215372	Enzo Doria	04/2015
2482	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
2483	2^714717+782897	215152	Enzo Doria	11/2016
2484	(19^168013-1)/80910356454	214837	Paul Vanderveen	05/2025
2485	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
2486	2^713241+1879157	214707	Enzo Doria	08/2016
2487	(23*10^214633+91)/3	214634	Robert Price	03/2023
2488	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
2489	2^712801-69553	214575	Enzo Doria	01/2016
2490	2^712603-25357	214515	Enzo Doria	09/2013
2491	2^711721-1846723	214250	Enzo Doria	07/2015
2492	999^71336+998	213978	Alfred Reich	04/2026
2493	2^710730-396765	213952	Enzo Doria	09/2013
2494	(19*10^213934-37)/9	213935	Alfred Reich	12/2023
2495	(19*10^213730-37)/9	213731	Alfred Reich	12/2023
2496	(713^74897-1)/712	213685	Jinyuan Wang	08/2023
2497	2^709773+25907	213663	Enzo Doria	12/2023
2498	2^708468-114329	213271	Enzo Doria	02/2015
2499	2^708293+27557	213218	Enzo Doria	01/2024
2500	379*10^213199+9	213202	Jason Yuen	01/2025

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303412 PRPs in the top)