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	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
2252	(85*10^184768+77)/9	184769	Robert Price	07/2022
2253	2^613715-1860727	184747	Enzo Doria	11/2015
2254	(4*10^184730+89)/3	184731	Robert Price	08/2021
2255	2*10^184723+41	184724	Robert Price	05/2018
2256	(49*10^184703+293)/9	184704	Robert Price	03/2021
2257	2^613487-349987	184678	Enzo Doria	07/2015
2258	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
2259	14^161089-161089^14	184629	Serge Batalov	05/2016
2260	2^613033-114621	184542	Enzo Doria	05/2015
2261	3*2^612759+5	184460	Jon Grantham	07/2023
2262	2^612587+213413	184408	Enzo Doria	09/2023
2263	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
2264	2^612424+212341	184358	Enzo Doria	08/2023
2265	2^612341-1604809	184334	Enzo Doria	05/2015
2266	(11*10^184308-161)/3	184309	Robert Price	11/2021
2267	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
2268	(14*10^184150+37)/3	184151	Robert Price	12/2018
2269	2^611731-4837	184150	Yves Minet	08/2018
2270	3*10^184124-7	184125	Robert Price	08/2015
2271	2^611644+29371	184124	Enzo Doria	02/2024
2272	9*10^184122-11	184123	Mischa Rodermond	04/2023
2273	2^611628-24537	184119	Enzo Doria	08/2013
2274	3*10^184110+13	184111	Robert Price	07/2018
2275	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
2276	(194*10^184093+1)/3	184095	Robert Price	01/2022
2277	2^611460+71881	184068	Enzo Doria	04/2016
2278	4*10^184004-63	184005	Robert Price	10/2018
2279	2^610982-1867301	183924	Enzo Doria	03/2016
2280	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
2281	3*10^183872-49	183873	Robert Price	07/2018
2282	2^610597+1178897	183809	Enzo Doria	05/2016
2283	(8*10^183773-269)/9	183773	Robert Price	09/2021
2284	(65*10^183768-29)/9	183769	Robert Price	01/2021
2285	(17*10^183764+31)/3	183765	Robert Price	01/2019
2286	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
2287	2^610401+1277	183750	Lelio R Paula	07/2013
2288	2^610356-1849019	183736	Enzo Doria	08/2015
2289	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
2290	23*10^183710-7	183712	Robert Price	02/2020
2291	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
2292	(4*10^183659+149)/9	183659	Robert Price	04/2018
2293	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
2294	7*10^183596+39	183597	Robert Price	01/2023
2295	2^609846-1834251	183582	Enzo Doria	07/2015
2296	10^183546+1547323	183547	Patrick De Geest	02/2021
2298	10^183546-800000001	183546	Robert Price	09/2020
2297	10^183546-584297	183546	Patrick De Geest	02/2021
2299	7*10^183511+39	183512	Robert Price	01/2023
2300	(23*10^183477-71)/3	183478	Robert Price	07/2020
2301	11^176176-240	183469	Enzo Doria	11/2012
2302	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
2303	6*10^183429+53	183430	Robert Price	05/2020
2304	(28*10^183403+191)/3	183404	Robert Price	02/2020
2305	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
2306	2^608965-113989	183317	Enzo Doria	10/2014
2307	A005165(43592)	183312	Serge Batalov	07/2017
2308	(61*10^183294+119)/9	183295	Robert Price	05/2019
2309	2^608814-461261	183272	Enzo Doria	06/2015
2310	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
2311	2^608541-608541^2	183190	Henri Lifchitz	02/2018
2312	2^608293+143807	183115	Enzo Doria	10/2016
2313	2^608164-462419	183076	Enzo Doria	08/2015
2314	2^607950-1862303	183012	Enzo Doria	12/2015
2315	5*3^383376+2^383376	182918	Jon Grantham	08/2023
2316	(46*10^182896+683)/9	182897	Robert Price	03/2019
2317	(2*10^182787+73)/3	182787	Robert Price	09/2020
2318	2^607101+1871987	182756	Enzo Doria	05/2016
2319	2^606869-69175	182686	Enzo Doria	11/2015
2320	8*10^182671+71	182672	Robert Price	05/2022
2321	(23*10^182666-71)/3	182667	Robert Price	07/2020
2322	3*10^182614-11	182615	Robert Price	07/2018
2323	2^606560-357	182593	Enzo Doria	05/2014
2324	66*10^182420+7	182422	Robert Price	07/2020
2325	2^605687+1866983	182330	Enzo Doria	03/2016
2326	2^605655-114445	182321	Enzo Doria	02/2015
2327	94*10^182291-3	182293	Robert Price	05/2020
2328	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
2329	(14*10^182177-221)/9	182178	Robert Price	04/2018
2330	2^605174-112751	182176	Enzo Doria	06/2014
2331	2^604761+1874507	182052	Enzo Doria	06/2016
2332	2^604705+1871957	182035	Enzo Doria	05/2016
2333	(14*10^182000+229)/9	182001	Robert Price	03/2018
2334	(10^181996+41)/3	181996	Robert Price	12/2017
2335	(17*10^181979+91)/9	181980	Robert Price	02/2022
2336	(5*10^181950-101)/3	181951	Robert Price	04/2018
2337	2^603915+75233	181797	Enzo Doria	04/2016
2338	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
2339	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
2340	7*10^181594-57	181595	Robert Price	06/2020
2341	8*10^181580+29	181581	Robert Price	11/2021
2342	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
2343	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
2344	3*10^181445+23	181446	Robert Price	03/2022
2345	(194*10^181369-11)/3	181371	Robert Price	09/2020
2346	11^174145-360	181354	Enzo Doria	10/2012
2347	2^602351-396765	181326	Enzo Doria	08/2013
2348	6*10^181306+17	181307	Robert Price	04/2019
2349	(353^71143-1)/352	181254	Anonymous	04/2024
2350	(286*10^181220-1)/3	181222	Robert Price	11/2020
2351	2^601957-113833	181208	Enzo Doria	09/2014
2352	66^99581-65^99581	181193	Robert Price	09/2013
2353	10^181182+383973	181183	Patrick De Geest	04/2016
2354	10^181182-21	181182	Serge Batalov	12/2014
2355	(797*10^181171-41)/9	181173	Robert Price	04/2022
2356	2^601722+74209	181137	Enzo Doria	08/2023
2357	(5*10^181127-29)/3	181128	Robert Price	03/2018
2358	2^601521-29143	181076	Enzo Doria	07/2015
2359	2^601442-2797811	181053	Enzo Doria	04/2016
2360	44*10^181029+3	181031	Robert Price	04/2020
2361	5*10^180992-9	180993	Robert Price	05/2015
2362	10^180979+79477	180980	Patrick De Geest	04/2016
2363	10^180979+107739	180980	Patrick De Geest	04/2016
2364	10^180979-11	180979	Serge Batalov	12/2014
2365	2^601023-113851	180926	Enzo Doria	10/2014
2366	(23*10^180862-143)/3	180863	Robert Price	12/2019
2367	3*10^180852+29	180853	Robert Price	05/2018
2368	(277*10^180782-7)/9	180784	Robert Price	02/2022
2369	2^600412+29851	180743	Enzo Doria	03/2024
2370	(8*10^180725-629)/9	180725	Robert Price	01/2022
2371	(79*10^180710-1)/3	180712	Robert Price	02/2020
2372	2^600300-1852559	180709	Enzo Doria	08/2015
2373	(2*10^180706-77)/3	180706	Robert Price	02/2021
2374	(10^180689+71)/9	180689	Serge Batalov	07/2015
2375	2^600209+76487	180681	Enzo Doria	05/2016
2376	2^599999+378461	180617	Norman Luhn	09/2023
2377	(8*10^180536-269)/9	180536	Robert Price	09/2021
2378	2^599702-369885	180529	Enzo Doria	11/2013
2379	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
2380	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
2381	(29*10^180432-17)/3	180433	Robert Price	09/2019
2382	4*10^180360+93	180361	Robert Price	08/2018
2383	2^599035+219323	180328	Enzo Doria	03/2024
2384	2^598942+80779	180300	Enzo Doria	07/2016
2385	(38*10^180296+403)/9	180297	Robert Price	10/2018
2386	(85*10^180241+77)/9	180242	Robert Price	07/2022
2387	2^598591-1844797	180194	Enzo Doria	06/2015
2388	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
2389	2^598301+28517	180107	Enzo Doria	01/2024
2390	(29*10^180072+691)/9	180073	Robert Price	08/2021
2391	(59*10^180038+157)/9	180039	Robert Price	12/2021
2392	95*10^180019-9	180021	Robert Price	01/2022
2393	6*10^179970+91	179971	Robert Price	05/2019
2394	(4*10^179963-79)/3	179964	Robert Price	02/2018
2395	(403*10^179944-43)/9	179946	Robert Price	06/2021
2396	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
2397	2^597424-1859729	179843	Enzo Doria	11/2015
2398	Phi(180683,10)	179760	Maksym Voznyy	09/2015
2399	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
2400	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
2401	(29*10^179697+223)/9	179698	Robert Price	09/2018
2402	2^596884+73	179680	Stefano Morozzi	04/2021
2403	(11*10^179679+13)/3	179680	Robert Price	03/2022
2404	(68*10^179656+7)/3	179658	Robert Price	01/2020
2405	(10^179643+173)/3	179643	Robert Price	05/2021
2406	2^596690-461261	179622	Enzo Doria	07/2015
2407	2^596684-113939	179620	Enzo Doria	10/2014
2408	2^596642+39	179608	Jon Grantham	08/2023
2409	2*10^179602+63	179603	Robert Price	05/2018
2410	32262^39815-39815^32262	179514	Frank Doornink	02/2024
2411	(25*10^179488-403)/9	179489	Robert Price	01/2021
2412	7*10^179460+99	179461	Robert Price	05/2021
2413	2^596127+74333	179453	Enzo Doria	07/2023
2414	3^375887-112696	179344	Enzo Doria	07/2014
2415	4*10^179265-71	179266	Robert Price	12/2018
2416	2*10^179193+83	179194	Robert Price	12/2021
2417	2^595144-1850429	179157	Enzo Doria	08/2015
2418	2^595122-5	179150	Stefano Morozzi	07/2022
2419	3*10^179138+89	179139	Robert Price	10/2018
2420	(52*10^179062-133)/9	179063	Robert Price	09/2021
2421	2^594531+82253	178972	Enzo Doria	09/2016
2422	(664*10^178939-61)/9	178941	Robert Price	09/2021
2423	2^594260-2787899	178891	Enzo Doria	11/2015
2424	(14*10^178822+67)/9	178823	Robert Price	05/2022
2425	(29*10^178732-119)/9	178733	Robert Price	12/2021
2426	2^593631+101381	178701	Jorge Menendez	04/2018
2427	10^178695+136719	178696	Patrick De Geest	05/2016
2428	10^178695-71	178695	Serge Batalov	12/2014
2429	(2*10^178649-161)/3	178649	Robert Price	12/2020
2430	(691^62903-1)/690	178609	Michael Stocker	05/2020
2431	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
2432	2^593242+28309	178584	Enzo Doria	01/2024
2433	2^593222-14145	178578	Jorge Menendez	10/2017
2434	7*10^178566+33	178567	Robert Price	06/2020
2435	2^593178+1867219	178565	Enzo Doria	03/2016
2436	2^593152+22441	178557	Enzo Doria	09/2023
2437	(38*10^178456+151)/9	178457	Robert Price	03/2022
2438	(302*10^178369+13)/9	178371	Robert Price	02/2020
2439	(26*10^178296-113)/3	178297	Robert Price	06/2020
2440	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
2441	(13*10^178233+137)/3	178234	Robert Price	06/2021
2442	(5*10^178206+91)/3	178207	Robert Price	04/2018
2443	2^591872-291929	178172	Enzo Doria	07/2015
2444	2^591682-286871	178115	Enzo Doria	07/2015
2445	(7^210761-5^210761)/2	178114	Jon Grantham	08/2023
2446	4*10^178091+9	178092	Robert Price	05/2015
2447	410747#+478483	178007	Makoto Morimoto	02/2016
2448	3*10^177872+73	177873	Robert Price	08/2018
2449	2^590762-396765	177838	Enzo Doria	08/2013
2450	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
2451	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
2452	Smr(37765)	177719	Eric W. Weisstein	12/2021
2453	(266*10^177577-11)/3	177579	Robert Price	04/2020
2454	(11*10^177466-113)/3	177467	Robert Price	10/2018
2455	3*10^177373-97	177374	Robert Price	07/2018
2456	2^589204+1881151	177369	Enzo Doria	11/2016
2457	2^589132-69479	177347	Enzo Doria	01/2016
2458	(101*10^177302-17)/3	177304	Robert Price	02/2020
2459	2^588912-113519	177281	Enzo Doria	08/2014
2460	(682*10^177266-7)/9	177268	Robert Price	08/2021
2461	15^150706+2	177245	Robert Price	06/2015
2462	(31208^39601-1)/(31208^199-1)	177084	Ryan Propper	11/2023
2463	2^588194-1861001	177065	Enzo Doria	11/2015
2464	5*10^177016-37	177017	Robert Price	11/2021
2465	fibonacci(846926)-4	176997	Jon Grantham	08/2023
2466	(23*10^176964-47)/3	176965	Robert Price	09/2019
2467	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
2468	(19*10^176932+521)/9	176933	Robert Price	05/2018
2469	(8*10^176908+43)/3	176909	Robert Price	06/2018
2470	(85*10^176900+203)/9	176901	Robert Price	09/2020
2471	2^587560-113699	176874	Enzo Doria	09/2014
2472	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
2473	(101*10^176815-17)/3	176817	Robert Price	02/2020
2474	(25*10^176715-37)/3	176716	Robert Price	10/2019
2475	5^252763-12862	176674	Enzo Doria	05/2014
2476	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
2477	2^586829+23961	176654	Enzo Doria	10/2023
2478	2^586804+81721	176646	Enzo Doria	08/2016
2479	(10^176584+77)/3	176584	Robert Price	01/2018
2480	2^586570+1874419	176576	Enzo Doria	06/2016
2481	(157*10^176482-1)/3	176484	Robert Price	01/2022
2482	5*2^586202+3	176466	Jon Grantham	07/2023
2483	27122^39799-39799^27122	176442	Frank Doornink	01/2024
2484	2^585994-3311	176402	Yves Minet	12/2014
2485	8*10^176383-81	176384	Robert Price	02/2021
2486	(23*10^176357+61)/3	176358	Robert Price	01/2022
2487	2^585832-112799	176354	Enzo Doria	07/2014
2488	fibonacci(843383)+4	176257	Jon Grantham	08/2023
2489	(29*10^176240+49)/3	176241	Robert Price	09/2021
2490	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
2491	2^585336-461039	176204	Enzo Doria	06/2015
2492	(25*10^176164+143)/3	176165	Robert Price	08/2020
2493	2^585095-1848127	176132	Enzo Doria	08/2015
2494	(5*10^176101-311)/9	176101	Robert Price	12/2021
2495	6*10^176092+77	176093	Robert Price	06/2020
2496	2^584950-115451	176088	Enzo Doria	07/2015
2497	(646*10^176044+11)/9	176046	Robert Price	10/2021
2498	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
2499	2^584671-3697	176004	Yves Minet	03/2017
2500	(13*10^175965-37)/3	175966	Robert Price	01/2019

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295107 PRPs in the top)