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 ?
2251	2^587560-113699	176874	Enzo Doria	09/2014
2252	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
2253	(101*10^176815-17)/3	176817	Robert Price	02/2020
2254	(25*10^176715-37)/3	176716	Robert Price	10/2019
2255	5^252763-12862	176674	Enzo Doria	05/2014
2256	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
2257	2^586829+23961	176654	Enzo Doria	10/2023
2258	2^586804+81721	176646	Enzo Doria	08/2016
2259	(10^176584+77)/3	176584	Robert Price	01/2018
2260	2^586570+1874419	176576	Enzo Doria	06/2016
2261	(157*10^176482-1)/3	176484	Robert Price	01/2022
2262	5*2^586202+3	176466	Jon Grantham	07/2023
2263	2^585994-3311	176402	Yves Minet	12/2014
2264	8*10^176383-81	176384	Robert Price	02/2021
2265	(23*10^176357+61)/3	176358	Robert Price	01/2022
2266	2^585832-112799	176354	Enzo Doria	07/2014
2267	fibonacci(843383)+4	176257	Jon Grantham	08/2023
2268	(29*10^176240+49)/3	176241	Robert Price	09/2021
2269	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
2270	2^585336-461039	176204	Enzo Doria	06/2015
2271	(25*10^176164+143)/3	176165	Robert Price	08/2020
2272	2^585095-1848127	176132	Enzo Doria	08/2015
2273	(5*10^176101-311)/9	176101	Robert Price	12/2021
2274	6*10^176092+77	176093	Robert Price	06/2020
2275	2^584950-115451	176088	Enzo Doria	07/2015
2276	(646*10^176044+11)/9	176046	Robert Price	10/2021
2277	(7^208283-5^208283)/2	176020	Jon Grantham	08/2023
2278	2^584671-3697	176004	Yves Minet	03/2017
2279	(13*10^175965-37)/3	175966	Robert Price	01/2019
2280	2*10^175860-87	175861	Robert Price	04/2018
2281	(86*10^175774-221)/9	175775	Robert Price	09/2019
2282	2^583614+216037	175686	Enzo Doria	11/2023
2283	9*10^175654+47	175655	Robert Price	01/2022
2284	10^175608+2971	175609	Mike Oakes	05/2010
2285	10^175608-55829	175608	Patrick De Geest	09/2013
2286	2^583051+1879793	175516	Enzo Doria	09/2016
2287	(76*10^175514+491)/9	175515	Robert Price	10/2021
2288	2^582860-23829	175459	Enzo Doria	08/2013
2289	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
2290	(28*10^175417-67)/3	175418	Robert Price	10/2020
2291	2^582670-23913	175402	Enzo Doria	08/2013
2292	2^582573-29563	175372	Enzo Doria	08/2015
2293	2^582435-1862767	175331	Enzo Doria	12/2015
2294	10^175295-40000001	175295	Robert Price	07/2022
2295	(11*10^175250-149)/3	175251	Robert Price	09/2018
2296	(29*10^175236+31)/3	175237	Robert Price	04/2021
2297	2^582072-1848599	175222	Enzo Doria	08/2015
2298	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
2299	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
2300	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
2301	(5*10^175117-311)/9	175117	Robert Price	12/2021
2302	10^175093-89	175093	Riley Fisher	10/2023
2303	(220221^32768+1)/2	175075	Serge Batalov	03/2018
2304	2^581560+1874911	175068	Enzo Doria	06/2016
2305	(25*10^174987-97)/9	174988	Robert Price	01/2022
2306	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
2307	(27398^39601-1)/(27398^199-1)	174855	Ryan Propper	11/2023
2308	(861^59557-1)/860	174798	Jinyuan Wang	11/2023
2309	(47*10^174790+493)/9	174791	Robert Price	03/2019
2310	2^580528-114035	174757	Enzo Doria	11/2014
2311	(19*10^174754+737)/9	174755	Robert Price	07/2018
2312	(35*10^174704-377)/9	174705	Robert Price	07/2018
2313	(49*10^174681+293)/9	174682	Robert Price	03/2021
2314	6*10^174681+11	174682	Robert Price	07/2022
2315	3*10^174665-97	174666	Robert Price	07/2018
2316	2^580046-459161	174612	Enzo Doria	05/2015
2317	2^579992-39779	174595	Enzo Doria	09/2015
2318	(29*10^174481-149)/3	174482	Robert Price	08/2022
2319	(4*10^174423+101)/3	174424	Robert Price	11/2021
2320	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
2321	(2*10^174301-71)/3	174301	Robert Price	12/2017
2322	14^152048+3	174267	Paul Bourdelais	12/2020
2323	(2^578696+1)/257	174203	Lelio R Paula	09/2015
2324	2^578656-1851809	174193	Enzo Doria	08/2015
2325	2^578583-113917	174171	Enzo Doria	10/2014
2326	2^578434-83	174126	Yves Minet	07/2017
2327	15^148048-2	174118	Robert Price	06/2015
2328	5*10^174101+81	174102	Robert Price	03/2019
2329	2^578346+2794249	174100	Enzo Doria	03/2016
2330	10^173947+1372429	173948	Patrick De Geest	08/2021
2332	10^173947-500000001	173947	Robert Price	12/2020
2331	10^173947-286391	173947	Patrick De Geest	08/2021
2333	5*10^173904-13	173905	Robert Price	01/2019
2334	(8*10^173862-59)/3	173863	Robert Price	08/2021
2335	(71*10^173854-287)/9	173855	Robert Price	09/2019
2336	(43*10^173826+101)/9	173827	Robert Price	11/2018
2337	2*10^173809-87	173810	Robert Price	04/2018
2338	(2^577372-23)/7	173806	Stefano Morozzi	08/2022
2339	(L!41532)/2	173772	Serge Batalov	07/2017
2340	2^577146-49877	173739	Enzo Doria	10/2015
2341	2^576889+49727	173661	Enzo Doria	09/2016
2342	(167*10^173571-17)/3	173573	Robert Price	03/2020
2343	37803^37916+37916^37803	173562	Norbert Schneider	06/2022
2344	5*10^173534+29	173535	Robert Price	12/2020
2345	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
2346	4*10^173509+99	173510	Robert Price	12/2020
2347	(13*10^173467-37)/3	173468	Robert Price	01/2019
2348	2^576016-113919	173399	Enzo Doria	11/2014
2349	2^575911-1849387	173367	Enzo Doria	08/2015
2350	2^575879+215843	173357	Enzo Doria	11/2023
2351	515^63898+63898^515	173280	Norbert Schneider	12/2022
2352	2^575614+9	173278	Stefano Morozzi	04/2021
2353	(16*10^173251+107)/3	173252	Robert Price	03/2019
2354	2^575196-114053	173152	Enzo Doria	11/2014
2355	7*10^173135-53	173136	Robert Price	06/2020
2356	(301*10^173047+23)/9	173049	Robert Price	06/2021
2357	2^574591-115387	172970	Enzo Doria	07/2015
2358	(202*10^172940-13)/9	172942	Robert Price	01/2020
2359	45^104608+104608^45	172940	Norbert Schneider	06/2021
2360	2^574328+81121	172890	Enzo Doria	07/2016
2361	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
2362	3*10^172812+13	172813	Robert Price	07/2018
2363	4*5^247217-9	172798	Lelio R Paula	10/2015
2364	6*10^172772-31	172773	Robert Price	07/2020
2365	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
2366	(34*10^172693-547)/9	172694	Robert Price	03/2021
2367	5*10^172692+57	172693	Robert Price	12/2018
2368	2^573668-2782319	172692	Enzo Doria	09/2015
2369	2^573444-1855109	172624	Enzo Doria	09/2015
2370	(14*10^172532-29)/3	172533	Robert Price	09/2021
2371	3^361608+2	172531	Robert Price	08/2014
2372	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
2373	2^572592-114893	172368	Enzo Doria	05/2015
2374	4*10^172354-39	172355	Robert Price	09/2020
2375	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
2376	(11*10^172322-119)/9	172323	Robert Price	11/2021
2377	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
2378	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
2379	(4*10^172241+89)/3	172242	Robert Price	08/2021
2380	3*10^172219+73	172220	Robert Price	08/2018
2381	A352736(15)	172032	Kellen Shenton	05/2022
2382	2^571300+25861	171979	Enzo Doria	11/2023
2383	(36^110503+1)/37	171975	Lelio R Paula	04/2017
2384	8*10^171934+71	171935	Robert Price	05/2022
2385	(11*10^171933+601)/9	171934	Robert Price	02/2022
2386	(22*10^171929-73)/3	171930	Robert Price	04/2019
2387	(49*10^171892-319)/9	171893	Robert Price	10/2021
2388	4*10^171891-63	171892	Robert Price	10/2018
2389	67*10^171882-9	171884	Robert Price	03/2021
2390	2^570980-2782289	171883	Enzo Doria	09/2015
2391	(25*10^171849-37)/3	171850	Robert Price	10/2019
2392	10^171832+387909	171833	Patrick De Geest	08/2021
2393	10^171832-10001	171832	Robert Price	02/2021
2395	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
2394	(2^570769-9)/7	171818	Stefano Morozzi	08/2022
2396	(74*10^171651-29)/9	171652	Robert Price	06/2022
2397	(536*10^171601-23)/9	171603	Robert Price	02/2020
2398	7*10^171535-99	171536	Robert Price	06/2019
2399	(28*10^171534+101)/3	171535	Robert Price	09/2020
2400	2^569563-1854607	171456	Enzo Doria	09/2015
2401	3*10^171391+59	171392	Robert Price	08/2018
2402	(13*10^171306-37)/3	171307	Robert Price	01/2019
2403	8*10^171296+87	171297	Robert Price	10/2019
2404	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
2405	(29*10^171275+67)/3	171276	Robert Price	12/2019
2406	(457*10^171248-7)/9	171250	Robert Price	09/2022
2407	(194*10^171193+1)/3	171195	Robert Price	01/2022
2408	2^568642+1876129	171179	Enzo Doria	07/2016
2409	4*10^171146-47	171147	Robert Price	10/2021
2410	(19*10^170970+131)/3	170971	Robert Price	06/2020
2411	(46*10^170932+143)/9	170933	Robert Price	01/2019
2412	(79*10^170901-1)/3	170903	Robert Price	02/2020
2413	(58*10^170842+221)/9	170843	Robert Price	02/2017
2414	(29*10^170830+583)/9	170831	Robert Price	06/2021
2415	3*10^170800+73	170801	Robert Price	08/2018
2416	(29*10^170799-119)/9	170800	Robert Price	12/2021
2417	11^164009-270	170798	Enzo Doria	10/2012
2418	2*10^170767+41	170768	Robert Price	05/2018
2419	3^357706-112358	170670	Enzo Doria	07/2014
2420	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
2421	2^566871+1876163	170646	Enzo Doria	07/2016
2422	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
2423	2^566496+7	170533	Donovan Johnson	07/2006
2424	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
2425	7*10^170348+33	170349	Robert Price	06/2020
2426	2^565183-352021	170138	Enzo Doria	07/2015
2427	2^565143-114457	170125	Enzo Doria	02/2015
2428	3*2^565024-5	170090	Jon Grantham	07/2023
2429	2^564976-49869	170075	Enzo Doria	10/2015
2430	(7*10^169944+23)/3	169945	Robert Price	06/2020
2431	(37*10^169943+251)/9	169944	Robert Price	09/2021
2432	2^564526-351401	169940	Enzo Doria	07/2015
2433	4*10^169759+19	169760	Robert Price	10/2018
2434	(2^563903-13)/5	169752	Stefano Morozzi	08/2022
2435	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
2436	2^563583+89	169656	Stefano Morozzi	04/2021
2437	2^563311+215813	169574	Enzo Doria	11/2023
2438	(4*10^169559+83)/3	169560	Robert Price	02/2018
2439	(194*10^169461-17)/3	169463	Robert Price	09/2020
2440	2^562749+2793047	169405	Enzo Doria	02/2016
2441	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
2442	(109*10^169337+11)/3	169339	Robert Price	06/2022
2443	(56*10^169311+691)/9	169312	Robert Price	05/2019
2444	2^562369-29503	169290	Enzo Doria	08/2015
2445	(17*10^169283+19)/9	169284	Robert Price	03/2021
2446	10^169074-5000000001	169074	Robert Price	09/2022
2447	8*10^169071+59	169072	Robert Price	11/2021
2448	(10^169044+173)/3	169044	Robert Price	05/2021
2449	(22*10^169019+383)/9	169020	Robert Price	05/2018
2450	(64*10^168935+143)/9	168936	Robert Price	05/2021
2451	(22*10^168906+47)/3	168907	Robert Price	06/2021
2452	5*10^168807+87	168808	Robert Price	02/2019
2453	(77*10^168803-149)/9	168804	Robert Price	03/2022
2454	4*10^168788-47	168789	Robert Price	10/2021
2455	(154*10^168781+17)/9	168783	Robert Price	06/2022
2456	(418*10^168751-31)/9	168753	Robert Price	05/2022
2457	(29*10^168711+691)/9	168712	Robert Price	08/2021
2458	2^560405-39943	168699	Enzo Doria	09/2015
2459	(397*10^168634+17)/9	168636	Robert Price	03/2022
2460	89*10^168614-7	168616	Robert Price	04/2020
2461	(23*10^168608-83)/3	168609	Robert Price	08/2019
2462	(94*10^168541+11)/3	168543	Robert Price	04/2020
2463	2^559686-350471	168483	Enzo Doria	06/2015
2464	2^559672-1855889	168479	Enzo Doria	09/2015
2465	(5*10^168379-473)/9	168379	Robert Price	01/2018
2466	2^559000-59939	168276	Enzo Doria	11/2015
2467	2^558830+25009	168225	Enzo Doria	11/2023
2468	(16*10^168181+41)/3	168182	Robert Price	03/2019
2469	(19*10^168173+77)/3	168174	Robert Price	05/2019
2470	(74*10^168170+529)/9	168171	Robert Price	02/2022
2471	2^558640-114149	168168	Enzo Doria	12/2014
2472	2^558498-1849277	168125	Enzo Doria	08/2015
2473	2^558476-1850249	168119	Enzo Doria	08/2015
2474	(7*10^168067+71)/3	168068	Robert Price	05/2018
2475	2^558150-1852211	168020	Enzo Doria	08/2015
2476	2^558125-113661	168013	Enzo Doria	09/2014
2477	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
2478	(8*10^167965-11)/3	167966	Robert Price	07/2023
2479	(13*10^167911+179)/3	167912	Robert Price	11/2018
2480	(26*10^167861-167)/3	167862	Robert Price	10/2019
2481	36^107827-107827	167812	Kellen Shenton	06/2023
2482	39^105456+2	167788	Robert Price	04/2015
2483	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
2484	6*10^167662-13	167663	Robert Price	07/2022
2485	10^167639+121911	167640	Patrick De Geest	07/2018
2486	10^167639-8001	167639	Robert Price	03/2018
2487	2^556504-462059	167525	Enzo Doria	07/2015
2488	(88*10^167522-637)/9	167523	Robert Price	11/2020
2489	5*10^167510+9	167511	Robert Price	08/2015
2490	7*10^167437-93	167438	Robert Price	08/2020
2491	11^160663+6	167314	Paul Bourdelais	02/2021
2492	(7*10^167308-493)/9	167308	Robert Price	04/2021
2493	2^555759+74333	167301	Enzo Doria	07/2023
2494	2^555343+1874333	167175	Enzo Doria	06/2016
2495	2^555210-461261	167135	Enzo Doria	07/2015
2496	9*10^166996+59	166997	Robert Price	01/2020
2497	(68*10^166976-329)/9	166977	Robert Price	03/2021
2498	(64*10^166901+683)/9	166902	Robert Price	06/2022
2499	2^554372+1880527	166883	Enzo Doria	11/2016
2500	2^554299+72173	166861	Enzo Doria	04/2016

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Probable Primes Top 10000

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