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	(509*10^162422+31)/9	162424	Robert Price	08/2022
2252	(91*10^162410+11)/3	162412	Robert Price	02/2020
2253	2^539346+81049	162360	Enzo Doria	07/2016
2254	2^539220-115499	162322	Enzo Doria	07/2015
2255	2^539217-113713	162321	Enzo Doria	09/2014
2256	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
2257	4*10^162263-39	162264	Robert Price	09/2020
2258	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
2259	(10^162138+11)/3	162138	Serge Batalov	07/2015
2260	(61*10^162100-403)/9	162101	Robert Price	10/2021
2261	2^538473-112723	162097	Enzo Doria	06/2014
2262	2^538157+79337	162002	Enzo Doria	06/2016
2263	2^538136-114749	161996	Enzo Doria	05/2015
2264	2^538104+1531	161986	Lelio R Paula	01/2013
2265	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
2266	((2^179294-1)^3+2)/11	161918	Serge Batalov	03/2023
2267	2^537815-22737	161899	Enzo Doria	07/2013
2268	2^537804-39839	161896	Enzo Doria	09/2015
2269	(754*10^161816-7)/9	161818	Robert Price	05/2020
2270	2^537458-59201	161791	Enzo Doria	10/2015
2271	2*10^161766+51	161767	Robert Price	05/2018
2272	(7*10^161760+131)/3	161761	Robert Price	06/2020
2273	2^537209-49849	161717	Enzo Doria	10/2015
2274	(58*10^161691+329)/9	161692	Robert Price	05/2019
2275	23*10^161668-3	161670	Robert Price	10/2021
2276	2^536937+1879397	161635	Enzo Doria	09/2016
2277	34*10^161593-9	161595	Robert Price	06/2020
2278	(31*10^161582-1)/3	161584	Robert Price	02/2020
2279	2^536569-22881	161524	Enzo Doria	07/2013
2280	(46*10^161505+593)/9	161506	Robert Price	04/2022
2281	10^161253+573493	161254	Patrick De Geest	07/2018
2282	10^161253-8001	161253	Robert Price	03/2018
2283	97*10^161247-3	161249	Robert Price	05/2020
2284	7*10^161192-9	161193	Robert Price	10/2015
2285	2^535415-19	161176	Stefano Morozzi	07/2022
2286	2^535269-113803	161133	Enzo Doria	09/2014
2287	2^535205-23295	161113	Enzo Doria	08/2013
2288	(49*10^161105+437)/9	161106	Robert Price	09/2021
2289	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
2290	2^534429-19	160880	Stefano Morozzi	07/2022
2291	2^534359-23229	160859	Enzo Doria	08/2013
2292	10^160836-1001	160836	Robert Price	10/2022
2293	457^60454+60454^457	160803	Norbert Schneider	07/2021
2294	8*10^160782+53	160783	Robert Price	08/2020
2295	67^88037-66^88037	160763	Robert Price	10/2013
2296	(88*10^160761-637)/9	160762	Robert Price	11/2020
2297	2^533948-1852559	160735	Enzo Doria	08/2015
2298	2^533665-23335	160650	Enzo Doria	08/2013
2299	(19*10^160619+77)/3	160620	Robert Price	05/2019
2300	2^533350-5	160555	Stefano Morozzi	07/2022
2301	(38*10^160508+151)/9	160509	Robert Price	03/2022
2302	3^336353-2^336353	160482	Mike Oakes	10/2007
2303	2*10^160339-63	160340	Robert Price	01/2022
2304	(91*10^160249+11)/3	160251	Robert Price	02/2020
2305	(772*10^160239-7)/9	160241	Robert Price	06/2022
2306	(2*10^160226+187)/9	160226	Robert Price	06/2022
2307	2^532253+1868417	160225	Enzo Doria	04/2016
2308	2^532108-291989	160181	Enzo Doria	07/2015
2309	(28*10^160171-79)/3	160172	Robert Price	02/2021
2310	(26*10^160166-131)/3	160167	Robert Price	10/2019
2311	55*10^160145+9	160147	Robert Price	03/2022
2312	(17*10^160143+67)/3	160144	Robert Price	01/2019
2313	(394^61637-1)/393	159977	Jinyuan Wang	04/2023
2314	(19*10^159921-49)/3	159922	Robert Price	05/2019
2315	2^531110-1853771	159881	Enzo Doria	09/2015
2316	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
2317	2^530992-1845299	159845	Enzo Doria	07/2015
2318	2^530810+25	159790	Stefano Morozzi	04/2021
2319	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
2320	2^530417-113833	159672	Enzo Doria	09/2014
2321	2^530406-69701	159669	Enzo Doria	02/2016
2322	5*10^159656+41	159657	Robert Price	03/2019
2323	8*10^159614+29	159615	Robert Price	11/2021
2324	7^188858-188858^7	159604	Norbert Schneider	05/2018
2325	7*10^159553-27	159554	Robert Price	11/2022
2326	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
2327	(17*10^159438-377)/9	159439	Robert Price	03/2018
2328	(203*10^159381+1)/3	159383	Robert Price	03/2020
2329	89*10^159258-9	159260	Robert Price	05/2020
2330	2^528944-461315	159229	Enzo Doria	07/2015
2331	(13*10^159147+161)/3	159148	Robert Price	11/2018
2332	2^528620-113879	159131	Enzo Doria	10/2014
2333	(47*10^159083+259)/9	159084	Robert Price	03/2022
2334	2^528000-23307	158944	Enzo Doria	08/2013
2335	(29*10^158909+61)/9	158910	Robert Price	08/2018
2336	2^527817+1876817	158889	Enzo Doria	07/2016
2337	2^527774-49451	158876	Enzo Doria	10/2015
2338	2^527745-291553	158868	Enzo Doria	07/2015
2339	(91*10^158862+11)/3	158864	Robert Price	02/2020
2340	2^527644-1856999	158837	Enzo Doria	10/2015
2341	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
2342	2^527573-1863253	158816	Enzo Doria	12/2015
2343	2^527553-23401	158810	Enzo Doria	08/2013
2344	(49*10^158783+437)/9	158784	Robert Price	09/2021
2345	10^158755+310207	158756	Patrick De Geest	08/2021
2346	10^158755-50001	158755	Robert Price	08/2020
2347	(61*10^158748-619)/9	158749	Robert Price	03/2022
2348	11^152420-210	158730	Enzo Doria	09/2012
2349	(13*10^158694+401)/9	158695	Robert Price	01/2018
2350	2^527052-69059	158659	Enzo Doria	11/2015
2351	2^526849-113233	158598	Enzo Doria	07/2014
2352	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
2353	(299*10^158544-17)/3	158546	Robert Price	04/2020
2354	2^526658-3551	158540	Yves Minet	03/2017
2355	7*10^158465-11	158466	Robert Price	06/2019
2356	2^526375-23115	158455	Enzo Doria	08/2013
2357	(77*10^158407-293)/9	158408	Robert Price	09/2019
2358	2^526028-112793	158351	Enzo Doria	07/2014
2359	(229*10^158339-1)/3	158341	Robert Price	07/2020
2360	2^525690-9221	158249	Lelio R Paula	01/2013
2361	2*10^158242-7	158243	Robert Price	10/2015
2362	2^525667-525667^2	158242	Henri Lifchitz	12/2017
2363	(56*10^158230+187)/9	158231	Robert Price	10/2021
2364	10^158209-7000000001	158209	Robert Price	12/2021
2365	2^525186-1857431	158097	Enzo Doria	10/2015
2366	2^524515-23245	157895	Enzo Doria	08/2013
2367	2^524499-109087	157890	Enzo Doria	04/2014
2368	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
2369	2^524288+189093	157827	Makoto Morimoto	01/2016
2370	2^524288-164073	157827	Matthias Baur	03/2020
2371	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
2372	(10^157792+359)/9	157792	Serge Batalov	12/2014
2373	2^524154+25	157787	Stefano Morozzi	04/2021
2374	2^523924+1876591	157717	Enzo Doria	07/2016
2375	(17*10^157705+67)/3	157706	Robert Price	01/2019
2376	(46^94841+1)/47	157696	Robert Price	01/2014
2377	2^523774+77839	157672	Enzo Doria	05/2016
2378	2^523587+2799143	157616	Enzo Doria	04/2016
2379	2^523371+1872113	157551	Enzo Doria	05/2016
2380	8*10^157477+27	157478	Robert Price	09/2021
2381	(8*10^157368+49)/3	157369	Robert Price	05/2020
2382	(82*10^157319+449)/9	157320	Robert Price	11/2019
2383	2^522535-351457	157299	Enzo Doria	07/2015
2384	2^522226+2799079	157206	Enzo Doria	04/2016
2385	(134*10^157191-11)/3	157193	Robert Price	01/2022
2386	2^522134-1849451	157178	Enzo Doria	08/2015
2387	9*10^157152+71	157153	Robert Price	08/2020
2388	4*10^157150+93	157151	Robert Price	08/2018
2389	2^521401-29593	156958	Enzo Doria	08/2015
2390	7*10^156956+87	156957	Robert Price	07/2019
2391	2^521348-23397	156942	Enzo Doria	08/2013
2392	10^156902+34509	156903	Patrick De Geest	08/2021
2394	10^156902-80000001	156902	Robert Price	04/2021
2393	10^156902-69789	156902	Patrick De Geest	08/2021
2395	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
2396	65^86522+64	156857	Lelio R Paula	04/2016
2397	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
2398	2^520977-1858183	156830	Enzo Doria	10/2015
2399	(8*10^156718-101)/3	156719	Robert Price	08/2018
2400	(10^156640+7)/53	156639	Alfred Reich	07/2021
2401	2^520314-1849481	156631	Enzo Doria	08/2015
2402	(16*10^156563-637)/9	156564	Robert Price	09/2022
2403	(13*10^156522+89)/3	156523	Robert Price	09/2018
2405	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
2404	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
2406	(4*10^156501+119)/3	156502	Robert Price	12/2021
2407	(83*10^156476-101)/9	156477	Robert Price	08/2021
2408	3*10^156435-97	156436	Robert Price	07/2018
2409	(8*10^156371-77)/3	156372	Robert Price	07/2018
2410	53^90679-52^90679	156356	Robert Price	01/2013
2411	(418*10^156309-31)/9	156311	Robert Price	05/2022
2412	2^519106-59141	156267	Enzo Doria	10/2015
2413	2^519053+6077	156251	Enzo Doria	02/2016
2414	2^518968-1860989	156225	Enzo Doria	11/2015
2415	(25*10^156221-7)/9	156222	Robert Price	05/2018
2416	2^518931-2782297	156214	Enzo Doria	09/2015
2417	2^518608-2939	156117	Yves Minet	09/2014
2418	10*27^109005+697	156027	Curtis Bright	05/2015
2419	(49*10^155933-319)/9	155934	Robert Price	10/2021
2420	2^517967-113485	155924	Enzo Doria	08/2014
2421	(103*10^155904+17)/3	155906	Robert Price	08/2020
2422	(8*10^155887-719)/9	155887	Robert Price	03/2021
2423	4*10^155853-39	155854	Robert Price	09/2020
2424	2^517698+4429	155843	Lelio R Paula	01/2013
2425	2^517543-113257	155796	Enzo Doria	07/2014
2426	(14*10^155740-143)/3	155741	Robert Price	11/2018
2427	31^104309-30^104309	155563	Henri Lifchitz	08/2013
2428	2^516742-39851	155555	Enzo Doria	09/2015
2429	(22*10^155543+47)/3	155544	Robert Price	06/2021
2430	(19*10^155504+131)/3	155505	Robert Price	06/2020
2431	7*10^155496+61	155497	Robert Price	08/2019
2432	2^516440+1878421	155464	Enzo Doria	08/2016
2433	2^515863-1867237	155291	Enzo Doria	03/2016
2434	2^515786-461861	155268	Enzo Doria	07/2015
2435	2^515644-113247	155225	Enzo Doria	07/2014
2436	(7*10^155203+107)/3	155204	Robert Price	02/2018
2437	10^155163+206871	155164	Patrick De Geest	05/2021
2438	10^155163-40001	155163	Robert Price	01/2021
2439	(17*10^155133-89)/9	155134	Robert Price	07/2018
2440	2^515227-114997	155099	Enzo Doria	06/2015
2442	EPrime(155025)	155025	Eric W. Weisstein	10/2010
2441	(14*10^155024-221)/9	155025	Robert Price	04/2018
2443	(4*10^155022+173)/3	155023	Robert Price	02/2018
2444	(266*10^154897+1)/3	154899	Robert Price	04/2020
2445	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
2446	(86*10^154853-221)/9	154854	Robert Price	09/2019
2447	2^514361+78167	154839	Enzo Doria	05/2016
2448	2^514281-115033	154815	Enzo Doria	06/2015
2449	2^514194-3311	154788	Yves Minet	12/2014
2450	(14*10^154773+37)/3	154774	Robert Price	12/2018
2451	(16*10^154748+131)/3	154749	Robert Price	03/2022
2452	6*10^154742-31	154743	Robert Price	07/2020
2453	(14*10^154645+139)/9	154646	Robert Price	11/2021
2454	5*10^154618-79	154619	Robert Price	03/2021
2455	(167*10^154595+1)/3	154597	Robert Price	04/2021
2456	2^513437+1879337	154560	Enzo Doria	09/2016
2457	2^513306-113201	154521	Enzo Doria	07/2014
2458	(10^154494-13)/3	154494	Robert Price	12/2017
2459	23462^35343+35343^23462	154462	Norbert Schneider	04/2023
2460	2^513042-113787	154442	Enzo Doria	09/2014
2461	(151*10^154434-7)/9	154436	Robert Price	01/2020
2462	(118*10^154428+11)/3	154430	Robert Price	03/2022
2463	(14*10^154413+139)/9	154414	Robert Price	11/2021
2464	(77*10^154389-149)/9	154390	Robert Price	03/2022
2465	10^154359+49	154360	Robert Price	02/2023
2466	2^512628-114053	154317	Enzo Doria	11/2014
2467	2^512529-49783	154287	Enzo Doria	10/2015
2468	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
2469	2^512315-115297	154223	Enzo Doria	06/2015
2470	(47*10^154221+241)/9	154222	Robert Price	06/2022
2471	(7*10^154211+173)/9	154211	Robert Price	01/2022
2472	2^512168+79561	154178	Enzo Doria	06/2016
2473	(77*10^154175+67)/9	154176	Robert Price	12/2021
2474	(5*10^154158-311)/9	154158	Robert Price	12/2021
2475	(89*10^154103-737)/9	154104	Robert Price	01/2022
2476	4*10^154078-57	154079	Robert Price	10/2018
2477	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
2478	7*10^154038-57	154039	Robert Price	06/2020
2479	2^511658-114371	154025	Enzo Doria	02/2015
2480	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2481	2^511580-1846679	154001	Enzo Doria	07/2015
2482	(259*10^153998-1)/3	154000	Robert Price	12/2020
2483	2^511541-113713	153990	Enzo Doria	09/2014
2484	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2485	10^153935+970801	153936	Patrick De Geest	05/2021
2486	10^153935-1000001	153935	Robert Price	08/2020
2487	(16*10^153868-73)/3	153869	Robert Price	07/2020
2488	9*10^153851-67	153852	Robert Price	11/2020
2489	2^511077-112723	153850	Enzo Doria	06/2014
2490	69^83653-68^83653	153826	Robert Price	12/2013
2491	2^510963-113707	153816	Enzo Doria	09/2014
2492	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2493	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2494	2*10^153746-3	153747	Robert Price	07/2015
2495	2^510626+1179379	153714	Enzo Doria	05/2016
2496	(7*10^153664+113)/3	153665	Robert Price	02/2018
2497	2^510420+81121	153652	Enzo Doria	07/2016
2498	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2499	2^509894-459161	153494	Enzo Doria	05/2015
2500	(74*10^153489+673)/9	153490	Robert Price	02/2022

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Probable Primes Top 10000

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