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	(58*10^170842+221)/9	170843	Robert Price	02/2017
2252	(29*10^170830+583)/9	170831	Robert Price	06/2021
2253	3*10^170800+73	170801	Robert Price	08/2018
2254	(29*10^170799-119)/9	170800	Robert Price	12/2021
2255	11^164009-270	170798	Enzo Doria	10/2012
2256	2*10^170767+41	170768	Robert Price	05/2018
2257	3^357706-112358	170670	Enzo Doria	07/2014
2258	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
2259	2^566871+1876163	170646	Enzo Doria	07/2016
2260	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
2261	2^566496+7	170533	Donovan Johnson	07/2006
2262	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
2263	7*10^170348+33	170349	Robert Price	06/2020
2264	2^565183-352021	170138	Enzo Doria	07/2015
2265	2^565143-114457	170125	Enzo Doria	02/2015
2266	3*2^565024-5	170090	Jon Grantham	07/2023
2267	2^564976-49869	170075	Enzo Doria	10/2015
2268	(7*10^169944+23)/3	169945	Robert Price	06/2020
2269	(37*10^169943+251)/9	169944	Robert Price	09/2021
2270	2^564526-351401	169940	Enzo Doria	07/2015
2271	4*10^169759+19	169760	Robert Price	10/2018
2272	(2^563903-13)/5	169752	Stefano Morozzi	08/2022
2273	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
2274	2^563583+89	169656	Stefano Morozzi	04/2021
2275	(4*10^169559+83)/3	169560	Robert Price	02/2018
2276	(194*10^169461-17)/3	169463	Robert Price	09/2020
2277	2^562749+2793047	169405	Enzo Doria	02/2016
2278	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
2279	(109*10^169337+11)/3	169339	Robert Price	06/2022
2280	(56*10^169311+691)/9	169312	Robert Price	05/2019
2281	2^562369-29503	169290	Enzo Doria	08/2015
2282	(17*10^169283+19)/9	169284	Robert Price	03/2021
2283	10^169074-5000000001	169074	Robert Price	09/2022
2284	8*10^169071+59	169072	Robert Price	11/2021
2285	(10^169044+173)/3	169044	Robert Price	05/2021
2286	(22*10^169019+383)/9	169020	Robert Price	05/2018
2287	(64*10^168935+143)/9	168936	Robert Price	05/2021
2288	(22*10^168906+47)/3	168907	Robert Price	06/2021
2289	5*10^168807+87	168808	Robert Price	02/2019
2290	(77*10^168803-149)/9	168804	Robert Price	03/2022
2291	4*10^168788-47	168789	Robert Price	10/2021
2292	(154*10^168781+17)/9	168783	Robert Price	06/2022
2293	(418*10^168751-31)/9	168753	Robert Price	05/2022
2294	(29*10^168711+691)/9	168712	Robert Price	08/2021
2295	2^560405-39943	168699	Enzo Doria	09/2015
2296	(397*10^168634+17)/9	168636	Robert Price	03/2022
2297	89*10^168614-7	168616	Robert Price	04/2020
2298	(23*10^168608-83)/3	168609	Robert Price	08/2019
2299	(94*10^168541+11)/3	168543	Robert Price	04/2020
2300	2^559686-350471	168483	Enzo Doria	06/2015
2301	2^559672-1855889	168479	Enzo Doria	09/2015
2302	(5*10^168379-473)/9	168379	Robert Price	01/2018
2303	2^559000-59939	168276	Enzo Doria	11/2015
2304	(16*10^168181+41)/3	168182	Robert Price	03/2019
2305	(19*10^168173+77)/3	168174	Robert Price	05/2019
2306	(74*10^168170+529)/9	168171	Robert Price	02/2022
2307	2^558640-114149	168168	Enzo Doria	12/2014
2308	2^558498-1849277	168125	Enzo Doria	08/2015
2309	2^558476-1850249	168119	Enzo Doria	08/2015
2310	(7*10^168067+71)/3	168068	Robert Price	05/2018
2311	2^558150-1852211	168020	Enzo Doria	08/2015
2312	2^558125-113661	168013	Enzo Doria	09/2014
2313	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
2314	(8*10^167965-11)/3	167966	Robert Price	07/2023
2315	(13*10^167911+179)/3	167912	Robert Price	11/2018
2316	(26*10^167861-167)/3	167862	Robert Price	10/2019
2317	36^107827-107827	167812	Kellen Shenton	06/2023
2318	39^105456+2	167788	Robert Price	04/2015
2319	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
2320	6*10^167662-13	167663	Robert Price	07/2022
2321	10^167639+121911	167640	Patrick De Geest	07/2018
2322	10^167639-8001	167639	Robert Price	03/2018
2323	2^556504-462059	167525	Enzo Doria	07/2015
2324	(88*10^167522-637)/9	167523	Robert Price	11/2020
2325	5*10^167510+9	167511	Robert Price	08/2015
2326	7*10^167437-93	167438	Robert Price	08/2020
2327	11^160663+6	167314	Paul Bourdelais	02/2021
2328	(7*10^167308-493)/9	167308	Robert Price	04/2021
2329	2^555759+74333	167301	Enzo Doria	07/2023
2330	2^555343+1874333	167175	Enzo Doria	06/2016
2331	2^555210-461261	167135	Enzo Doria	07/2015
2332	9*10^166996+59	166997	Robert Price	01/2020
2333	(68*10^166976-329)/9	166977	Robert Price	03/2021
2334	(64*10^166901+683)/9	166902	Robert Price	06/2022
2335	2^554372+1880527	166883	Enzo Doria	11/2016
2336	2^554299+72173	166861	Enzo Doria	04/2016
2337	(185*10^166837+7)/3	166839	Robert Price	03/2020
2338	(14*10^166813+139)/9	166814	Robert Price	11/2021
2339	2^554037-2797063	166782	Enzo Doria	03/2016
2340	(49*10^166721-139)/9	166722	Robert Price	03/2019
2341	2*10^166646+69	166647	Robert Price	06/2020
2342	2^553484-29819	166616	Enzo Doria	08/2015
2343	(188*10^166611+7)/3	166613	Robert Price	03/2020
2344	2^553383-2784217	166585	Enzo Doria	10/2015
2345	2^553069+76427	166491	Enzo Doria	05/2016
2346	2*10^166458+51	166459	Robert Price	05/2018
2347	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
2348	11^159756-2424	166369	Mike Oakes	06/2010
2349	2^552649-361275	166364	Enzo Doria	05/2014
2350	2^552628-113669	166358	Enzo Doria	09/2014
2351	(19*10^166325+137)/3	166326	Robert Price	03/2022
2352	10^166324+550603	166325	Patrick De Geest	07/2018
2353	10^166324-801	166324	Robert Price	02/2018
2354	(85*10^166297-1)/3	166299	Robert Price	02/2020
2355	8*10^166227+87	166228	Robert Price	10/2019
2356	2^552137+1879397	166210	Enzo Doria	09/2016
2357	(103*10^166126+11)/3	166128	Robert Price	01/2021
2358	(22*10^166077+179)/3	166078	Robert Price	02/2022
2359	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
2360	2^551542+19249	166031	Payam Samidoost	08/2002
2361	2^551535-23821	166029	Enzo Doria	08/2013
2362	2^551507-23557	166021	Enzo Doria	08/2013
2363	10^165947-7000000001	165947	Robert Price	12/2021
2364	4*10^165938-47	165939	Robert Price	10/2021
2365	7*10^165916-3	165917	Robert Price	08/2015
2366	(29*10^165796+67)/3	165797	Robert Price	12/2019
2367	81^86837-80^86837	165728	Robert Price	01/2015
2368	(71*10^165716-17)/9	165717	Serge Batalov	01/2023
2369	fibonacci(792909)+3	165708	Jon Grantham	08/2023
2370	(71*10^165663-539)/9	165664	Robert Price	07/2019
2371	2^550270-69551	165648	Enzo Doria	12/2015
2372	(202*10^165569-13)/9	165571	Robert Price	01/2020
2373	2^550000-23625	165567	Enzo Doria	08/2013
2374	2^549675-1852057	165469	Enzo Doria	08/2015
2375	2^549663+212543	165466	Enzo Doria	08/2023
2376	(529*10^165394-7)/9	165396	Robert Price	08/2021
2377	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
2378	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
2379	2^549278+1879669	165350	Enzo Doria	09/2016
2380	(7*10^165350-439)/9	165350	Robert Price	02/2018
2381	2^549252-351269	165342	Enzo Doria	06/2015
2382	67*10^165327-9	165329	Robert Price	03/2021
2384	(14*10^165282+73)/3	165283	Robert Price	12/2018
2383	(8*10^165283-629)/9	165283	Robert Price	01/2022
2385	2^549049+2797607	165281	Enzo Doria	04/2016
2386	(218*10^165258+7)/9	165260	Robert Price	06/2022
2387	(7*10^165239+107)/3	165240	Robert Price	02/2018
2388	5*2^548778+3	165200	Jon Grantham	07/2023
2389	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
2390	(7*10^165134+107)/3	165135	Robert Price	02/2018
2391	(301*10^165082+23)/9	165084	Robert Price	06/2021
2392	(23*10^165060-83)/3	165061	Robert Price	08/2019
2393	7*10^165023-27	165024	Robert Price	11/2022
2394	(76*10^164984+77)/9	164985	Robert Price	10/2019
2395	(4*10^164929-211)/9	164929	Robert Price	03/2022
2396	10^164878-500001	164878	Robert Price	03/2022
2397	9*10^164791-89	164792	Robert Price	04/2020
2398	2^547178-1856501	164717	Enzo Doria	10/2015
2399	11^158160-60	164707	Enzo Doria	07/2012
2400	(26*10^164643-167)/3	164644	Robert Price	10/2019
2401	(10^164643+83)/3	164643	Robert Price	08/2021
2402	2^546398-59201	164483	Enzo Doria	10/2015
2403	2^546332-114893	164463	Enzo Doria	05/2015
2404	(65*10^164427+277)/9	164428	Robert Price	08/2021
2405	2^545958+1876189	164350	Enzo Doria	07/2016
2406	2^545878-49841	164326	Enzo Doria	10/2015
2407	(10^164284+77)/3	164284	Robert Price	01/2018
2408	2^545668-4019	164263	Yves Minet	04/2017
2409	10^164216+780639	164217	Patrick De Geest	08/2021
2411	10^164216-50000000001	164216	Robert Price	12/2020
2410	10^164216-891051	164216	Patrick De Geest	08/2021
2412	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
2413	(16*10^164122+197)/3	164123	Robert Price	04/2019
2414	2^545185+76757	164118	Enzo Doria	05/2016
2415	2^545076-114329	164085	Enzo Doria	01/2015
2416	(2*10^164043-143)/3	164043	Robert Price	03/2018
2417	(29^112153+1)/30	164011	Lelio R Paula	03/2017
2418	2^544757+1874777	163989	Enzo Doria	06/2016
2419	2^544723+211193	163978	Enzo Doria	08/2023
2420	2^544444-457199	163894	Enzo Doria	01/2015
2421	2^544264-343529	163840	Enzo Doria	07/2015
2422	7*10^163780+9	163781	Robert Price	09/2015
2423	2^543989+2793047	163758	Enzo Doria	02/2016
2424	(28*10^163709+113)/3	163710	Robert Price	03/2020
2425	(23*10^163523+301)/9	163524	Robert Price	06/2021
2426	(68*10^163521-329)/9	163522	Robert Price	03/2021
2427	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
2428	2^542870-69551	163421	Enzo Doria	12/2015
2429	2^542395+72533	163278	Enzo Doria	04/2016
2430	2^542072-3683	163180	Yves Minet	03/2017
2431	fibonacci(780566)-4	163129	Jon Grantham	08/2023
2432	(682*10^163106-7)/9	163108	Robert Price	08/2021
2433	2^541779-1867357	163092	Enzo Doria	04/2016
2434	(29*10^163056+313)/9	163057	Robert Price	04/2021
2435	8*10^162924+9	162925	Robert Price	12/2015
2436	2^540905+81557	162829	Enzo Doria	08/2016
2437	2^540628-2939	162746	Yves Minet	09/2014
2438	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
2439	(203*10^162689+1)/3	162691	Robert Price	03/2020
2440	3*10^162620-59	162621	Robert Price	09/2018
2441	3^340694-112960	162553	Enzo Doria	07/2014
2442	2^539807-114081	162499	Enzo Doria	12/2014
2443	414^62093+62093^414	162498	Norbert Schneider	03/2022
2444	2^539654-114893	162453	Enzo Doria	05/2015
2445	9*10^162449-71	162450	Robert Price	11/2020
2446	2^539617-1851583	162441	Enzo Doria	08/2015
2447	(509*10^162422+31)/9	162424	Robert Price	08/2022
2448	(91*10^162410+11)/3	162412	Robert Price	02/2020
2449	2^539346+81049	162360	Enzo Doria	07/2016
2450	2^539220-115499	162322	Enzo Doria	07/2015
2451	2^539217-113713	162321	Enzo Doria	09/2014
2452	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
2453	4*10^162263-39	162264	Robert Price	09/2020
2454	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
2455	(10^162138+11)/3	162138	Serge Batalov	07/2015
2456	(61*10^162100-403)/9	162101	Robert Price	10/2021
2457	2^538473-112723	162097	Enzo Doria	06/2014
2458	2^538157+79337	162002	Enzo Doria	06/2016
2459	2^538136-114749	161996	Enzo Doria	05/2015
2460	2^538104+1531	161986	Lelio R Paula	01/2013
2461	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
2462	((2^179294-1)^3+2)/11	161918	Serge Batalov	03/2023
2463	2^537815-22737	161899	Enzo Doria	07/2013
2464	2^537804-39839	161896	Enzo Doria	09/2015
2465	(754*10^161816-7)/9	161818	Robert Price	05/2020
2466	2^537458-59201	161791	Enzo Doria	10/2015
2467	2*10^161766+51	161767	Robert Price	05/2018
2468	(7*10^161760+131)/3	161761	Robert Price	06/2020
2469	2^537209-49849	161717	Enzo Doria	10/2015
2470	(58*10^161691+329)/9	161692	Robert Price	05/2019
2471	23*10^161668-3	161670	Robert Price	10/2021
2472	2^536937+1879397	161635	Enzo Doria	09/2016
2473	3*2^536868-5	161614	Jon Grantham	07/2023
2474	34*10^161593-9	161595	Robert Price	06/2020
2475	(31*10^161582-1)/3	161584	Robert Price	02/2020
2476	2^536569-22881	161524	Enzo Doria	07/2013
2477	(46*10^161505+593)/9	161506	Robert Price	04/2022
2478	10^161253+573493	161254	Patrick De Geest	07/2018
2479	10^161253-8001	161253	Robert Price	03/2018
2480	97*10^161247-3	161249	Robert Price	05/2020
2481	7*10^161192-9	161193	Robert Price	10/2015
2482	2^535415-19	161176	Stefano Morozzi	07/2022
2483	2^535269-113803	161133	Enzo Doria	09/2014
2484	2^535205-23295	161113	Enzo Doria	08/2013
2485	(49*10^161105+437)/9	161106	Robert Price	09/2021
2486	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
2487	2^534429-19	160880	Stefano Morozzi	07/2022
2488	2^534359-23229	160859	Enzo Doria	08/2013
2489	10^160836-1001	160836	Robert Price	10/2022
2490	457^60454+60454^457	160803	Norbert Schneider	07/2021
2491	8*10^160782+53	160783	Robert Price	08/2020
2492	67^88037-66^88037	160763	Robert Price	10/2013
2493	(88*10^160761-637)/9	160762	Robert Price	11/2020
2494	2^533948-1852559	160735	Enzo Doria	08/2015
2495	2^533665-23335	160650	Enzo Doria	08/2013
2496	(19*10^160619+77)/3	160620	Robert Price	05/2019
2497	2^533350-5	160555	Stefano Morozzi	07/2022
2498	(38*10^160508+151)/9	160509	Robert Price	03/2022
2499	3^336353-2^336353	160482	Mike Oakes	10/2007
2500	2*10^160339-63	160340	Robert Price	01/2022

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PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)