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 (> 30000)	Who ?	When ?
2251	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
2252	2^378128-262977	113828	Enzo Doria	05/2014
2253	2^378123-113215	113827	Enzo Doria	07/2014
2254	6^146274-18893	113824	Enzo Doria	03/2013
2255	2^378078+75	113813	Lelio R Paula	03/2013
2256	2^377940+63	113772	Lelio R Paula	03/2013
2257	2^377941-2785843	113772	Enzo Doria	04/2016
2258	2^377810+1875109	113733	Enzo Doria	09/2016
2259	2^377803-1838635	113731	Enzo Doria	05/2015
2260	2^377799+52223	113729	Yves Minet	08/2010
2261	11^109190-270	113710	Enzo Doria	12/2012
2262	7*10^113693+9	113694	Robert Price	09/2015
2263	(2*10^113631+529)/9	113631	Robert Price	01/2018
2264	2^377408-2798279	113612	Enzo Doria	04/2016
2265	2^377222+93679	113556	Yves Minet	02/2011
2266	262147#+316847	113552	Makoto Morimoto	02/2016
2267	2^377026-458903	113497	Enzo Doria	04/2015
2268	35^73477-34^73477	113454	Robert Price	05/2012
2269	2^376790+27	113426	Lelio R Paula	03/2013
2270	2^376786-112701	113424	Enzo Doria	06/2014
2271	2^376731+21	113408	Lelio R Paula	03/2013
2272	2^376634+1871245	113379	Enzo Doria	05/2016
2273	(4^188318+17)/3	113379	Robert Price	02/2017
2274	2^376576-344369	113361	Enzo Doria	07/2015
2275	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
2276	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
2277	2^376128-21237	113226	Enzo Doria	06/2013
2278	2^375638-1787171	113079	Enzo Doria	03/2016
2279	2^375537+4847	113048	Yves Minet	02/2011
2280	(17^91837+16^91837)/33	113000	Robert Price	08/2013
2281	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
2282	2^375350-3221	112992	Yves Minet	07/2011
2284	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
2283	2^375305+76757	112979	Enzo Doria	05/2016
2285	2^375258+1874989	112964	Enzo Doria	07/2016
2286	(29^77237-1)/28	112950	Robert Price	04/2012
2287	2^375154+74959	112933	Enzo Doria	04/2016
2288	2^374993-2787163	112885	Enzo Doria	11/2015
2289	123^53970+2	112793	Lelio R Paula	06/2013
2290	p(22852)#/2+512	112745	Robert Price	05/2017
2291	2^374441-21049	112718	Enzo Doria	06/2013
2292	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
2293	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
2294	3^236011-8828	112606	Enzo Doria	05/2014
2295	39^70666+2	112435	Lelio R Paula	11/2013
2296	(2^373350-7)/3	112390	Lelio R Paula	03/2014
2297	2^373306-1840931	112377	Enzo Doria	06/2015
2298	2^373117+1872107	112320	Enzo Doria	05/2016
2299	2^373040+2792761	112297	Enzo Doria	03/2016
2300	EPrime(112280)	112280	Eric W. Weisstein	10/2010
2301	2^372950+7	112270	Lelio R Paula	03/2013
2302	2^372945+1872167	112268	Enzo Doria	05/2016
2303	2^372695+72113	112193	Enzo Doria	04/2016
2304	2^372689-2563	112191	Yves Minet	07/2014
2305	2^372638-1859441	112176	Enzo Doria	03/2016
2306	3^235074-113056	112159	Enzo Doria	07/2014
2307	(91*10^112098-1)/9	112100	Robert Price	04/2015
2308	2^372310-85061	112077	Paul Bourdelais	02/2012
2309	(10^112067+53)/9	112067	Serge Batalov	07/2015
2310	75^59760+2	112054	Lelio R Paula	08/2013
2311	2^372108+74221	112016	Enzo Doria	04/2016
2312	2^371970-459491	111975	Enzo Doria	05/2015
2313	41^69427-40^69427	111971	Robert Price	07/2012
2314	(10^111902+71)/9	111902	Serge Batalov	07/2015
2315	2^371440-112865	111815	Enzo Doria	06/2014
2316	2^371426-459161	111811	Enzo Doria	05/2015
2317	2^371276-461267	111766	Enzo Doria	07/2015
2318	2^371098-113261	111712	Enzo Doria	07/2014
2319	(7*10^111706-61)/9	111706	Erik Branger	01/2011
2320	2^371044+1869391	111696	Enzo Doria	05/2016
2321	88^57416+87	111645	Norbert Schneider	11/2015
2322	2^370829-109693	111631	Enzo Doria	04/2014
2323	15^94906-2	111619	Lelio R Paula	11/2013
2325	2^370643-37	111575	Yves Minet	01/2012
2324	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
2326	2^370610-3911	111565	Yves Minet	04/2017
2327	286^45405+45405^286	111532	Norbert Schneider	04/2015
2328	4*5^159563-9	111531	Lelio R Paula	11/2014
2329	2^370393-2797093	111500	Enzo Doria	03/2016
2330	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
2331	2^370292-2791979	111469	Enzo Doria	03/2016
2332	2^370177-461551	111435	Enzo Doria	07/2015
2333	109^54683-108	111413	Norbert Schneider	02/2017
2334	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
2335	2^369974+733	111374	Lelio R Paula	05/2013
2336	2^369915-286267	111356	Enzo Doria	07/2015
2337	2^369855-1615	111338	Lelio R Paula	05/2017
2338	7*10^111325+3	111326	Robert Price	08/2015
2339	51^65176+2	111293	Lelio R Paula	08/2013
2340	2^369643-1865767	111274	Enzo Doria	03/2016
2341	2^369603+885	111262	Lelio R Paula	05/2017
2342	L(532277)	111240	Renaud Lifchitz	03/2004
2343	105^55033-2	111233	Lelio R Paula	10/2017
2344	2^369392+29835	111199	Lelio R Paula	05/2017
2345	2^369354-3413	111187	Yves Minet	12/2016
2346	2^369296-27	111170	Lelio R Paula	02/2013
2347	2^369239-109837	111153	Enzo Doria	05/2014
2348	2^369224-291839	111148	Enzo Doria	07/2015
2349	2^369216+2798881	111146	Enzo Doria	04/2016
2350	10^111111+163849	111112	Patrick De Geest	03/2017
2351	10^111111-312911	111111	Patrick De Geest	03/2017
2352	2^369092-216923	111108	Enzo Doria	05/2014
2353	2^369081-55	111105	Lelio R Paula	02/2013
2354	88^57124-87	111077	Norbert Schneider	11/2015
2355	2^368980+753	111075	Lelio R Paula	05/2013
2356	2^368946-3623	111064	Yves Minet	03/2017
2357	2^368929+29835	111059	Lelio R Paula	05/2017
2358	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
2359	111^54298+110	111057	Norbert Schneider	04/2017
2360	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
2361	2^368641-460303	110972	Enzo Doria	06/2015
2362	2^368619-109087	110966	Enzo Doria	04/2014
2363	3*2^368489+7	110927	Lelio R Paula	09/2014
2364	97411!4-2	110913	Robert Price	07/2017
2365	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
2366	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
2367	2^368050-64875	110795	Lelio R Paula	05/2017
2368	2^368048+25	110794	Lelio R Paula	02/2013
2369	69^60239-2	110771	Lelio R Paula	10/2013
2370	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
2371	2^367924-69	110757	Lelio R Paula	02/2013
2372	2^367709-109723	110692	Enzo Doria	04/2014
2373	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
2374	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
2375	2^367215+1879223	110543	Enzo Doria	09/2016
2376	2^367141+41	110521	Lelio R Paula	02/2013
2377	2^367126+29835	110516	Lelio R Paula	05/2017
2378	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
2379	2^366853+5711	110434	Lelio R Paula	05/2017
2380	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
2381	2^366816+315	110423	Lelio R Paula	05/2017
2382	2^366775-2787037	110411	Enzo Doria	03/2016
2383	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
2384	2^366751+2797553	110404	Enzo Doria	03/2016
2385	2^366748+255	110403	Lelio R Paula	05/2017
2386	2^366738-2985	110400	Yves Minet	09/2014
2387	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
2388	2^366716+1871791	110393	Enzo Doria	05/2016
2389	2^366649+1871687	110373	Enzo Doria	05/2016
2390	2^366629-351205	110367	Enzo Doria	06/2015
2391	2^366558+1874479	110345	Enzo Doria	06/2016
2392	18^87853-4409	110280	Enzo Doria	03/2013
2393	2^366218-23	110243	Lelio R Paula	02/2013
2394	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
2395	2^366178-343991	110231	Enzo Doria	07/2015
2396	2^365944+1871341	110161	Enzo Doria	05/2016
2397	2^365838-461267	110129	Enzo Doria	07/2015
2398	2^365763-6555	110106	Lelio R Paula	04/2017
2399	(2^365689+2^182845+1)/5	110083		11/2006
2400	2^365666-459161	110077	Enzo Doria	05/2015
2401	3*10^110076-7	110077	Robert Price	08/2015
2402	13^98785-72	110041	Lelio R Paula	03/2017
2403	(25^78707+1)/26	110027	Robert Price	06/2013
2404	(7*10^110006-151)/9	110006	Robert Price	02/2018
2405	6^141361-7	110001	Lelio R Paula	11/2014
2406	20^84536+81	109984	Lelio R Paula	03/2017
2407	5*2^365347-9	109982	Lelio R Paula	09/2014
2408	9*6^141303+7	109957	Lelio R Paula	11/2014
2409	78^58099+77	109929	Norbert Schneider	02/2015
2410	2*10^109928-7	109929	Robert Price	10/2015
2411	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
2412	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
2413	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
2414	18^87533-11	109878	Lelio R Paula	04/2017
2415	2^364982-5	109871	Henri Lifchitz	04/2006
2416	2^364936-1867979	109857	Enzo Doria	04/2016
2417	2^364867-112087	109836	Enzo Doria	06/2014
2418	4^182415-85061	109825	Mike Oakes	06/2011
2419	(17^89227+16^89227)/33	109788	Robert Price	08/2013
2420	2^364687-187	109782	Lelio R Paula	01/2012
2421	2^364644+67	109769	Lelio R Paula	01/2012
2422	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
2423	(2^364616+5)/9	109760	Lelio R Paula	01/2014
2424	12^101694+73	109747	Lelio R Paula	03/2017
2425	13^98518-66	109744	Lelio R Paula	03/2017
2426	2^364478-113261	109719	Enzo Doria	07/2014
2427	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
2428	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
2429	3^229824+340	109654	Lelio R Paula	03/2017
2430	(2*10^109645-71)/3	109645	Robert Price	12/2017
2431	2^364169-112813	109626	Enzo Doria	06/2014
2432	10^109615+21	109616	Lelio R Paula	03/2017
2433	10^109615-456267	109615	Patrick De Geest	03/2017
2434	2^364094-113	109604	Lelio R Paula	01/2012
2435	(4^182026+11)/3	109591	Robert Price	02/2017
2436	2^364041-6883	109588	Lelio R Paula	09/2011
2437	12^101545+11	109586	Lelio R Paula	03/2017
2438	2^363842-2787101	109528	Enzo Doria	03/2016
2439	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
2440	2^363769+5711	109506	Lelio R Paula	04/2017
2441	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
2442	p(22245)#/2-8	109462	Robert Price	01/2017
2443	2^363556+55	109442	Lelio R Paula	01/2012
2444	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
2445	2^363406+1871569	109397	Enzo Doria	05/2016
2446	(2^363349+7)/9	109378	Lelio R Paula	01/2014
2447	3^229236+100	109374	Lelio R Paula	03/2017
2448	2^363268-58695	109355	Lelio R Paula	04/2017
2449	2^363191-112321	109332	Enzo Doria	06/2014
2450	2^363120+3	109311	Donovan Johnson	04/2006
2451	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
2452	2^363042-114641	109287	Enzo Doria	04/2015
2453	2^363020-112793	109280	Enzo Doria	06/2014
2454	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
2455	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
2456	5^156181+38	109166	Lelio R Paula	02/2017
2457	3^228750+68	109142	Lelio R Paula	03/2017
2458	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
2459	65^60167-64^60167	109078	Robert Price	08/2013
2460	7*3^228589-2	109066	Lelio R Paula	09/2014
2461	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
2462	2*7^129008+9	109025	Lelio R Paula	11/2014
2463	2^361957+76367	108960	Enzo Doria	05/2016
2464	2^361873-1411	108935	Yves Minet	01/2013
2465	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
2466	13^97745-24	108883	Lelio R Paula	03/2017
2467	17^88475+8	108864	Lelio R Paula	04/2017
2468	2^361567+51	108843	Lelio R Paula	01/2012
2469	2^361563-109501	108842	Enzo Doria	04/2014
2470	12^100852+83	108838	Lelio R Paula	03/2017
2471	2^361497+767	108822	Lelio R Paula	01/2012
2472	2^361280-112349	108757	Enzo Doria	06/2014
2473	2^361271-5955	108754	Lelio R Paula	04/2017
2474	12^100757+19	108736	Lelio R Paula	03/2017
2475	14^94849-61	108710	Lelio R Paula	05/2017
2476	(19^85009-5^85009)/14	108705	Robert Price	07/2013
2477	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
2478	2^360973+1299	108664	Lelio R Paula	04/2017
2479	2^360959-109101	108660	Enzo Doria	04/2014
2480	6*5^155454+7	108659	Lelio R Paula	11/2014
2481	10^108656+79	108657	Lelio R Paula	02/2017
2482	10^108656-50001	108656	Patrick De Geest	03/2017
2483	2^360918-35	108648	Lelio R Paula	01/2012
2484	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
2485	2^360706-458903	108584	Enzo Doria	04/2015
2486	2^360641-113185	108564	Enzo Doria	07/2014
2487	2^360618+75019	108557	Enzo Doria	04/2016
2488	(14*10^108545-221)/9	108546	Robert Price	04/2018
2489	3*5^155286+2	108541	Lelio R Paula	11/2014
2490	7^128422+4	108530	Lelio R Paula	11/2014
2491	7^128421-80	108529	Lelio R Paula	03/2017
2492	2^360497+53807	108521	Yves Minet	07/2010
2493	2^360366+1459	108481	Lelio R Paula	09/2011
2494	2^360364-1499	108481	Yves Minet	05/2013
2495	14^94642-23	108472	Lelio R Paula	05/2017
2496	4*10^108412+9	108413	Robert Price	05/2015
2497	2^360093-351103	108399	Enzo Doria	06/2015
2498	2^360042+723	108384	Lelio R Paula	01/2012
2499	85^56164-2	108364	Lelio R Paula	10/2013
2500	2^359937-29323	108352	Enzo Doria	07/2015

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Probable Primes Top 10000

(205873 PRPs in the top)