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	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2252	2^490550+1179439	147671	Enzo Doria	06/2016
2253	(23*10^147649-59)/9	147650	Robert Price	05/2018
2254	2^490303+2793653	147596	Enzo Doria	03/2016
2255	2^490266+255255	147585	Paul Bourdelais	10/2021
2256	199^64181-2	147543	Lelio R Paula	11/2017
2257	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2258	2^489871-286987	147466	Enzo Doria	07/2015
2259	2^489864-351899	147464	Enzo Doria	07/2015
2260	175^65724-2	147422	Lelio R Paula	11/2017
2261	2^489712+1874851	147419	Enzo Doria	06/2016
2262	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2263	63^81896-2	147359	Lelio R Paula	10/2017
2264	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2265	(11*10^147313-107)/3	147314	Robert Price	09/2018
2266	2^489305-59815	147296	Enzo Doria	10/2015
2267	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2268	2*10^147264-61	147265	Robert Price	10/2021
2269	2*10^147260+29	147261	Robert Price	02/2021
2270	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2271	2^489125+80357	147242	Enzo Doria	06/2016
2272	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2273	(19*10^147213-97)/3	147214	Robert Price	10/2021
2274	(148*10^147139-1)/3	147141	Robert Price	03/2020
2275	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2276	2^488648-112799	147098	Enzo Doria	07/2014
2277	2^488627-350317	147092	Enzo Doria	06/2015
2278	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2279	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2280	2^488280-2165	146987	Yves Minet	07/2014
2281	2^488278+45	146987	Lelio R Paula	12/2017
2282	2^487927-39	146881	Lelio R Paula	12/2017
2283	(7*10^146860-13)/3	146861	Robert Price	07/2018
2284	(26*10^146856-77)/3	146857	Robert Price	11/2019
2285	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2286	42596^2799+2799^42596	146829	Hans Havermann	12/2020
2287	2^487726-1863341	146821	Enzo Doria	12/2015
2288	43838^2229+2229^43838	146775	Hans Havermann	11/2020
2289	35005^15594+15594^35005	146775	Hans Havermann	11/2020
2290	(167*10^146764+7)/3	146766	Robert Price	04/2021
2291	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
2292	32963^28234+28234^32963	146711	Hans Havermann	12/2020
2293	(22*10^146661-19)/3	146662	Robert Price	04/2019
2294	33958^20825+20825^33958	146651	Hans Havermann	12/2020
2295	2^487121-39523	146639	Enzo Doria	09/2015
2296	61063^252+252^61063	146637	Hans Havermann	12/2020
2297	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
2298	34099^19900+19900^34099	146587	Hans Havermann	11/2020
2299	2^486893-79	146570	Yves Minet	09/2017
2300	36818^9567+9567^36818	146565	Hans Havermann	12/2020
2301	2^486840+1879141	146554	Enzo Doria	08/2016
2302	2^486774-87	146534	Lelio R Paula	12/2017
2303	38655^6176+6176^38655	146530	Hans Havermann	11/2020
2304	8*10^146522-81	146523	Robert Price	02/2021
2305	32820^29059+29059^32820	146485	Hans Havermann	12/2020
2306	37261^8530+8530^37261	146472	Hans Havermann	12/2020
2307	66953^154+154^66953	146462	Hans Havermann	12/2020
2308	96^73877-95^73877	146445	Robert Price	10/2015
2309	8*10^146421+81	146422	Robert Price	08/2019
2310	33153^26090+26090^33153	146420	Hans Havermann	11/2020
2311	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
2312	179^64935+2	146290	Lelio R Paula	10/2017
2313	32595^30758+30758^32595	146285	Hans Havermann	11/2020
2314	34972^15157+15157^34972	146205	Hans Havermann	12/2020
2315	(19*10^146181-49)/3	146182	Robert Price	05/2019
2316	2^485531-114621	146160	Enzo Doria	05/2015
2317	2^485473-933075	146142	Paul Bourdelais	06/2021
2318	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
2319	2^485389+81887	146117	Enzo Doria	08/2016
2320	32554^30773+30773^32554	146108	Hans Havermann	11/2020
2321	(10^146063+71)/9	146063	Serge Batalov	07/2015
2322	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
2323	(22*10^146029+257)/9	146030	Robert Price	06/2018
2324	7*10^145982-53	145983	Robert Price	06/2020
2325	2^484743+1872923	145923	Enzo Doria	05/2016
2326	33140^25287+25287^33140	145913	Hans Havermann	01/2021
2327	37875^7112+7112^37875	145895	Hans Havermann	01/2021
2328	32862^27473+27473^32862	145872	Hans Havermann	01/2021
2329	32836^27587+27587^32836	145815	Hans Havermann	01/2021
2330	2^484341+1879157	145802	Enzo Doria	08/2016
2331	2*10^145784-91	145785	Robert Price	04/2020
2332	2^484271-51	145781	Lelio R Paula	11/2017
2333	70^78989-69^78989	145743	Robert Price	01/2014
2334	51^85334+2	145714	Robert Price	07/2015
2335	2^483886-1857101	145665	Enzo Doria	10/2015
2336	33350^23307+23307^33350	145656	Hans Havermann	01/2021
2337	(19*10^145585+131)/3	145586	Robert Price	06/2020
2338	2^483563-1863457	145567	Enzo Doria	12/2015
2339	2^483516-1861409	145553	Enzo Doria	11/2015
2340	2^483384-115019	145514	Enzo Doria	06/2015
2341	(259*10^145501-1)/3	145503	Robert Price	12/2020
2342	(19*10^145499-61)/3	145500	Robert Price	05/2019
2343	2^483302-3221	145489	Lelio R Paula	12/2012
2344	35523^12434+12434^35523	145453	Hans Havermann	01/2021
2345	2^483046+1874029	145412	Enzo Doria	06/2016
2346	2^482991-2789317	145395	Enzo Doria	12/2015
2347	2^482978-2789711	145391	Enzo Doria	12/2015
2348	2^482966-2789711	145388	Enzo Doria	12/2015
2349	2^482817-1858843	145343	Enzo Doria	10/2015
2350	2^482751-113635	145323	Enzo Doria	08/2014
2351	2^482705-459763	145309	Enzo Doria	05/2015
2352	(4^241306+11)/3	145281	Robert Price	03/2017
2353	(238*10^145276-1)/3	145278	Robert Price	04/2020
2354	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
2355	53^84239-52^84239	145252	Robert Price	01/2013
2356	47952^1067+1067^47952	145207	Hans Havermann	01/2021
2357	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
2358	2^482087+72623	145123	Enzo Doria	04/2016
2359	2^482016-286565	145102	Enzo Doria	07/2015
2360	(19*10^145093+101)/3	145094	Robert Price	09/2019
2361	2^481956+121	145084	Stefano Morozzi	04/2021
2362	2^481840+15	145049	Robert Price	09/2015
2363	2^481801-481801	145037	Henri Lifchitz	03/2005
2364	2^481775+1869083	145029	Enzo Doria	05/2016
2365	29^99167+2	145022	Ray Chandler	08/2011
2366	2^481663+1875653	144996	Enzo Doria	07/2016
2367	8*10^144977+27	144978	Robert Price	09/2021
2368	36486^9379+9379^36486	144929	Hans Havermann	12/2020
2369	35111^13378+13378^35111	144882	Hans Havermann	01/2021
2370	2^481149-459073	144841	Enzo Doria	05/2015
2371	34619^15246+15246^34619	144817	Hans Havermann	01/2021
2372	2^481045-113215	144809	Enzo Doria	07/2014
2373	(64*10^144797+287)/9	144798	Robert Price	04/2019
2374	2^480859-113695	144753	Enzo Doria	09/2014
2375	(106*10^144744+17)/3	144746	Robert Price	04/2021
2376	2^480766-2787191	144725	Enzo Doria	11/2015
2377	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
2378	2^480678+1874239	144699	Enzo Doria	06/2016
2379	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
2380	L(692147)	144651	Henri Lifchitz	10/2008
2381	(76*10^144648+77)/9	144649	Robert Price	10/2019
2382	32672^26721+26721^32672	144635	Hans Havermann	01/2021
2383	2^480417+35	144620	Robert Price	11/2015
2384	2^480296-59879	144584	Enzo Doria	10/2015
2385	33157^22878+22878^33157	144546	Hans Havermann	12/2020
2386	45494^1497+1497^45494	144454	Hans Havermann	12/2020
2387	2^479844+3	144448	Donovan Johnson	06/2006
2388	33442^20803+20803^33442	144407	Hans Havermann	01/2021
2389	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
2390	44917^1638+1638^44917	144378	Hans Havermann	12/2020
2391	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
2392	(56*10^144336+583)/9	144337	Robert Price	08/2021
2393	2^479348-2792219	144299	Enzo Doria	02/2016
2394	3^302389-6242	144277	Enzo Doria	05/2014
2395	33778^18641+18641^33778	144248	Hans Havermann	01/2021
2396	2*10^144220-3	144221	Robert Price	07/2015
2397	2^478904-109109	144165	Enzo Doria	04/2014
2398	43698^1987+1987^43698	144125	Hans Havermann	12/2020
2399	36128^9723+9723^36128	144072	Hans Havermann	01/2021
2400	32817^24518+24518^32817	144050	Hans Havermann	12/2020
2401	34295^15828+15828^34295	144020	Hans Havermann	01/2021
2402	2^478337-115333	143994	Enzo Doria	07/2015
2403	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
2404	88^74047-87^74047	143984	Robert Price	05/2015
2405	33242^21441+21441^33242	143980	Hans Havermann	01/2021
2406	(19*10^143963+467)/9	143964	Robert Price	02/2018
2407	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
2408	33490^19859+19859^33490	143939	Hans Havermann	01/2021
2409	(853*10^143931-7)/9	143933	Robert Price	07/2021
2410	2^478088+27	143919	Robert Price	11/2015
2411	7*10^143857-93	143858	Robert Price	08/2020
2412	3*10^143844+61	143845	Robert Price	09/2020
2413	41358^3005+3005^41358	143837	Hans Havermann	01/2021
2414	2^477475-22071	143735	Enzo Doria	07/2013
2415	2^477417-22123	143717	Enzo Doria	07/2013
2416	2^477359-3577	143700	Yves Minet	03/2017
2417	39435^4402+4402^39435	143688	Hans Havermann	01/2021
2418	(14*10^143662-71)/3	143663	Robert Price	12/2018
2419	6^184614+5	143658	Paul Bourdelais	01/2021
2420	46371^1252+1252^46371	143640	Hans Havermann	12/2020
2421	34975^12748+12748^34975	143588	Hans Havermann	01/2021
2422	2^476936-396765	143573	Enzo Doria	07/2013
2423	2^476888-2791229	143558	Enzo Doria	01/2016
2424	2^476868-1859939	143552	Enzo Doria	11/2015
2425	40807^3294+3294^40807	143548	Hans Havermann	12/2020
2426	755^49878+49878^755	143547	Norbert Schneider	04/2019
2427	(19^112247-4^112247)/15	143536	Robert Price	03/2021
2428	35561^10872+10872^35561	143536	Hans Havermann	06/2021
2429	37637^6492+6492^37637	143487	Hans Havermann	05/2021
2430	61567^214+214^61567	143477	Hans Havermann	05/2021
2431	2^476558-113627	143459	Enzo Doria	08/2014
2432	2^476478-45	143435	Lelio R Paula	11/2017
2433	36380^8757+8757^36380	143423	Hans Havermann	06/2021
2434	32510^25707+25707^32510	143371	Hans Havermann	05/2021
2435	8*10^143361+17	143362	Robert Price	07/2021
2436	(2^475854+9)/73	143245	Lelio R Paula	08/2015
2437	2^475813-113239	143234	Enzo Doria	07/2014
2438	32218^27849+27849^32218	143203	Hans Havermann	04/2021
2439	2^475624-114059	143178	Enzo Doria	11/2014
2440	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
2441	2^475480-2786129	143134	Enzo Doria	10/2015
2442	33912^16621+16621^33912	143131	Hans Havermann	05/2021
2443	(19*10^143129-43)/3	143130	Robert Price	05/2019
2444	31830^31373+31373^31830	143126	Hans Havermann	05/2021
2445	6*10^143105-53	143106	Robert Price	05/2021
2446	(14*10^143097+73)/3	143098	Robert Price	12/2018
2447	2^475299-111937	143080	Enzo Doria	05/2014
2448	35488^10753+10753^35488	143071	Hans Havermann	04/2021
2449	2^475160-2797859	143038	Enzo Doria	04/2016
2450	(2^475069+3)/395	143008	Lelio R Paula	08/2015
2451	2^475027-461437	142998	Enzo Doria	07/2015
2452	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
2453	(8*10^142932+43)/3	142933	Robert Price	06/2018
2454	35055^11942+11942^35055	142922	Hans Havermann	05/2021
2455	37650^6239+6239^37650	142887	Hans Havermann	05/2021
2456	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
2457	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
2458	2^474417-59923	142814	Enzo Doria	10/2015
2459	4*10^142810-21	142811	Robert Price	09/2018
2460	32287^26494+26494^32287	142811	Hans Havermann	06/2021
2461	37162^6965+6965^37162	142811	Hans Havermann	06/2021
2462	37456^6493+6493^37456	142799	Hans Havermann	05/2021
2463	35141^11572+11572^35141	142793	Hans Havermann	05/2021
2464	32231^26908+26908^32231	142780	Hans Havermann	05/2021
2465	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
2466	2^474053+2897	142705	Lelio R Paula	08/2012
2467	(10^142699+359)/9	142699	Serge Batalov	12/2014
2468	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
2469	2^473740-1856639	142610	Enzo Doria	09/2015
2470	(25*10^142573-403)/9	142574	Robert Price	12/2020
2471	2^473617-114223	142573	Enzo Doria	12/2014
2472	36115^8856+8856^36115	142555	Hans Havermann	05/2021
2473	2^473257+1873217	142465	Enzo Doria	06/2016
2474	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
2475	32750^22371+22371^32750	142453	Hans Havermann	06/2021
2476	(61*10^142446-1)/3	142448	Robert Price	01/2020
2477	(14*10^142440+61)/3	142441	Robert Price	12/2018
2478	(10^142425+359)/9	142425	Serge Batalov	12/2014
2479	2^473101+773027	142418	Enzo Doria	05/2016
2480	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
2481	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
2482	36915^7162+7162^36915	142309	Hans Havermann	05/2021
2483	2^472634-109511	142278	Enzo Doria	04/2014
2484	31870^28997+28997^31870	142216	Hans Havermann	06/2021
2485	(48^84589+1)/49	142213	Robert Price	01/2014
2486	7*10^142189+87	142190	Robert Price	07/2019
2487	2^472258+7	142164	Lelio R Paula	08/2015
2488	40135^3484+3484^40135	142162	Hans Havermann	05/2021
2489	(23*10^142105+91)/3	142106	Robert Price	08/2019
2490	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
2491	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
2492	(16*10^142058+197)/3	142059	Robert Price	04/2019
2493	9*10^142037+91	142038	Robert Price	10/2020
2494	2^471792+1880881	142024	Enzo Doria	11/2016
2495	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
2496	(4*10^141926-79)/3	141927	Robert Price	02/2018
2497	2^471464-111546435	141925	Paul Bourdelais	10/2021
2498	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
2499	(14*10^141853+37)/3	141854	Robert Price	12/2018
2500	(41*10^141836-59)/9	141837	Robert Price	10/2018

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Probable Primes Top 10000

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