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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(86*10^139315+121)/9	139316	Robert Price	08/2019
2252	2^462786-292043	139313	Enzo Doria	08/2015
2253	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
2254	(17*10^139239+67)/3	139240	Robert Price	01/2019
2255	2^462238-935	139148	Yves Minet	02/2014
2256	2^461228+1870441	138844	Enzo Doria	05/2016
2257	2^461204-113675	138837	Enzo Doria	08/2014
2258	(2^461139-7)/47	138815	Lelio R Paula	08/2015
2259	(17*10^138812-521)/9	138813	Robert Price	04/2018
2260	3*10^138811-11	138812	Robert Price	07/2018
2261	(28*10^138768+173)/3	138769	Robert Price	12/2019
2262	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
2263	(379*10^138737-1)/9	138739	Robert Price	02/2020
2264	(43*10^138648+101)/9	138649	Robert Price	11/2018
2265	2^460567-113541	138645	Enzo Doria	08/2014
2266	7*10^138604+3	138605	Robert Price	08/2015
2267	2^460330+69	138574	Lelio R Paula	09/2017
2268	(17*10^138569-77)/3	138570	Robert Price	08/2019
2269	2^460078-69581	138498	Enzo Doria	12/2015
2270	2^459768+1531	138404	Lelio R Paula	06/2012
2271	(266*10^138328-17)/3	138330	Robert Price	07/2020
2272	2^459343-113611	138277	Enzo Doria	08/2014
2273	(28*10^138240+113)/3	138241	Robert Price	03/2020
2274	2^459199+1874393	138233	Enzo Doria	06/2016
2275	2^459063-345307	138192	Enzo Doria	06/2015
2276	2*10^138162-43	138163	Robert Price	04/2018
2277	2^458927-112747	138151	Enzo Doria	06/2014
2278	2^458927-69217	138151	Enzo Doria	11/2015
2279	555555*2^458524+1513	138036	Darren Bedwell	08/2009
2280	2^458465+2^32+1	138012	T. D. Noe	06/2007
2281	2^458321-113053	137969	Enzo Doria	07/2014
2282	2^458298+79459	137962	Enzo Doria	06/2016
2283	2^458248-21815	137947	Enzo Doria	07/2013
2284	2^458194+1876549	137931	Enzo Doria	07/2016
2285	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
2286	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
2287	2^457937+57	137853	Lelio R Paula	09/2017
2288	(8*10^137845+13)/3	137846	Robert Price	06/2018
2289	2^457822+105	137819	Donovan Johnson	06/2006
2290	2^457754-113711	137798	Enzo Doria	09/2014
2291	11^132315-360	137792	Enzo Doria	09/2012
2292	2^457347-37	137676	Lelio R Paula	09/2017
2293	2^457322-2786393	137668	Enzo Doria	10/2015
2294	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
2295	2^457240-59939	137643	Enzo Doria	10/2015
2296	(856*10^137633-1)/9	137635	Robert Price	03/2020
2297	2^457120-21575	137607	Enzo Doria	07/2013
2298	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
2299	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
2300	419^52446+52446^419	137525	Norbert Schneider	11/2020
2301	2^456796-113513	137510	Enzo Doria	08/2014
2302	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
2303	2^456503-114361	137422	Enzo Doria	01/2015
2304	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
2305	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
2306	2^455922+76249	137247	Enzo Doria	05/2016
2307	14^119741-119741^14	137239	Serge Batalov	04/2016
2308	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
2310	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
2309	124^65536+57^65536	137195	Serge Batalov	03/2018
2311	2^455689+72677	137177	Enzo Doria	04/2016
2312	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
2313	(37^87421-1)/36	137093	Robert Price	03/2012
2314	2^455323-57	137066	Lelio R Paula	09/2017
2315	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
2316	2^455025-112723	136977	Enzo Doria	06/2014
2317	66*10^136894+7	136896	Robert Price	07/2020
2318	2^454675-1777	136871	Yves Minet	10/2011
2319	3*10^136829+29	136830	Robert Price	05/2018
2320	4*10^136813-57	136814	Robert Price	10/2018
2321	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
2322	2^454348-53	136773	Lelio R Paula	09/2017
2323	31^91680-2	136729	Lelio R Paula	05/2017
2324	2^454199-113697	136728	Enzo Doria	09/2014
2325	7*10^136716+69	136717	Robert Price	07/2019
2326	6*10^136692+53	136693	Robert Price	05/2020
2327	(13*10^136687+47)/3	136688	Robert Price	10/2018
2328	2^453935-2791357	136649	Enzo Doria	01/2016
2329	2^453906-69131	136640	Enzo Doria	11/2015
2330	2^453791+1873913	136605	Enzo Doria	06/2016
2331	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
2332	580^49413+49413^580	136550	Norbert Schneider	02/2019
2333	2^453503-2788297	136519	Enzo Doria	11/2015
2334	34989^7958+7958^34989	136486	Hans Havermann	12/2020
2335	31007^25158+25158^31007	136452	Hans Havermann	11/2020
2336	2^453267-113827	136447	Enzo Doria	09/2014
2337	32234^17085+17085^32234	136435	Hans Havermann	12/2020
2338	2^453102+1877629	136398	Enzo Doria	08/2016
2339	31016^24981+24981^31016	136397	Hans Havermann	12/2020
2340	(62*10^136384-791)/9	136385	Robert Price	06/2019
2341	34171^9798+9798^34171	136382	Hans Havermann	12/2020
2342	32756^14541+14541^32756	136350	Hans Havermann	11/2020
2343	32205^17086+17086^32205	136313	Hans Havermann	12/2020
2344	(25*10^136303+161)/3	136304	Robert Price	09/2019
2345	35337^7196+7196^35337	136299	Hans Havermann	12/2020
2346	(182*10^136291+1)/3	136293	Robert Price	02/2020
2347	23*10^136225-7	136227	Robert Price	02/2020
2348	L(651821)	136223	Henri Lifchitz	09/2008
2349	2^452460+77701	136205	Enzo Doria	05/2016
2350	2^452440-114755	136199	Enzo Doria	04/2015
2351	32286^16489+16489^32286	136157	Hans Havermann	11/2020
2352	(47*10^136141+493)/9	136142	Robert Price	03/2019
2353	40392^2339+2339^40392	136082	Hans Havermann	12/2020
2354	2*10^136057-43	136058	Robert Price	04/2018
2355	(2^451956-5)/181	136051	Lelio R Paula	07/2015
2356	2^451947-22165	136050	Enzo Doria	07/2013
2357	2^451787-21805	136002	Enzo Doria	07/2013
2358	2^451734-112817	135986	Enzo Doria	06/2014
2359	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
2360	2^451705-21879	135977	Enzo Doria	07/2013
2361	2^451560-112349	135934	Enzo Doria	06/2014
2362	2^451530+45	135925	Lelio R Paula	08/2017
2363	31622^19875+19875^31622	135922	Hans Havermann	11/2020
2364	(25*10^135906-73)/3	135907	Robert Price	09/2019
2365	2^451450-21743	135900	Enzo Doria	07/2013
2366	35218^7199+7199^35218	135846	Hans Havermann	11/2020
2367	35661^6446+6446^35661	135844	Hans Havermann	11/2020
2368	31869^18248+18248^31869	135801	Hans Havermann	12/2020
2369	2^450805+65	135706	Lelio R Paula	08/2017
2370	30761^25728+25728^30761	135669	Hans Havermann	12/2020
2371	2*10^135663+69	135664	Robert Price	06/2020
2372	33962^9867+9867^33962	135651	Hans Havermann	11/2020
2373	34474^8605+8605^34474	135647	Hans Havermann	11/2020
2374	34501^8508+8508^34501	135583	Hans Havermann	12/2020
2375	35487^6614+6614^35487	135577	Hans Havermann	12/2020
2376	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
2377	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
2378	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
2379	40387^2260+2260^40387	135463	Hans Havermann	12/2020
2380	2^449944-113247	135447	Enzo Doria	07/2014
2381	2^449770-113247	135395	Enzo Doria	07/2014
2382	2^449637-21471	135355	Enzo Doria	07/2013
2383	2^449571-75	135335	Lelio R Paula	08/2017
2384	(14*10^135301-53)/3	135302	Robert Price	12/2018
2385	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
2386	(13*10^135279+437)/9	135280	Robert Price	04/2018
2387	2^449330-35	135262	Lelio R Paula	08/2017
2388	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2389	(13*10^135184-43)/3	135185	Robert Price	11/2018
2390	2^449049-115309	135178	Enzo Doria	07/2015
2391	(10^135174+191)/3	135174	Robert Price	02/2018
2392	2^449030-15	135172	Lelio R Paula	08/2017
2393	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
2394	32221^15586+15586^32221	135095	Hans Havermann	12/2020
2395	2^448762-351401	135091	Enzo Doria	07/2015
2396	2*10^135083-43	135084	Robert Price	04/2018
2397	31357^20278+20278^31357	135056	Hans Havermann	12/2020
2398	32242^15445+15445^32242	135055	Hans Havermann	12/2020
2399	k(198476)	135054	Robert Price	07/2020
2400	32461^14470+14470^32461	135053	Hans Havermann	12/2020
2401	31353^20288+20288^31353	135045	Hans Havermann	12/2020
2402	5*10^135019+77	135020	Robert Price	12/2018
2403	(10^135011+719)/9	135011	Serge Batalov	12/2014
2404	(197*10^134978+7)/3	134980	Robert Price	12/2020
2405	2^448386-2786261	134978	Enzo Doria	03/2016
2406	(73*10^134939+143)/9	134940	Robert Price	07/2019
2407	33957^9392+9392^33957	134903	Hans Havermann	12/2020
2408	2^448113-113949	134896	Enzo Doria	11/2014
2409	30958^22755+22755^30958	134887	Hans Havermann	12/2020
2410	2^447888-2786639	134828	Enzo Doria	03/2016
2411	2^447870-396765	134823	Enzo Doria	07/2013
2412	2^447766-21791	134791	Enzo Doria	07/2013
2413	(19*10^134786-49)/3	134787	Robert Price	05/2019
2414	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
2415	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
2416	2^447552-1019	134727	Yves Minet	02/2014
2417	(2*10^134720-41)/3	134720	Robert Price	02/2018
2418	2^447437-113569	134692	Enzo Doria	08/2014
2419	2^447426-65	134689	Lelio R Paula	08/2017
2420	2^447357-2797573	134668	Enzo Doria	04/2016
2421	2^447278+93	134645	Lelio R Paula	08/2017
2422	33193^11370+11370^33193	134623	Hans Havermann	12/2020
2423	30736^23979+23979^30736	134619	Hans Havermann	11/2020
2424	2^447094-113193	134589	Enzo Doria	07/2014
2425	3^282041-9934	134568	Enzo Doria	05/2014
2426	2^447019-109039	134567	Enzo Doria	04/2014
2427	31376^19437+19437^31376	134561	Hans Havermann	12/2020
2428	2^446990-22041	134558	Enzo Doria	07/2013
2429	123^64370+122	134528	Karsten Bonath	04/2018
2430	30100^29461+29461^30100	134525	Hans Havermann	11/2020
2431	31251^20158+20158^31251	134519	Hans Havermann	11/2020
2432	2^446782-39701	134495	Enzo Doria	09/2015
2433	31817^16858+16858^31817	134485	Hans Havermann	12/2020
2434	32448^13937+13937^32448	134471	Hans Havermann	12/2020
2435	2^446494-16485	134409	Enzo Doria	04/2013
2436	30042^29785+29785^30042	134408	Hans Havermann	12/2020
2437	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
2438	2^446441+65	134393	Lelio R Paula	08/2017
2439	(10^134385+719)/9	134385	Serge Batalov	12/2014
2440	30043^29688+29688^30043	134370	Hans Havermann	12/2020
2441	(2*10^134364+529)/9	134364	Robert Price	01/2018
2442	34657^7512+7512^34657	134323	Hans Havermann	11/2020
2443	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
2444	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
2445	42035^1564+1564^42035	134270	Hans Havermann	12/2020
2447	(2^446022-7)/339	134264	Lelio R Paula	07/2015
2446	30621^24248+24248^30621	134264	Hans Havermann	12/2020
2448	30341^26562+26562^30341	134237	Hans Havermann	11/2020
2449	29976^29953+29953^29976	134186	Hans Havermann	12/2020
2450	35038^6755+6755^35038	134183	Hans Havermann	12/2020
2451	63^74568+2	134174	Lelio R Paula	06/2017
2452	2^445671-22071	134161	Enzo Doria	07/2013
2453	532^49205+49205^532	134129	Norbert Schneider	02/2019
2454	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
2455	2^445515-113859	134114	Enzo Doria	10/2014
2456	(22*10^134111-37)/3	134112	Robert Price	04/2019
2457	2^445328-216917	134058	Enzo Doria	05/2014
2458	2^445202+1874899	134020	Enzo Doria	06/2016
2459	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
2460	(35*10^133979-593)/9	133980	Robert Price	07/2018
2461	2*10^133955+51	133956	Robert Price	05/2018
2462	2^444964-113639	133948	Enzo Doria	08/2014
2463	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
2464	10^133902-100001	133902	Robert Price	07/2020
2465	2^444784-113859	133894	Enzo Doria	10/2014
2466	(266*10^133603+1)/3	133605	Robert Price	04/2020
2467	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
2468	62^74521-61^74521	133571	Robert Price	05/2013
2469	(182*10^133543+1)/3	133545	Robert Price	02/2020
2470	2^443198-1867301	133416	Enzo Doria	03/2016
2471	(19*10^133390+101)/3	133391	Robert Price	09/2019
2472	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
2473	2^442799+1874633	133296	Enzo Doria	06/2016
2474	L(637751)	133283	Henri Lifchitz	09/2008
2475	109^65410-2	133269	Lelio R Paula	10/2017
2476	2^442688-113489	133263	Enzo Doria	08/2014
2477	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
2478	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
2479	2^442437-1849993	133187	Enzo Doria	08/2015
2480	2^442430-2791721	133185	Enzo Doria	03/2016
2481	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
2482	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
2483	452^50145+50145^452	133142	Norbert Schneider	09/2020
2484	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
2485	2^441781-2787883	132990	Enzo Doria	03/2016
2486	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
2487	2^441618+37	132941	Lelio R Paula	08/2017
2488	2^441521-113575	132912	Enzo Doria	08/2014
2489	7*10^132884-99	132885	Robert Price	06/2019
2490	(103*10^132879+17)/3	132881	Robert Price	08/2020
2491	2^441396-65	132874	Lelio R Paula	08/2017
2492	2^441330+1871959	132854	Enzo Doria	05/2016
2493	2^441063+383	132774	Lelio R Paula	06/2012
2494	(22*10^132746+53)/3	132747	Robert Price	07/2019
2495	2^440846+1870909	132708	Enzo Doria	05/2016
2496	2^440656-113489	132651	Enzo Doria	08/2014
2497	numbpart(14180123587)	132646	Serge Batalov	04/2017
2498	(19*10^132550+191)/3	132551	Robert Price	05/2019
2499	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
2500	(38^83891+1)/39	132529	Robert Price	09/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(277034 PRPs in the top)