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 ?
5001	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
5002	31287^24128+24128^31287	137116	Hans Havermann	05/2021
5003	(37^87421-1)/36	137093	Robert Price	03/2012
5004	36233^6070+6070^36233	137077	Hans Havermann	05/2021
5005	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
5006	38418^3697+3697^38418	137070	Hans Havermann	04/2021
5007	2^455323-57	137066	Lelio R Paula	09/2017
5008	(56*10^137019+583)/9	137020	Robert Price	08/2021
5009	25017^31148-31148^25017	136997	Frank Doornink	12/2023
5010	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
5011	2^455025-112723	136977	Enzo Doria	06/2014
5012	33876^11039+11039^33876	136959	Hans Havermann	05/2021
5013	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
5014	(251^57059-1)/250	136921	Anonymous	04/2024
5015	35142^7873+7873^35142	136919	Hans Havermann	05/2021
5016	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
5017	66*10^136894+7	136896	Robert Price	07/2020
5018	28766^30697-30697^28766	136875	Frank Doornink	05/2024
5019	2^454675-1777	136871	Yves Minet	10/2011
5020	31676^20931+20931^31676	136866	Hans Havermann	05/2021
5021	3*10^136829+29	136830	Robert Price	05/2018
5022	4*10^136813-57	136814	Robert Price	10/2018
5023	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
5024	fibonacci(654572)-2	136798	Jon Grantham	08/2023
5025	37359^4588+4588^37359	136795	Hans Havermann	05/2021
5026	2^454348-53	136773	Lelio R Paula	09/2017
5027	31^91680-2	136729	Lelio R Paula	05/2017
5028	2^454199-113697	136728	Enzo Doria	09/2014
5029	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5030	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5032	7*10^136716+69	136717	Robert Price	07/2019
5031	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5033	6*10^136692+53	136693	Robert Price	05/2020
5034	(13*10^136687+47)/3	136688	Robert Price	10/2018
5035	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5036	2^453935-2791357	136649	Enzo Doria	01/2016
5037	2^453906-69131	136640	Enzo Doria	11/2015
5038	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5039	2^453791+1873913	136605	Enzo Doria	06/2016
5040	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5041	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5042	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5043	580^49413+49413^580	136550	Norbert Schneider	02/2019
5044	2^453503-2788297	136519	Enzo Doria	11/2015
5045	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5046	(2*10^136484+187)/9	136484	Robert Price	06/2022
5047	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5048	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5049	2^453267-113827	136447	Enzo Doria	09/2014
5050	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5051	2^453102+1877629	136398	Enzo Doria	08/2016
5052	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5053	(62*10^136384-791)/9	136385	Robert Price	06/2019
5054	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5055	(17*10^136354-113)/3	136355	Robert Price	06/2021
5056	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5057	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5058	(25*10^136303+161)/3	136304	Robert Price	09/2019
5059	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5060	(182*10^136291+1)/3	136293	Robert Price	02/2020
5061	(88*10^136234+83)/9	136235	Robert Price	03/2022
5062	23*10^136225-7	136227	Robert Price	02/2020
5063	L(651821)	136223	Henri Lifchitz	09/2008
5064	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5065	2^452460+77701	136205	Enzo Doria	05/2016
5066	2^452440-114755	136199	Enzo Doria	04/2015
5067	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5068	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5069	(47*10^136141+493)/9	136142	Robert Price	03/2019
5070	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5071	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5072	2*10^136057-43	136058	Robert Price	04/2018
5073	2^451971+21563	136057	Enzo Doria	08/2023
5074	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5075	2^451947-22165	136050	Enzo Doria	07/2013
5076	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5077	2^451787-21805	136002	Enzo Doria	07/2013
5078	2^451734-112817	135986	Enzo Doria	06/2014
5079	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5080	2^451705-21879	135977	Enzo Doria	07/2013
5081	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5082	2^451560-112349	135934	Enzo Doria	06/2014
5083	2^451530+45	135925	Lelio R Paula	08/2017
5084	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5085	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5086	(25*10^135906-73)/3	135907	Robert Price	09/2019
5087	2^451450-21743	135900	Enzo Doria	07/2013
5088	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5089	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5090	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5091	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5092	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5093	(77*10^135789+157)/9	135790	Robert Price	05/2022
5094	2^450958+60529	135752	Enzo Doria	08/2023
5095	2^450805+65	135706	Lelio R Paula	08/2017
5096	10^135669+21	135670	Boyan Hu	12/2024
5097	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5098	2*10^135663+69	135664	Robert Price	06/2020
5099	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5100	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5101	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5102	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5103	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5104	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5105	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5106	(76*10^135553-49)/9	135554	Robert Price	07/2022
5107	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5108	(844*10^135527-7)/9	135529	Robert Price	05/2021
5109	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5110	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5111	2^449944-113247	135447	Enzo Doria	07/2014
5112	2^449770-113247	135395	Enzo Doria	07/2014
5113	2^449637-21471	135355	Enzo Doria	07/2013
5114	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5115	2^449571-75	135335	Lelio R Paula	08/2017
5116	(14*10^135301-53)/3	135302	Robert Price	12/2018
5117	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5118	(13*10^135279+437)/9	135280	Robert Price	04/2018
5119	2^449330-35	135262	Lelio R Paula	08/2017
5120	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5121	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5122	(13*10^135184-43)/3	135185	Robert Price	11/2018
5123	2^449049-115309	135178	Enzo Doria	07/2015
5124	(10^135174+191)/3	135174	Robert Price	02/2018
5125	2^449030-15	135172	Lelio R Paula	08/2017
5126	(157*10^135151-1)/3	135153	Robert Price	01/2022
5127	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5128	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5129	(37*10^135099+251)/9	135100	Robert Price	09/2021
5130	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5131	2^448762-351401	135091	Enzo Doria	07/2015
5132	2*10^135083-43	135084	Robert Price	04/2018
5133	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5134	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5135	k(198476)	135054	Robert Price	07/2020
5136	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5137	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5138	5*10^135019+77	135020	Robert Price	12/2018
5139	(10^135011+719)/9	135011	Serge Batalov	12/2014
5140	(197*10^134978+7)/3	134980	Robert Price	12/2020
5141	2^448386-2786261	134978	Enzo Doria	03/2016
5142	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5143	(73*10^134939+143)/9	134940	Robert Price	07/2019
5144	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5145	2^448122+20809	134899	Enzo Doria	08/2023
5146	2^448113-113949	134896	Enzo Doria	11/2014
5147	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5148	2^447888-2786639	134828	Enzo Doria	03/2016
5149	2^447870-396765	134823	Enzo Doria	07/2013
5150	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5151	2^447766-21791	134791	Enzo Doria	07/2013
5152	(19*10^134786-49)/3	134787	Robert Price	05/2019
5153	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5154	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5155	2^447552-1019	134727	Yves Minet	02/2014
5156	(2*10^134720-41)/3	134720	Robert Price	02/2018
5157	(25*10^134695-97)/9	134696	Robert Price	01/2022
5158	2^447437-113569	134692	Enzo Doria	08/2014
5159	2^447426-65	134689	Lelio R Paula	08/2017
5160	2^447357-2797573	134668	Enzo Doria	04/2016
5161	2^447278+93	134645	Lelio R Paula	08/2017
5162	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5163	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5164	2^447094-113193	134589	Enzo Doria	07/2014
5165	3^282041-9934	134568	Enzo Doria	05/2014
5166	2^447019-109039	134567	Enzo Doria	04/2014
5167	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5168	2^446990-22041	134558	Enzo Doria	07/2013
5169	123^64370+122	134528	Karsten Bonath	04/2018
5170	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5171	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5172	2^446782-39701	134495	Enzo Doria	09/2015
5173	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5174	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5175	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5176	2^446494-16485	134409	Enzo Doria	04/2013
5177	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5178	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5179	2^446441+65	134393	Lelio R Paula	08/2017
5180	(10^134385+719)/9	134385	Serge Batalov	12/2014
5181	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5182	(2*10^134364+529)/9	134364	Robert Price	01/2018
5183	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5184	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5185	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5186	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5188	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5187	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5189	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5190	(189^58967-1)/188	134234	Anonymous	06/2024
5191	10^134209+99867	134210	Patrick De Geest	05/2021
5192	10^134209-80000001	134209	Robert Price	04/2021
5193	10^134209-323283	134209	Patrick De Geest	05/2021
5194	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5195	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5196	63^74568+2	134174	Lelio R Paula	06/2017
5197	2^445671-22071	134161	Enzo Doria	07/2013
5198	532^49205+49205^532	134129	Norbert Schneider	02/2019
5199	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5200	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5201	2^445515-113859	134114	Enzo Doria	10/2014
5203	(22*10^134111-37)/3	134112	Robert Price	04/2019
5202	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5204	3*2^445478+5	134103	Jon Grantham	07/2023
5205	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5206	5*2^445380-3	134074	Jon Grantham	07/2023
5207	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5208	(277*10^134059-7)/9	134061	Robert Price	02/2022
5209	2^445328-216917	134058	Enzo Doria	05/2014
5210	2^445202+1874899	134020	Enzo Doria	06/2016
5211	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5212	(35*10^134003-89)/9	134004	Robert Price	02/2022
5213	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5214	(35*10^133979-593)/9	133980	Robert Price	07/2018
5215	2*10^133955+51	133956	Robert Price	05/2018
5216	(49*10^133952+437)/9	133953	Robert Price	09/2021
5217	2^444964-113639	133948	Enzo Doria	08/2014
5218	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5219	10^133902+167841	133903	Patrick De Geest	05/2021
5221	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5220	10^133902-100001	133902	Robert Price	07/2020
5222	2^444784-113859	133894	Enzo Doria	10/2014
5223	(132^63127-1)/131	133864	Anonymous	06/2024
5224	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5225	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5226	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5227	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5228	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5229	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5230	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5231	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5232	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5233	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5234	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5235	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5236	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5237	(266*10^133603+1)/3	133605	Robert Price	04/2020
5238	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5239	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5240	(134*10^133573-11)/3	133575	Robert Price	01/2022
5241	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5242	2^443721+39527	133574	Enzo Doria	11/2024
5243	62^74521-61^74521	133571	Robert Price	05/2013
5244	(182*10^133543+1)/3	133545	Robert Price	02/2020
5245	(103*10^133535+11)/3	133537	Robert Price	01/2021
5246	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5247	L(638839)/274700771	133502	Serge Batalov	07/2024
5248	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5249	8*10^133487-37	133488	Robert Price	03/2022
5250	30135^26882+26882^30135	133482	Hans Havermann	04/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301969 PRPs in the top)