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 ?
4002	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
4001	124^65536+57^65536	137195	Serge Batalov	03/2018
4003	2^455689+72677	137177	Enzo Doria	04/2016
4004	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
4005	31287^24128+24128^31287	137116	Hans Havermann	05/2021
4006	(37^87421-1)/36	137093	Robert Price	03/2012
4007	36233^6070+6070^36233	137077	Hans Havermann	05/2021
4008	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
4009	38418^3697+3697^38418	137070	Hans Havermann	04/2021
4010	2^455323-57	137066	Lelio R Paula	09/2017
4011	(56*10^137019+583)/9	137020	Robert Price	08/2021
4012	25017^31148-31148^25017	136997	Frank Doornink	12/2023
4013	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
4014	2^455025-112723	136977	Enzo Doria	06/2014
4015	33876^11039+11039^33876	136959	Hans Havermann	05/2021
4016	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
4017	(251^57059-1)/250	136921	Anonymous	04/2024
4018	35142^7873+7873^35142	136919	Hans Havermann	05/2021
4019	66*10^136894+7	136896	Robert Price	07/2020
4020	2^454675-1777	136871	Yves Minet	10/2011
4021	31676^20931+20931^31676	136866	Hans Havermann	05/2021
4022	3*10^136829+29	136830	Robert Price	05/2018
4023	4*10^136813-57	136814	Robert Price	10/2018
4024	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
4025	fibonacci(654572)-2	136798	Jon Grantham	08/2023
4026	37359^4588+4588^37359	136795	Hans Havermann	05/2021
4027	2^454348-53	136773	Lelio R Paula	09/2017
4028	31^91680-2	136729	Lelio R Paula	05/2017
4029	2^454199-113697	136728	Enzo Doria	09/2014
4030	30785^27622+27622^30785	136725	Hans Havermann	05/2021
4031	32973^14014+14014^32973	136725	Hans Havermann	05/2021
4033	7*10^136716+69	136717	Robert Price	07/2019
4032	36002^6273+6273^36002	136717	Hans Havermann	05/2021
4034	6*10^136692+53	136693	Robert Price	05/2020
4035	(13*10^136687+47)/3	136688	Robert Price	10/2018
4036	2^453935-2791357	136649	Enzo Doria	01/2016
4037	2^453906-69131	136640	Enzo Doria	11/2015
4038	33232^12915+12915^33232	136620	Hans Havermann	05/2021
4039	2^453791+1873913	136605	Enzo Doria	06/2016
4040	34166^9951+9951^34166	136592	Hans Havermann	05/2021
4041	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
4042	31102^24635+24635^31102	136587	Hans Havermann	05/2021
4043	580^49413+49413^580	136550	Norbert Schneider	02/2019
4044	2^453503-2788297	136519	Enzo Doria	11/2015
4045	34989^7958+7958^34989	136486	Hans Havermann	12/2020
4046	(2*10^136484+187)/9	136484	Robert Price	06/2022
4047	31007^25158+25158^31007	136452	Hans Havermann	11/2020
4048	2^453267-113827	136447	Enzo Doria	09/2014
4049	32234^17085+17085^32234	136435	Hans Havermann	12/2020
4050	2^453102+1877629	136398	Enzo Doria	08/2016
4051	31016^24981+24981^31016	136397	Hans Havermann	12/2020
4052	(62*10^136384-791)/9	136385	Robert Price	06/2019
4053	34171^9798+9798^34171	136382	Hans Havermann	12/2020
4054	(17*10^136354-113)/3	136355	Robert Price	06/2021
4055	32756^14541+14541^32756	136350	Hans Havermann	11/2020
4056	32205^17086+17086^32205	136313	Hans Havermann	12/2020
4057	(25*10^136303+161)/3	136304	Robert Price	09/2019
4058	35337^7196+7196^35337	136299	Hans Havermann	12/2020
4059	(182*10^136291+1)/3	136293	Robert Price	02/2020
4060	(88*10^136234+83)/9	136235	Robert Price	03/2022
4061	23*10^136225-7	136227	Robert Price	02/2020
4062	L(651821)	136223	Henri Lifchitz	09/2008
4063	25519^30908-30908^25519	136208	Frank Doornink	02/2024
4064	2^452460+77701	136205	Enzo Doria	05/2016
4065	2^452440-114755	136199	Enzo Doria	04/2015
4066	32286^16489+16489^32286	136157	Hans Havermann	11/2020
4067	(47*10^136141+493)/9	136142	Robert Price	03/2019
4068	27140^30699-30699^27140	136108	Frank Doornink	01/2024
4069	40392^2339+2339^40392	136082	Hans Havermann	12/2020
4070	2*10^136057-43	136058	Robert Price	04/2018
4071	2^451971+21563	136057	Enzo Doria	08/2023
4072	(2^451956-5)/181	136051	Lelio R Paula	07/2015
4073	2^451947-22165	136050	Enzo Doria	07/2013
4074	2^451787-21805	136002	Enzo Doria	07/2013
4075	2^451734-112817	135986	Enzo Doria	06/2014
4076	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
4077	2^451705-21879	135977	Enzo Doria	07/2013
4078	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
4079	2^451560-112349	135934	Enzo Doria	06/2014
4080	2^451530+45	135925	Lelio R Paula	08/2017
4081	26594^30719-30719^26594	135925	Frank Doornink	03/2024
4082	31622^19875+19875^31622	135922	Hans Havermann	11/2020
4083	(25*10^135906-73)/3	135907	Robert Price	09/2019
4084	2^451450-21743	135900	Enzo Doria	07/2013
4085	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
4086	35218^7199+7199^35218	135846	Hans Havermann	11/2020
4087	35661^6446+6446^35661	135844	Hans Havermann	11/2020
4088	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
4089	31869^18248+18248^31869	135801	Hans Havermann	12/2020
4090	(77*10^135789+157)/9	135790	Robert Price	05/2022
4091	2^450958+60529	135752	Enzo Doria	08/2023
4092	2^450805+65	135706	Lelio R Paula	08/2017
4093	30761^25728+25728^30761	135669	Hans Havermann	12/2020
4094	2*10^135663+69	135664	Robert Price	06/2020
4095	33962^9867+9867^33962	135651	Hans Havermann	11/2020
4096	34474^8605+8605^34474	135647	Hans Havermann	11/2020
4097	34501^8508+8508^34501	135583	Hans Havermann	12/2020
4098	35487^6614+6614^35487	135577	Hans Havermann	12/2020
4099	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
4100	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
4101	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
4102	(76*10^135553-49)/9	135554	Robert Price	07/2022
4103	5*3^284077+2^284077	135540	Jon Grantham	08/2023
4104	(844*10^135527-7)/9	135529	Robert Price	05/2021
4105	27191^30560-30560^27191	135517	Frank Doornink	01/2024
4106	40387^2260+2260^40387	135463	Hans Havermann	12/2020
4107	2^449944-113247	135447	Enzo Doria	07/2014
4108	2^449770-113247	135395	Enzo Doria	07/2014
4109	2^449637-21471	135355	Enzo Doria	07/2013
4110	26061^30650-30650^26061	135351	Frank Doornink	03/2024
4111	2^449571-75	135335	Lelio R Paula	08/2017
4112	(14*10^135301-53)/3	135302	Robert Price	12/2018
4113	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
4114	(13*10^135279+437)/9	135280	Robert Price	04/2018
4115	2^449330-35	135262	Lelio R Paula	08/2017
4116	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
4117	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
4118	(13*10^135184-43)/3	135185	Robert Price	11/2018
4119	2^449049-115309	135178	Enzo Doria	07/2015
4120	(10^135174+191)/3	135174	Robert Price	02/2018
4121	2^449030-15	135172	Lelio R Paula	08/2017
4122	(157*10^135151-1)/3	135153	Robert Price	01/2022
4123	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
4124	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
4125	(37*10^135099+251)/9	135100	Robert Price	09/2021
4126	32221^15586+15586^32221	135095	Hans Havermann	12/2020
4127	2^448762-351401	135091	Enzo Doria	07/2015
4128	2*10^135083-43	135084	Robert Price	04/2018
4129	31357^20278+20278^31357	135056	Hans Havermann	12/2020
4130	32242^15445+15445^32242	135055	Hans Havermann	12/2020
4131	k(198476)	135054	Robert Price	07/2020
4132	32461^14470+14470^32461	135053	Hans Havermann	12/2020
4133	31353^20288+20288^31353	135045	Hans Havermann	12/2020
4134	5*10^135019+77	135020	Robert Price	12/2018
4135	(10^135011+719)/9	135011	Serge Batalov	12/2014
4136	(197*10^134978+7)/3	134980	Robert Price	12/2020
4137	2^448386-2786261	134978	Enzo Doria	03/2016
4138	26480^30517-30517^26480	134975	Frank Doornink	03/2024
4139	(73*10^134939+143)/9	134940	Robert Price	07/2019
4140	33957^9392+9392^33957	134903	Hans Havermann	12/2020
4141	2^448122+20809	134899	Enzo Doria	08/2023
4142	2^448113-113949	134896	Enzo Doria	11/2014
4143	30958^22755+22755^30958	134887	Hans Havermann	12/2020
4144	2^447888-2786639	134828	Enzo Doria	03/2016
4145	2^447870-396765	134823	Enzo Doria	07/2013
4146	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
4147	2^447766-21791	134791	Enzo Doria	07/2013
4148	(19*10^134786-49)/3	134787	Robert Price	05/2019
4149	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
4150	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
4151	2^447552-1019	134727	Yves Minet	02/2014
4152	(2*10^134720-41)/3	134720	Robert Price	02/2018
4153	(25*10^134695-97)/9	134696	Robert Price	01/2022
4154	2^447437-113569	134692	Enzo Doria	08/2014
4155	2^447426-65	134689	Lelio R Paula	08/2017
4156	2^447357-2797573	134668	Enzo Doria	04/2016
4157	2^447278+93	134645	Lelio R Paula	08/2017
4158	33193^11370+11370^33193	134623	Hans Havermann	12/2020
4159	30736^23979+23979^30736	134619	Hans Havermann	11/2020
4160	2^447094-113193	134589	Enzo Doria	07/2014
4161	3^282041-9934	134568	Enzo Doria	05/2014
4162	2^447019-109039	134567	Enzo Doria	04/2014
4163	31376^19437+19437^31376	134561	Hans Havermann	12/2020
4164	2^446990-22041	134558	Enzo Doria	07/2013
4165	123^64370+122	134528	Karsten Bonath	04/2018
4166	30100^29461+29461^30100	134525	Hans Havermann	11/2020
4167	31251^20158+20158^31251	134519	Hans Havermann	11/2020
4168	2^446782-39701	134495	Enzo Doria	09/2015
4169	31817^16858+16858^31817	134485	Hans Havermann	12/2020
4170	32448^13937+13937^32448	134471	Hans Havermann	12/2020
4171	5^192321+3^192321-1	134427	Jon Grantham	08/2023
4172	2^446494-16485	134409	Enzo Doria	04/2013
4173	30042^29785+29785^30042	134408	Hans Havermann	12/2020
4174	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
4175	2^446441+65	134393	Lelio R Paula	08/2017
4176	(10^134385+719)/9	134385	Serge Batalov	12/2014
4177	30043^29688+29688^30043	134370	Hans Havermann	12/2020
4178	(2*10^134364+529)/9	134364	Robert Price	01/2018
4179	34657^7512+7512^34657	134323	Hans Havermann	11/2020
4180	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
4181	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
4182	42035^1564+1564^42035	134270	Hans Havermann	12/2020
4184	(2^446022-7)/339	134264	Lelio R Paula	07/2015
4183	30621^24248+24248^30621	134264	Hans Havermann	12/2020
4185	30341^26562+26562^30341	134237	Hans Havermann	11/2020
4186	10^134209+99867	134210	Patrick De Geest	05/2021
4187	10^134209-80000001	134209	Robert Price	04/2021
4188	10^134209-323283	134209	Patrick De Geest	05/2021
4189	29976^29953+29953^29976	134186	Hans Havermann	12/2020
4190	35038^6755+6755^35038	134183	Hans Havermann	12/2020
4191	63^74568+2	134174	Lelio R Paula	06/2017
4192	2^445671-22071	134161	Enzo Doria	07/2013
4193	532^49205+49205^532	134129	Norbert Schneider	02/2019
4194	36453^4780+4780^36453	134127	Hans Havermann	04/2021
4195	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
4196	2^445515-113859	134114	Enzo Doria	10/2014
4198	(22*10^134111-37)/3	134112	Robert Price	04/2019
4197	31083^20636+20636^31083	134112	Hans Havermann	04/2021
4199	3*2^445478+5	134103	Jon Grantham	07/2023
4200	31622^17379+17379^31622	134079	Hans Havermann	04/2021
4201	5*2^445380-3	134074	Jon Grantham	07/2023
4202	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
4203	(277*10^134059-7)/9	134061	Robert Price	02/2022
4204	2^445328-216917	134058	Enzo Doria	05/2014
4205	2^445202+1874899	134020	Enzo Doria	06/2016
4206	5^191739-3^191739-1	134020	Jon Grantham	08/2023
4207	(35*10^134003-89)/9	134004	Robert Price	02/2022
4208	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
4209	(35*10^133979-593)/9	133980	Robert Price	07/2018
4210	2*10^133955+51	133956	Robert Price	05/2018
4211	(49*10^133952+437)/9	133953	Robert Price	09/2021
4212	2^444964-113639	133948	Enzo Doria	08/2014
4213	31811^16240+16240^31811	133943	Hans Havermann	04/2021
4214	10^133902+167841	133903	Patrick De Geest	05/2021
4216	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
4215	10^133902-100001	133902	Robert Price	07/2020
4217	2^444784-113859	133894	Enzo Doria	10/2014
4218	32303^13914+13914^32303	133846	Hans Havermann	04/2021
4219	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
4220	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
4221	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
4222	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
4223	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
4224	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
4225	30739^22458+22458^30739	133757	Hans Havermann	04/2021
4226	34942^6721+6721^34942	133739	Hans Havermann	04/2021
4227	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
4228	34792^6935+6935^34792	133638	Hans Havermann	04/2021
4229	(266*10^133603+1)/3	133605	Robert Price	04/2020
4230	32261^13842+13842^32261	133600	Hans Havermann	04/2021
4231	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
4232	(134*10^133573-11)/3	133575	Robert Price	01/2022
4233	26726^30173-30173^26726	133574	Frank Doornink	03/2024
4234	62^74521-61^74521	133571	Robert Price	05/2013
4235	(182*10^133543+1)/3	133545	Robert Price	02/2020
4236	(103*10^133535+11)/3	133537	Robert Price	01/2021
4237	32589^12520+12520^32589	133537	Hans Havermann	03/2021
4238	34516^7373+7373^34516	133496	Hans Havermann	04/2021
4239	8*10^133487-37	133488	Robert Price	03/2022
4240	30135^26882+26882^30135	133482	Hans Havermann	04/2021
4241	2^443198-1867301	133416	Enzo Doria	03/2016
4242	(19*10^133390+101)/3	133391	Robert Price	09/2019
4243	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
4244	36117^4910+4910^36117	133311	Hans Havermann	04/2021
4245	2^442799+1874633	133296	Enzo Doria	06/2016
4246	L(637751)	133283	Henri Lifchitz	09/2008
4247	109^65410-2	133269	Lelio R Paula	10/2017
4248	2^442688-113489	133263	Enzo Doria	08/2014
4249	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
4250	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015

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Probable Primes Top 10000

(295036 PRPs in the top)