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 ?
4001	2^411932-111546435	124004	Paul Bourdelais	10/2021
4002	2^411884-113279	123990	Enzo Doria	07/2014
4003	(2^411832+1)/257	123972	Lelio R Paula	05/2014
4004	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
4005	(26*10^123970-89)/9	123971	Robert Price	06/2018
4006	2^411790-1853531	123962	Enzo Doria	08/2015
4007	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
4008	(101*10^123950+7)/9	123952	Robert Price	02/2022
4009	2^411711-113257	123938	Enzo Doria	07/2014
4010	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
4011	36289^2598+2598^36289	123914	Hans Havermann	03/2021
4012	(11*10^123899-179)/3	123900	Robert Price	09/2018
4013	32276^6879+6879^32276	123860	Hans Havermann	02/2021
4014	2^411325-351103	123822	Enzo Doria	06/2015
4015	(646*10^123817+11)/9	123819	Robert Price	10/2021
4016	30738^10643+10643^30738	123784	Hans Havermann	03/2021
4017	31074^9607+9607^31074	123755	Hans Havermann	03/2021
4018	2^411052+1872481	123739	Enzo Doria	05/2016
4019	34365^3986+3986^34365	123733	Hans Havermann	03/2021
4020	2^410997+39	123723	Lelio R Paula	05/2014
4021	(649^43987-1)/648	123700	Michael Stocker	05/2020
4022	(148*10^123688-1)/3	123690	Robert Price	03/2020
4023	36825^2284+2284^36825	123684	Hans Havermann	03/2021
4024	29582^15171+15171^29582	123683	Hans Havermann	03/2021
4025	10^123671+3593037	123672	Paul Bourdelais	10/2021
4026	8*10^123657+87	123658	Robert Price	10/2019
4027	30505^11302+11302^30505	123642	Hans Havermann	03/2021
4028	29956^13401+13401^29956	123633	Hans Havermann	03/2021
4029	155^56438+154	123618	Norbert Schneider	01/2019
4030	2^410596-39	123602	Lelio R Paula	05/2014
4031	(41*10^123600-221)/9	123601	Robert Price	10/2021
4032	28995^18302+18302^28995	123592	Hans Havermann	03/2021
4033	28302^23269+23269^28302	123589	Hans Havermann	03/2021
4034	2^410540-115079	123585	Enzo Doria	06/2015
4035	(7*10^123563+107)/3	123564	Robert Price	02/2018
4036	9*10^123549+89	123550	Robert Price	11/2019
4037	(197*10^123545+7)/3	123547	Robert Price	12/2020
4038	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
4039	(29*10^123510+277)/9	123511	Robert Price	11/2021
4040	28118^24687+24687^28118	123508	Hans Havermann	03/2021
4041	39994^1225+1225^39994	123507	Hans Havermann	03/2021
4042	2^410206-113081	123485	Enzo Doria	07/2014
4043	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
4044	28974^18215+18215^28974	123442	Hans Havermann	03/2021
4045	28901^18618+18618^28901	123406	Hans Havermann	03/2021
4046	2^409909-189	123395	Enzo Doria	05/2014
4047	2^409896-109043	123391	Enzo Doria	04/2014
4048	2^409890+75409	123390	Enzo Doria	04/2016
4049	81254^33+33^81254	123386	Hans Havermann	03/2021
4050	33463^4854+4854^33463	123348	Hans Havermann	03/2021
4051	34061^4182+4182^34061	123348	Hans Havermann	03/2021
4052	133^58076-2	123345	Lelio R Paula	10/2017
4053	F(590041)	123311	Henri Lifchitz	01/2005
4054	(82*10^123299+377)/9	123300	Robert Price	03/2022
4055	2^409566-113501	123292	Enzo Doria	08/2014
4056	2^409533+77747	123282	Enzo Doria	05/2016
4057	2^409436-112799	123253	Enzo Doria	06/2014
4058	28212^23321+23321^28212	123223	Hans Havermann	03/2021
4059	2^409225+1873787	123189	Enzo Doria	06/2016
4060	2^409174+73009	123174	Enzo Doria	04/2016
4061	2^409058-112685	123139	Enzo Doria	06/2014
4062	(13*10^123137-61)/3	123138	Robert Price	11/2018
4063	4*10^123113+21	123114	Robert Price	12/2018
4064	2^408778+77689	123055	Enzo Doria	05/2016
4065	2^408690-75	123028	Lelio R Paula	11/2013
4066	28327^22032+22032^28327	123026	Hans Havermann	03/2021
4067	(29*10^122996+673)/9	122997	Robert Price	12/2018
4068	(65*10^122994-101)/9	122995	Robert Price	01/2022
4069	2^408574-2787341	122994	Enzo Doria	03/2016
4070	3*10^122977+37	122978	Robert Price	08/2018
4071	(7*10^122976-67)/3	122977	Robert Price	10/2021
4072	Phi(157825,10)	122961	Maksym Voznyy	06/2015
4073	(68*10^122933-419)/9	122934	Robert Price	07/2019
4074	29712^13721+13721^29712	122931	Hans Havermann	03/2021
4075	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
4076	(266*10^122872-17)/3	122874	Robert Price	07/2020
4077	(16*10^122871+77)/3	122872	Robert Price	03/2019
4078	30395^11022+11022^30395	122865	Hans Havermann	03/2021
4079	4*10^122859-69	122860	Robert Price	01/2022
4080	(10^122857+167)/3	122857	Robert Price	05/2021
4081	33331^4852+4852^33331	122856	Hans Havermann	03/2021
4082	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
4083	(19*10^122836-43)/3	122837	Robert Price	05/2019
4084	28420^20969+20969^28420	122820	Hans Havermann	03/2021
4085	(16*10^122818+179)/3	122819	Robert Price	11/2021
4086	29865^12934+12934^29865	122797	Hans Havermann	03/2021
4087	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
4088	(32*10^122733-77)/9	122734	Robert Price	06/2018
4089	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
4091	(22*10^122681+161)/3	122682	Robert Price	05/2019
4090	29513^14350+14350^29513	122682	Hans Havermann	03/2021
4092	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
4093	(26*10^122625-131)/3	122626	Robert Price	10/2019
4094	27925^24562+24562^27925	122599	Hans Havermann	03/2021
4095	(73*10^122592-1)/9	122593	Robert Price	01/2015
4096	(5*10^122592+91)/3	122593	Robert Price	04/2018
4097	36751^2166+2166^36751	122589	Hans Havermann	03/2021
4098	(85*10^122585-1)/3	122587	Robert Price	02/2020
4099	29368^14931+14931^29368	122585	Hans Havermann	03/2021
4100	2^407179-112075	122574	Enzo Doria	06/2014
4101	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
4102	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
4103	(646*10^122533+11)/9	122535	Robert Price	10/2021
4104	2^407008-1867919	122522	Enzo Doria	04/2016
4105	11^117642-300	122512	Enzo Doria	10/2012
4106	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
4107	2^406949+72197	122504	Enzo Doria	04/2016
4108	(19*10^122501+149)/3	122502	Robert Price	05/2019
4109	28632^18977+18977^28632	122495	Hans Havermann	03/2021
4110	31815^7076+7076^31815	122481	Hans Havermann	03/2021
4111	2^406826-65	122467	Lelio R Paula	11/2013
4112	2^406821-2797363	122466	Enzo Doria	04/2016
4113	(7*10^122456-331)/9	122456	Robert Price	03/2022
4114	2^406758-17	122447	Lelio R Paula	11/2013
4115	29941^12282+12282^29941	122437	Hans Havermann	03/2021
4116	(30^82883-1)/29	122427	Robert Price	12/2011
4117	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
4118	28732^18215+18215^28732	122411	Hans Havermann	03/2021
4119	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
4120	4*10^122377+19	122378	Robert Price	10/2018
4121	28227^21634+21634^28227	122368	Hans Havermann	03/2021
4122	Phi(246362,10)	122365	Makoto Kamada	09/2019
4123	3*10^122345-97	122346	Robert Price	07/2018
4124	97^61575-2	122336	Lelio R Paula	12/2014
4125	2*10^122319+47	122320	Robert Price	12/2021
4126	208^52765+52765^208	122313	Norbert Schneider	11/2020
4127	2^406298+2799109	122308	Enzo Doria	04/2016
4128	7*10^122294+57	122295	Robert Price	06/2019
4129	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
4130	2^406229-1849993	122288	Enzo Doria	08/2015
4131	3*10^122274+7	122275	Robert Price	07/2015
4132	2^406117+1876577	122254	Enzo Doria	07/2016
4133	29308^14835+14835^29308	122253	Hans Havermann	03/2021
4134	28119^22268+22268^28119	122253	Hans Havermann	03/2021
4135	32167^6312+6312^32167	122240	Hans Havermann	03/2021
4136	3^256199-2^256199	122238	Mike Oakes	06/2005
4137	27678^26053+26053^27678	122223	Hans Havermann	03/2021
4138	2^405992-78557	122216	Jorge Menendez	03/2018
4139	(8*10^122203+43)/3	122204	Robert Price	06/2018
4140	(58*10^122170+329)/9	122171	Robert Price	05/2019
4141	2^405774+179149	122151	Enzo Doria	06/2016
4142	(218*10^122109+7)/9	122111	Robert Price	06/2022
4143	29189^15246+15246^29189	122103	Hans Havermann	03/2021
4145	34*10^122082-9	122084	Robert Price	06/2020
4144	33442^4473+4473^33442	122084	Hans Havermann	03/2021
4146	5*10^122082+41	122083	Robert Price	03/2019
4147	31849^6808+6808^31849	122078	Hans Havermann	03/2021
4149	2^405514-3311	122072	Yves Minet	12/2014
4150	2^405514-115511	122072	Enzo Doria	07/2015
4148	23*10^122070-7	122072	Robert Price	02/2020
4151	2^405422-113261	122045	Enzo Doria	07/2014
4152	2^405173+71237	121970	Enzo Doria	04/2016
4153	(154*10^121953+17)/9	121955	Robert Price	06/2022
4154	(34*10^121924+191)/9	121925	Robert Price	08/2021
4155	(2^405016+1)/257	121920	Lelio R Paula	04/2014
4156	28557^18590+18590^28557	121918	Hans Havermann	03/2021
4157	28641^18002+18002^28641	121877	Hans Havermann	03/2021
4158	2^404858+71329	121875	Enzo Doria	04/2016
4159	2^404813-114703	121861	Enzo Doria	04/2015
4160	2^404764+77791	121847	Enzo Doria	05/2016
4161	28830^16841+16841^28830	121847	Hans Havermann	03/2021
4162	(4*10^121825+89)/3	121826	Robert Price	08/2021
4163	317^48694+48694^317	121787	Norbert Schneider	08/2015
4164	2^404536-115259	121778	Enzo Doria	06/2015
4165	2^404501-631	121767	Yves Minet	07/2012
4166	5*10^121764-69	121765	Robert Price	02/2021
4167	28236^20485+20485^28236	121738	Hans Havermann	02/2021
4168	(382*10^121694-31)/9	121696	Robert Price	06/2022
4169	63^67620+2	121672	Lelio R Paula	08/2015
4170	(16*10^121633+167)/3	121634	Robert Price	06/2019
4171	29955^11494+11494^29955	121632	Hans Havermann	02/2021
4172	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
4173	31088^8163+8163^31088	121612	Hans Havermann	02/2021
4174	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
4175	(10^121543-79)/3	121543	Robert Price	01/2018
4176	2^403676+76831	121519	Enzo Doria	05/2016
4177	(7*10^121487+143)/3	121488	Robert Price	03/2018
4178	27965^22086+22086^27965	121484	Hans Havermann	02/2021
4179	(893*10^121470+7)/9	121472	Robert Price	06/2021
4180	(206*10^121462-11)/3	121464	Robert Price	02/2022
4181	(77*10^121455+67)/9	121456	Robert Price	12/2021
4182	2^403363-113635	121425	Enzo Doria	08/2014
4183	(17*10^121418-113)/3	121419	Robert Price	06/2021
4184	2^403336-1861469	121417	Enzo Doria	03/2016
4185	27929^22186+22186^27929	121382	Hans Havermann	02/2021
4186	p(24442)#/2-64	121381	Robert Price	04/2017
4187	11^116555-720	121380	Enzo Doria	11/2012
4188	2^403100-461267	121346	Enzo Doria	07/2015
4189	2^403093-112213	121344	Enzo Doria	06/2014
4190	29404^13385+13385^29404	121340	Hans Havermann	02/2021
4191	28106^20745+20745^28106	121332	Hans Havermann	02/2021
4192	(316^48539+1)/317	121330	Eric Chen	10/2017
4193	(23*10^121320-71)/3	121321	Robert Price	07/2020
4194	2^403004+1866361	121317	Enzo Doria	03/2016
4195	2^402953+89	121301	Lelio R Paula	10/2013
4196	2^402944-2788319	121299	Enzo Doria	03/2016
4197	(44*10^121297-719)/9	121298	Robert Price	12/2018
4198	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
4199	2^402828-113183	121264	Enzo Doria	07/2014
4200	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
4201	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
4203	2^402715+1874223	121230	Enzo Doria	06/2016
4202	(35*10^121229-593)/9	121230	Robert Price	07/2018
4204	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
4205	28719^16568+16568^28719	121174	Hans Havermann	02/2021
4206	7*10^121144+9	121145	Robert Price	09/2015
4207	27490^25467+25467^27490	121121	Hans Havermann	02/2021
4208	34575^3182+3182^34575	121106	Hans Havermann	02/2021
4209	5*10^121100-37	121101	Robert Price	11/2021
4210	29954^10935+10935^29954	120979	Hans Havermann	02/2021
4211	33585^3992+3992^33585	120946	Hans Havermann	02/2021
4212	40296^1003+1003^40296	120941	Hans Havermann	02/2021
4213	2^401725-113251	120932	Enzo Doria	07/2014
4214	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
4215	2^401652+73711	120910	Enzo Doria	04/2016
4216	(2^401632+3)/79	120902	Lelio R Paula	04/2014
4217	40450^973+973^40450	120870	Hans Havermann	01/2021
4218	10^120841+88417	120842	Patrick De Geest	04/2020
4219	10^120841-123456789	120841	Robert Price	02/2020
4220	10^120841-176853	120841	Patrick De Geest	04/2020
4221	2^401406-2791331	120836	Enzo Doria	03/2016
4222	(28^83497+1)/29	120832	Robert Price	07/2013
4223	(22*10^120828+161)/3	120829	Robert Price	05/2019
4224	2^401369+1867367	120825	Enzo Doria	03/2016
4225	(5*10^120821+43)/3	120822	Robert Price	12/2021
4226	(10^120782+29)/3	120782	Serge Batalov	12/2014
4227	2^401215-1657	120778	Yves Minet	07/2014
4228	2^401159+53	120761	Lelio R Paula	10/2013
4229	27782^22179+22179^27782	120739	Hans Havermann	01/2021
4230	32974^4585+4585^32974	120730	Hans Havermann	02/2021
4231	2^401031-113047	120723	Enzo Doria	07/2014
4232	30598^8813+8813^30598	120713	Hans Havermann	02/2021
4233	(71*10^120703-287)/9	120704	Robert Price	09/2019
4234	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
4235	34793^2940+2940^34793	120675	Hans Havermann	02/2021
4236	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
4237	(166*10^120654+11)/3	120656	Robert Price	03/2021
4238	34066^3481+3481^34066	120652	Hans Havermann	02/2021
4239	8*10^120637-27	120638	Robert Price	10/2021
4240	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
4241	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
4242	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
4243	9*10^120617-61	120618	Robert Price	06/2021
4244	(29*10^120590-71)/3	120591	Robert Price	07/2021
4245	2^400571-15	120584	Lelio R Paula	10/2013
4246	(10^120574+359)/9	120574	Serge Batalov	12/2014
4247	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
4248	27431^24810+24810^27431	120550	Hans Havermann	02/2021
4249	2^400424-216413	120540	Enzo Doria	04/2013
4250	29090^13911+13911^29090	120531	Hans Havermann	02/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(292102 PRPs in the top)