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 ?
4001	28974^18215+18215^28974	123442	Hans Havermann	03/2021
4002	28901^18618+18618^28901	123406	Hans Havermann	03/2021
4003	2^409909-189	123395	Enzo Doria	05/2014
4004	2^409896-109043	123391	Enzo Doria	04/2014
4005	2^409890+75409	123390	Enzo Doria	04/2016
4006	81254^33+33^81254	123386	Hans Havermann	03/2021
4007	33463^4854+4854^33463	123348	Hans Havermann	03/2021
4008	34061^4182+4182^34061	123348	Hans Havermann	03/2021
4009	133^58076-2	123345	Lelio R Paula	10/2017
4010	F(590041)	123311	Henri Lifchitz	01/2005
4011	(82*10^123299+377)/9	123300	Robert Price	03/2022
4012	2^409566-113501	123292	Enzo Doria	08/2014
4013	2^409533+77747	123282	Enzo Doria	05/2016
4014	2^409436-112799	123253	Enzo Doria	06/2014
4015	28212^23321+23321^28212	123223	Hans Havermann	03/2021
4016	2^409225+1873787	123189	Enzo Doria	06/2016
4017	2^409174+73009	123174	Enzo Doria	04/2016
4018	2^409058-112685	123139	Enzo Doria	06/2014
4019	(13*10^123137-61)/3	123138	Robert Price	11/2018
4020	4*10^123113+21	123114	Robert Price	12/2018
4021	2^408778+77689	123055	Enzo Doria	05/2016
4022	2^408690-75	123028	Lelio R Paula	11/2013
4023	28327^22032+22032^28327	123026	Hans Havermann	03/2021
4024	(29*10^122996+673)/9	122997	Robert Price	12/2018
4025	(65*10^122994-101)/9	122995	Robert Price	01/2022
4026	2^408574-2787341	122994	Enzo Doria	03/2016
4027	3*10^122977+37	122978	Robert Price	08/2018
4028	(7*10^122976-67)/3	122977	Robert Price	10/2021
4029	Phi(157825,10)	122961	Maksym Voznyy	06/2015
4030	(68*10^122933-419)/9	122934	Robert Price	07/2019
4031	29712^13721+13721^29712	122931	Hans Havermann	03/2021
4032	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
4033	(266*10^122872-17)/3	122874	Robert Price	07/2020
4034	(16*10^122871+77)/3	122872	Robert Price	03/2019
4035	30395^11022+11022^30395	122865	Hans Havermann	03/2021
4036	4*10^122859-69	122860	Robert Price	01/2022
4037	(10^122857+167)/3	122857	Robert Price	05/2021
4038	33331^4852+4852^33331	122856	Hans Havermann	03/2021
4039	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
4040	(19*10^122836-43)/3	122837	Robert Price	05/2019
4041	28420^20969+20969^28420	122820	Hans Havermann	03/2021
4042	(16*10^122818+179)/3	122819	Robert Price	11/2021
4043	29865^12934+12934^29865	122797	Hans Havermann	03/2021
4044	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
4045	(32*10^122733-77)/9	122734	Robert Price	06/2018
4046	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
4048	(22*10^122681+161)/3	122682	Robert Price	05/2019
4047	29513^14350+14350^29513	122682	Hans Havermann	03/2021
4049	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
4050	(26*10^122625-131)/3	122626	Robert Price	10/2019
4051	27925^24562+24562^27925	122599	Hans Havermann	03/2021
4052	(73*10^122592-1)/9	122593	Robert Price	01/2015
4053	(5*10^122592+91)/3	122593	Robert Price	04/2018
4054	36751^2166+2166^36751	122589	Hans Havermann	03/2021
4055	(85*10^122585-1)/3	122587	Robert Price	02/2020
4056	29368^14931+14931^29368	122585	Hans Havermann	03/2021
4057	2^407179-112075	122574	Enzo Doria	06/2014
4058	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
4059	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
4060	(646*10^122533+11)/9	122535	Robert Price	10/2021
4061	2^407008-1867919	122522	Enzo Doria	04/2016
4062	11^117642-300	122512	Enzo Doria	10/2012
4063	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
4064	2^406949+72197	122504	Enzo Doria	04/2016
4065	(19*10^122501+149)/3	122502	Robert Price	05/2019
4066	28632^18977+18977^28632	122495	Hans Havermann	03/2021
4067	31815^7076+7076^31815	122481	Hans Havermann	03/2021
4068	2^406826-65	122467	Lelio R Paula	11/2013
4069	2^406821-2797363	122466	Enzo Doria	04/2016
4070	(7*10^122456-331)/9	122456	Robert Price	03/2022
4071	2^406758-17	122447	Lelio R Paula	11/2013
4072	29941^12282+12282^29941	122437	Hans Havermann	03/2021
4073	(30^82883-1)/29	122427	Robert Price	12/2011
4074	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
4075	28732^18215+18215^28732	122411	Hans Havermann	03/2021
4076	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
4077	4*10^122377+19	122378	Robert Price	10/2018
4078	28227^21634+21634^28227	122368	Hans Havermann	03/2021
4079	Phi(246362,10)	122365	Makoto Kamada	09/2019
4080	3*10^122345-97	122346	Robert Price	07/2018
4081	97^61575-2	122336	Lelio R Paula	12/2014
4082	2*10^122319+47	122320	Robert Price	12/2021
4083	208^52765+52765^208	122313	Norbert Schneider	11/2020
4084	2^406298+2799109	122308	Enzo Doria	04/2016
4085	7*10^122294+57	122295	Robert Price	06/2019
4086	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
4087	2^406229-1849993	122288	Enzo Doria	08/2015
4088	3*10^122274+7	122275	Robert Price	07/2015
4089	2^406117+1876577	122254	Enzo Doria	07/2016
4090	29308^14835+14835^29308	122253	Hans Havermann	03/2021
4091	28119^22268+22268^28119	122253	Hans Havermann	03/2021
4092	32167^6312+6312^32167	122240	Hans Havermann	03/2021
4093	3^256199-2^256199	122238	Mike Oakes	06/2005
4094	27678^26053+26053^27678	122223	Hans Havermann	03/2021
4095	2^405992-78557	122216	Jorge Menendez	03/2018
4096	(8*10^122203+43)/3	122204	Robert Price	06/2018
4097	(58*10^122170+329)/9	122171	Robert Price	05/2019
4098	2^405774+179149	122151	Enzo Doria	06/2016
4099	(218*10^122109+7)/9	122111	Robert Price	06/2022
4100	29189^15246+15246^29189	122103	Hans Havermann	03/2021
4102	34*10^122082-9	122084	Robert Price	06/2020
4101	33442^4473+4473^33442	122084	Hans Havermann	03/2021
4103	5*10^122082+41	122083	Robert Price	03/2019
4104	31849^6808+6808^31849	122078	Hans Havermann	03/2021
4106	2^405514-3311	122072	Yves Minet	12/2014
4107	2^405514-115511	122072	Enzo Doria	07/2015
4105	23*10^122070-7	122072	Robert Price	02/2020
4108	2^405422-113261	122045	Enzo Doria	07/2014
4109	2^405173+71237	121970	Enzo Doria	04/2016
4110	(154*10^121953+17)/9	121955	Robert Price	06/2022
4111	(34*10^121924+191)/9	121925	Robert Price	08/2021
4112	(2^405016+1)/257	121920	Lelio R Paula	04/2014
4113	28557^18590+18590^28557	121918	Hans Havermann	03/2021
4114	28641^18002+18002^28641	121877	Hans Havermann	03/2021
4115	2^404858+71329	121875	Enzo Doria	04/2016
4116	2^404813-114703	121861	Enzo Doria	04/2015
4117	2^404764+77791	121847	Enzo Doria	05/2016
4118	28830^16841+16841^28830	121847	Hans Havermann	03/2021
4119	(4*10^121825+89)/3	121826	Robert Price	08/2021
4120	317^48694+48694^317	121787	Norbert Schneider	08/2015
4121	2^404536-115259	121778	Enzo Doria	06/2015
4122	2^404501-631	121767	Yves Minet	07/2012
4123	5*10^121764-69	121765	Robert Price	02/2021
4124	28236^20485+20485^28236	121738	Hans Havermann	02/2021
4125	(382*10^121694-31)/9	121696	Robert Price	06/2022
4126	63^67620+2	121672	Lelio R Paula	08/2015
4127	(16*10^121633+167)/3	121634	Robert Price	06/2019
4128	29955^11494+11494^29955	121632	Hans Havermann	02/2021
4129	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
4130	31088^8163+8163^31088	121612	Hans Havermann	02/2021
4131	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
4132	(10^121543-79)/3	121543	Robert Price	01/2018
4133	2^403676+76831	121519	Enzo Doria	05/2016
4134	(7*10^121487+143)/3	121488	Robert Price	03/2018
4135	27965^22086+22086^27965	121484	Hans Havermann	02/2021
4136	(893*10^121470+7)/9	121472	Robert Price	06/2021
4137	(206*10^121462-11)/3	121464	Robert Price	02/2022
4138	(77*10^121455+67)/9	121456	Robert Price	12/2021
4139	2^403363-113635	121425	Enzo Doria	08/2014
4140	(17*10^121418-113)/3	121419	Robert Price	06/2021
4141	2^403336-1861469	121417	Enzo Doria	03/2016
4142	27929^22186+22186^27929	121382	Hans Havermann	02/2021
4143	p(24442)#/2-64	121381	Robert Price	04/2017
4144	11^116555-720	121380	Enzo Doria	11/2012
4145	2^403100-461267	121346	Enzo Doria	07/2015
4146	2^403093-112213	121344	Enzo Doria	06/2014
4147	29404^13385+13385^29404	121340	Hans Havermann	02/2021
4148	28106^20745+20745^28106	121332	Hans Havermann	02/2021
4149	(316^48539+1)/317	121330	Eric Chen	10/2017
4150	(23*10^121320-71)/3	121321	Robert Price	07/2020
4151	2^403004+1866361	121317	Enzo Doria	03/2016
4152	2^402953+89	121301	Lelio R Paula	10/2013
4153	2^402944-2788319	121299	Enzo Doria	03/2016
4154	(44*10^121297-719)/9	121298	Robert Price	12/2018
4155	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
4156	2^402828-113183	121264	Enzo Doria	07/2014
4157	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
4158	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
4160	2^402715+1874223	121230	Enzo Doria	06/2016
4159	(35*10^121229-593)/9	121230	Robert Price	07/2018
4161	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
4162	28719^16568+16568^28719	121174	Hans Havermann	02/2021
4163	7*10^121144+9	121145	Robert Price	09/2015
4164	27490^25467+25467^27490	121121	Hans Havermann	02/2021
4165	34575^3182+3182^34575	121106	Hans Havermann	02/2021
4166	5*10^121100-37	121101	Robert Price	11/2021
4167	29954^10935+10935^29954	120979	Hans Havermann	02/2021
4168	33585^3992+3992^33585	120946	Hans Havermann	02/2021
4169	40296^1003+1003^40296	120941	Hans Havermann	02/2021
4170	2^401725-113251	120932	Enzo Doria	07/2014
4171	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
4172	2^401652+73711	120910	Enzo Doria	04/2016
4173	(2^401632+3)/79	120902	Lelio R Paula	04/2014
4174	40450^973+973^40450	120870	Hans Havermann	01/2021
4175	10^120841+88417	120842	Patrick De Geest	04/2020
4176	10^120841-123456789	120841	Robert Price	02/2020
4177	10^120841-176853	120841	Patrick De Geest	04/2020
4178	2^401406-2791331	120836	Enzo Doria	03/2016
4179	(28^83497+1)/29	120832	Robert Price	07/2013
4180	(22*10^120828+161)/3	120829	Robert Price	05/2019
4181	2^401369+1867367	120825	Enzo Doria	03/2016
4182	(5*10^120821+43)/3	120822	Robert Price	12/2021
4183	(10^120782+29)/3	120782	Serge Batalov	12/2014
4184	2^401215-1657	120778	Yves Minet	07/2014
4185	2^401159+53	120761	Lelio R Paula	10/2013
4186	27782^22179+22179^27782	120739	Hans Havermann	01/2021
4187	32974^4585+4585^32974	120730	Hans Havermann	02/2021
4188	2^401031-113047	120723	Enzo Doria	07/2014
4189	30598^8813+8813^30598	120713	Hans Havermann	02/2021
4190	(71*10^120703-287)/9	120704	Robert Price	09/2019
4191	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
4192	34793^2940+2940^34793	120675	Hans Havermann	02/2021
4193	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
4194	(166*10^120654+11)/3	120656	Robert Price	03/2021
4195	34066^3481+3481^34066	120652	Hans Havermann	02/2021
4196	8*10^120637-27	120638	Robert Price	10/2021
4197	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
4198	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
4199	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
4200	9*10^120617-61	120618	Robert Price	06/2021
4201	(29*10^120590-71)/3	120591	Robert Price	07/2021
4202	2^400571-15	120584	Lelio R Paula	10/2013
4203	(10^120574+359)/9	120574	Serge Batalov	12/2014
4204	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
4205	27431^24810+24810^27431	120550	Hans Havermann	02/2021
4206	2^400424-216413	120540	Enzo Doria	04/2013
4207	29090^13911+13911^29090	120531	Hans Havermann	02/2021
4208	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
4209	27899^20868+20868^27899	120510	Hans Havermann	02/2021
4210	33740^3729+3729^33740	120506	Hans Havermann	02/2021
4211	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
4212	2^400166+1874899	120462	Enzo Doria	06/2016
4213	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
4214	37078^1771+1771^37078	120438	Hans Havermann	02/2021
4215	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
4216	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
4217	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
4218	2^399966+73759	120402	Enzo Doria	04/2016
4219	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
4220	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
4221	2^399918-95	120388	Lelio R Paula	04/2013
4222	(28*10^120381-67)/3	120382	Robert Price	10/2020
4223	(49*10^120380-139)/9	120381	Robert Price	03/2019
4224	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
4225	2^399792-1849259	120350	Enzo Doria	08/2015
4226	9*10^120342-7	120343	Robert Price	09/2015
4227	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
4228	(331*10^120332-7)/9	120334	Robert Price	04/2022
4229	(13*10^120306-37)/3	120307	Robert Price	01/2019
4230	(23*10^120299+37)/3	120300	Robert Price	02/2022
4231	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
4232	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
4233	2^399526-1861721	120270	Enzo Doria	11/2015
4234	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
4235	32016^5687+5687^32016	120217	Hans Havermann	01/2021
4236	(205*10^120212-1)/3	120214	Robert Price	11/2021
4237	2^399322-2798111	120208	Enzo Doria	04/2016
4238	30438^8867+8867^30438	120163	Hans Havermann	02/2021
4240	72^64693-71^64693	120157	Robert Price	03/2014
4239	(17*10^120156-161)/9	120157	Robert Price	02/2021
4241	2^399111-28489	120145	Enzo Doria	08/2015
4242	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
4243	30254^9333+9333^30254	120110	Hans Havermann	02/2021
4244	30882^7745+7745^30882	120101	Hans Havermann	02/2021
4245	2^398877+105	120074	Donovan Johnson	01/2006
4246	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
4247	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
4248	2^398710+57	120024	Lelio R Paula	04/2013
4249	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
4250	2^398691-115057	120018	Enzo Doria	06/2015

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Probable Primes Top 10000

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