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 ?
5001	(10^122857+167)/3	122857	Robert Price	05/2021
5002	33331^4852+4852^33331	122856	Hans Havermann	03/2021
5003	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
5004	(19*10^122836-43)/3	122837	Robert Price	05/2019
5005	28420^20969+20969^28420	122820	Hans Havermann	03/2021
5006	(16*10^122818+179)/3	122819	Robert Price	11/2021
5007	29865^12934+12934^29865	122797	Hans Havermann	03/2021
5008	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
5009	(32*10^122733-77)/9	122734	Robert Price	06/2018
5010	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
5012	(22*10^122681+161)/3	122682	Robert Price	05/2019
5011	29513^14350+14350^29513	122682	Hans Havermann	03/2021
5013	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
5014	(26*10^122625-131)/3	122626	Robert Price	10/2019
5015	(643*33^80753+3709)/32	122626	Eric Chen	12/2023
5016	27925^24562+24562^27925	122599	Hans Havermann	03/2021
5017	(73*10^122592-1)/9	122593	Robert Price	01/2015
5018	(5*10^122592+91)/3	122593	Robert Price	04/2018
5019	36751^2166+2166^36751	122589	Hans Havermann	03/2021
5020	(85*10^122585-1)/3	122587	Robert Price	02/2020
5021	29368^14931+14931^29368	122585	Hans Havermann	03/2021
5022	2^407179-112075	122574	Enzo Doria	06/2014
5023	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
5024	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
5025	(646*10^122533+11)/9	122535	Robert Price	10/2021
5026	2^407008-1867919	122522	Enzo Doria	04/2016
5027	11^117642-300	122512	Enzo Doria	10/2012
5028	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
5029	2^406949+72197	122504	Enzo Doria	04/2016
5030	(19*10^122501+149)/3	122502	Robert Price	05/2019
5031	28632^18977+18977^28632	122495	Hans Havermann	03/2021
5032	31815^7076+7076^31815	122481	Hans Havermann	03/2021
5033	2^406826-65	122467	Lelio R Paula	11/2013
5034	2^406821-2797363	122466	Enzo Doria	04/2016
5035	(7*10^122456-331)/9	122456	Robert Price	03/2022
5036	2^406758-17	122447	Lelio R Paula	11/2013
5037	29941^12282+12282^29941	122437	Hans Havermann	03/2021
5038	(30^82883-1)/29	122427	Robert Price	12/2011
5039	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
5040	28732^18215+18215^28732	122411	Hans Havermann	03/2021
5041	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
5042	4*10^122377+19	122378	Robert Price	10/2018
5043	28227^21634+21634^28227	122368	Hans Havermann	03/2021
5044	Phi(246362,10)	122365	Makoto Kamada	09/2019
5045	3*10^122345-97	122346	Robert Price	07/2018
5046	97^61575-2	122336	Lelio R Paula	12/2014
5047	2*10^122319+47	122320	Robert Price	12/2021
5048	208^52765+52765^208	122313	Norbert Schneider	11/2020
5050	2^406298+2799109	122308	Enzo Doria	04/2016
5049	2^406296+213691	122308	Enzo Doria	09/2023
5051	7*10^122294+57	122295	Robert Price	06/2019
5052	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
5053	2^406229-1849993	122288	Enzo Doria	08/2015
5054	3*10^122274+7	122275	Robert Price	07/2015
5055	2^406117+1876577	122254	Enzo Doria	07/2016
5056	29308^14835+14835^29308	122253	Hans Havermann	03/2021
5057	28119^22268+22268^28119	122253	Hans Havermann	03/2021
5058	32167^6312+6312^32167	122240	Hans Havermann	03/2021
5059	3^256199-2^256199	122238	Mike Oakes	06/2005
5060	27678^26053+26053^27678	122223	Hans Havermann	03/2021
5061	2^405992-78557	122216	Jorge Menendez	03/2018
5062	(8*10^122203+43)/3	122204	Robert Price	06/2018
5063	(58*10^122170+329)/9	122171	Robert Price	05/2019
5064	2^405774+179149	122151	Enzo Doria	06/2016
5065	2^405693+20417	122126	Enzo Doria	07/2023
5066	(218*10^122109+7)/9	122111	Robert Price	06/2022
5067	29189^15246+15246^29189	122103	Hans Havermann	03/2021
5069	34*10^122082-9	122084	Robert Price	06/2020
5068	33442^4473+4473^33442	122084	Hans Havermann	03/2021
5070	5*10^122082+41	122083	Robert Price	03/2019
5071	31849^6808+6808^31849	122078	Hans Havermann	03/2021
5073	2^405514-3311	122072	Yves Minet	12/2014
5074	2^405514-115511	122072	Enzo Doria	07/2015
5072	23*10^122070-7	122072	Robert Price	02/2020
5075	2^405422-113261	122045	Enzo Doria	07/2014
5076	2^405173+71237	121970	Enzo Doria	04/2016
5077	fibonacci(583574)+2	121960	Jon Grantham	08/2023
5078	(154*10^121953+17)/9	121955	Robert Price	06/2022
5079	(34*10^121924+191)/9	121925	Robert Price	08/2021
5080	(2^405016+1)/257	121920	Lelio R Paula	04/2014
5081	28557^18590+18590^28557	121918	Hans Havermann	03/2021
5082	28641^18002+18002^28641	121877	Hans Havermann	03/2021
5083	2^404858+71329	121875	Enzo Doria	04/2016
5084	2^404813-114703	121861	Enzo Doria	04/2015
5085	2^404764+77791	121847	Enzo Doria	05/2016
5086	28830^16841+16841^28830	121847	Hans Havermann	03/2021
5087	(4*10^121825+89)/3	121826	Robert Price	08/2021
5088	317^48694+48694^317	121787	Norbert Schneider	08/2015
5089	2^404536-115259	121778	Enzo Doria	06/2015
5090	2^404501-631	121767	Yves Minet	07/2012
5091	5*10^121764-69	121765	Robert Price	02/2021
5092	28236^20485+20485^28236	121738	Hans Havermann	02/2021
5093	(382*10^121694-31)/9	121696	Robert Price	06/2022
5094	63^67620+2	121672	Lelio R Paula	08/2015
5095	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
5096	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
5097	(16*10^121633+167)/3	121634	Robert Price	06/2019
5098	29955^11494+11494^29955	121632	Hans Havermann	02/2021
5099	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
5100	31088^8163+8163^31088	121612	Hans Havermann	02/2021
5101	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
5102	(211^52301-1)/210	121560	Anonymous	04/2024
5103	(10^121543-79)/3	121543	Robert Price	01/2018
5104	2^403676+76831	121519	Enzo Doria	05/2016
5105	(7*10^121487+143)/3	121488	Robert Price	03/2018
5106	27965^22086+22086^27965	121484	Hans Havermann	02/2021
5107	(893*10^121470+7)/9	121472	Robert Price	06/2021
5108	(206*10^121462-11)/3	121464	Robert Price	02/2022
5109	26282^27481-27481^26282	121457	Frank Doornink	03/2024
5110	(77*10^121455+67)/9	121456	Robert Price	12/2021
5111	2^403363-113635	121425	Enzo Doria	08/2014
5112	25531^27552-27552^25531	121424	Frank Doornink	02/2024
5113	(17*10^121418-113)/3	121419	Robert Price	06/2021
5114	2^403336-1861469	121417	Enzo Doria	03/2016
5115	27929^22186+22186^27929	121382	Hans Havermann	02/2021
5116	p(24442)#/2-64	121381	Robert Price	04/2017
5117	11^116555-720	121380	Enzo Doria	11/2012
5118	2^403100-461267	121346	Enzo Doria	07/2015
5119	2^403093-112213	121344	Enzo Doria	06/2014
5120	29404^13385+13385^29404	121340	Hans Havermann	02/2021
5121	28106^20745+20745^28106	121332	Hans Havermann	02/2021
5122	(316^48539+1)/317	121330	Eric Chen	10/2017
5123	(23*10^121320-71)/3	121321	Robert Price	07/2020
5124	2^403004+1866361	121317	Enzo Doria	03/2016
5125	2^402953+89	121301	Lelio R Paula	10/2013
5126	2^402944-2788319	121299	Enzo Doria	03/2016
5127	(44*10^121297-719)/9	121298	Robert Price	12/2018
5128	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
5129	2^402828-113183	121264	Enzo Doria	07/2014
5130	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
5131	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
5133	2^402715+1874223	121230	Enzo Doria	06/2016
5132	(35*10^121229-593)/9	121230	Robert Price	07/2018
5134	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
5135	28719^16568+16568^28719	121174	Hans Havermann	02/2021
5136	7*10^121144+9	121145	Robert Price	09/2015
5137	27490^25467+25467^27490	121121	Hans Havermann	02/2021
5138	34575^3182+3182^34575	121106	Hans Havermann	02/2021
5139	5*10^121100-37	121101	Robert Price	11/2021
5140	25592^27467-27467^25592	121078	Frank Doornink	02/2024
5141	29954^10935+10935^29954	120979	Hans Havermann	02/2021
5142	33585^3992+3992^33585	120946	Hans Havermann	02/2021
5143	40296^1003+1003^40296	120941	Hans Havermann	02/2021
5144	2^401725-113251	120932	Enzo Doria	07/2014
5145	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
5146	2^401652+73711	120910	Enzo Doria	04/2016
5147	(2^401632+3)/79	120902	Lelio R Paula	04/2014
5148	40450^973+973^40450	120870	Hans Havermann	01/2021
5149	(8*10^120851-11)/3	120852	Robert Price	07/2023
5150	10^120841+88417	120842	Patrick De Geest	04/2020
5151	10^120841-123456789	120841	Robert Price	02/2020
5152	10^120841-176853	120841	Patrick De Geest	04/2020
5153	2^401406-2791331	120836	Enzo Doria	03/2016
5154	(28^83497+1)/29	120832	Robert Price	07/2013
5155	(22*10^120828+161)/3	120829	Robert Price	05/2019
5156	2^401369+1867367	120825	Enzo Doria	03/2016
5157	(5*10^120821+43)/3	120822	Robert Price	12/2021
5158	26990^27263-27263^26990	120808	Frank Doornink	03/2024
5159	(10^120782+29)/3	120782	Serge Batalov	12/2014
5160	2^401215-1657	120778	Yves Minet	07/2014
5161	2^401159+53	120761	Lelio R Paula	10/2013
5162	27782^22179+22179^27782	120739	Hans Havermann	01/2021
5163	32974^4585+4585^32974	120730	Hans Havermann	02/2021
5164	2^401031-113047	120723	Enzo Doria	07/2014
5165	30598^8813+8813^30598	120713	Hans Havermann	02/2021
5166	(71*10^120703-287)/9	120704	Robert Price	09/2019
5167	25671^27370-27370^25671	120687	Frank Doornink	02/2024
5168	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
5169	34793^2940+2940^34793	120675	Hans Havermann	02/2021
5170	26028^27329-27329^26028	120670	Frank Doornink	03/2024
5171	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5172	(166*10^120654+11)/3	120656	Robert Price	03/2021
5173	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5174	8*10^120637-27	120638	Robert Price	10/2021
5175	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5176	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5177	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5178	9*10^120617-61	120618	Robert Price	06/2021
5179	(29*10^120590-71)/3	120591	Robert Price	07/2021
5180	2^400571-15	120584	Lelio R Paula	10/2013
5181	(10^120574+359)/9	120574	Serge Batalov	12/2014
5182	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5183	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5184	2^400424-216413	120540	Enzo Doria	04/2013
5185	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5186	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5187	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5188	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5189	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5190	2^400166+1874899	120462	Enzo Doria	06/2016
5191	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5192	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5193	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5194	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5195	2^399999+54173	120412	Norman Luhn	08/2023
5196	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5197	2^399966+73759	120402	Enzo Doria	04/2016
5198	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5199	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5201	2^399918-95	120388	Lelio R Paula	04/2013
5200	2^399918+214009	120388	Enzo Doria	10/2023
5202	(28*10^120381-67)/3	120382	Robert Price	10/2020
5203	(49*10^120380-139)/9	120381	Robert Price	03/2019
5204	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
5205	2^399792-1849259	120350	Enzo Doria	08/2015
5206	9*10^120342-7	120343	Robert Price	09/2015
5207	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
5208	(331*10^120332-7)/9	120334	Robert Price	04/2022
5209	(13*10^120306-37)/3	120307	Robert Price	01/2019
5210	(23*10^120299+37)/3	120300	Robert Price	02/2022
5211	25935^27254-27254^25935	120297	Frank Doornink	03/2024
5212	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
5213	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
5214	2^399526-1861721	120270	Enzo Doria	11/2015
5215	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
5216	32016^5687+5687^32016	120217	Hans Havermann	01/2021
5217	(205*10^120212-1)/3	120214	Robert Price	11/2021
5218	2^399322-2798111	120208	Enzo Doria	04/2016
5219	30438^8867+8867^30438	120163	Hans Havermann	02/2021
5220	3^251841-5*2^251841	120159	Jon Grantham	08/2023
5222	72^64693-71^64693	120157	Robert Price	03/2014
5221	(17*10^120156-161)/9	120157	Robert Price	02/2021
5223	2^399111-28489	120145	Enzo Doria	08/2015
5224	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
5225	30254^9333+9333^30254	120110	Hans Havermann	02/2021
5226	30882^7745+7745^30882	120101	Hans Havermann	02/2021
5228	2^398877+105	120074	Donovan Johnson	01/2006
5227	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
5229	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
5230	2^398710+57	120024	Lelio R Paula	04/2013
5231	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
5232	2^398691-115057	120018	Enzo Doria	06/2015
5233	L(574219)	120005	Renaud Lifchitz	03/2004
5234	2^398571+60413	119982	Yves Minet	03/2011
5235	28623^15538+15538^28623	119971	Hans Havermann	02/2021
5236	p(24179)#/2-64	119949	Robert Price	04/2017
5237	2^398448+1872001	119945	Enzo Doria	05/2016
5238	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
5239	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
5240	(191*10^119941-17)/3	119943	Robert Price	11/2021
5241	634^42803+42803^634	119938	Norbert Schneider	07/2019
5242	31083^7220+7220^31083	119935	Hans Havermann	01/2021
5243	(68*10^119931-11)/3	119933	Robert Price	01/2020
5244	8*10^119930-3	119931	Ray Chandler	04/2011
5245	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
5246	(10^119880+179)/9	119880	Serge Batalov	12/2014
5247	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
5248	(10^119836+77)/3	119836	Robert Price	01/2018
5249	26681^27074-27074^26681	119835	Frank Doornink	03/2024
5250	28179^17870+17870^28179	119821	Hans Havermann	02/2021

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Probable Primes Top 10000

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