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	(7*10^122456-331)/9	122456	Robert Price	03/2022
5002	2^406758-17	122447	Lelio R Paula	11/2013
5003	29941^12282+12282^29941	122437	Hans Havermann	03/2021
5004	(30^82883-1)/29	122427	Robert Price	12/2011
5005	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
5006	28732^18215+18215^28732	122411	Hans Havermann	03/2021
5007	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
5008	4*10^122377+19	122378	Robert Price	10/2018
5009	28227^21634+21634^28227	122368	Hans Havermann	03/2021
5010	Phi(246362,10)	122365	Makoto Kamada	09/2019
5011	3*10^122345-97	122346	Robert Price	07/2018
5012	97^61575-2	122336	Lelio R Paula	12/2014
5013	2*10^122319+47	122320	Robert Price	12/2021
5014	208^52765+52765^208	122313	Norbert Schneider	11/2020
5016	2^406298+2799109	122308	Enzo Doria	04/2016
5015	2^406296+213691	122308	Enzo Doria	09/2023
5017	7*10^122294+57	122295	Robert Price	06/2019
5018	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
5019	2^406229-1849993	122288	Enzo Doria	08/2015
5020	3*10^122274+7	122275	Robert Price	07/2015
5021	2^406117+1876577	122254	Enzo Doria	07/2016
5022	29308^14835+14835^29308	122253	Hans Havermann	03/2021
5023	28119^22268+22268^28119	122253	Hans Havermann	03/2021
5024	32167^6312+6312^32167	122240	Hans Havermann	03/2021
5025	3^256199-2^256199	122238	Mike Oakes	06/2005
5026	27678^26053+26053^27678	122223	Hans Havermann	03/2021
5027	2^405992-78557	122216	Jorge Menendez	03/2018
5028	(8*10^122203+43)/3	122204	Robert Price	06/2018
5029	(58*10^122170+329)/9	122171	Robert Price	05/2019
5030	2^405774+179149	122151	Enzo Doria	06/2016
5031	2^405693+20417	122126	Enzo Doria	07/2023
5032	(218*10^122109+7)/9	122111	Robert Price	06/2022
5033	29189^15246+15246^29189	122103	Hans Havermann	03/2021
5035	34*10^122082-9	122084	Robert Price	06/2020
5034	33442^4473+4473^33442	122084	Hans Havermann	03/2021
5036	5*10^122082+41	122083	Robert Price	03/2019
5037	31849^6808+6808^31849	122078	Hans Havermann	03/2021
5039	2^405514-3311	122072	Yves Minet	12/2014
5040	2^405514-115511	122072	Enzo Doria	07/2015
5038	23*10^122070-7	122072	Robert Price	02/2020
5041	2^405422-113261	122045	Enzo Doria	07/2014
5042	2^405173+71237	121970	Enzo Doria	04/2016
5043	fibonacci(583574)+2	121960	Jon Grantham	08/2023
5044	(154*10^121953+17)/9	121955	Robert Price	06/2022
5045	(34*10^121924+191)/9	121925	Robert Price	08/2021
5046	(2^405016+1)/257	121920	Lelio R Paula	04/2014
5047	28557^18590+18590^28557	121918	Hans Havermann	03/2021
5048	28641^18002+18002^28641	121877	Hans Havermann	03/2021
5049	2^404858+71329	121875	Enzo Doria	04/2016
5050	2^404813-114703	121861	Enzo Doria	04/2015
5051	2^404764+77791	121847	Enzo Doria	05/2016
5052	28830^16841+16841^28830	121847	Hans Havermann	03/2021
5053	(4*10^121825+89)/3	121826	Robert Price	08/2021
5054	317^48694+48694^317	121787	Norbert Schneider	08/2015
5055	2^404536-115259	121778	Enzo Doria	06/2015
5056	2^404501-631	121767	Yves Minet	07/2012
5057	5*10^121764-69	121765	Robert Price	02/2021
5058	28236^20485+20485^28236	121738	Hans Havermann	02/2021
5059	(382*10^121694-31)/9	121696	Robert Price	06/2022
5060	63^67620+2	121672	Lelio R Paula	08/2015
5061	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
5062	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
5063	(16*10^121633+167)/3	121634	Robert Price	06/2019
5064	29955^11494+11494^29955	121632	Hans Havermann	02/2021
5065	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
5066	31088^8163+8163^31088	121612	Hans Havermann	02/2021
5067	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
5068	(211^52301-1)/210	121560	Anonymous	04/2024
5069	(10^121543-79)/3	121543	Robert Price	01/2018
5070	2^403676+76831	121519	Enzo Doria	05/2016
5071	(7*10^121487+143)/3	121488	Robert Price	03/2018
5072	27965^22086+22086^27965	121484	Hans Havermann	02/2021
5073	(893*10^121470+7)/9	121472	Robert Price	06/2021
5074	(206*10^121462-11)/3	121464	Robert Price	02/2022
5075	26282^27481-27481^26282	121457	Frank Doornink	03/2024
5076	(77*10^121455+67)/9	121456	Robert Price	12/2021
5077	2^403363-113635	121425	Enzo Doria	08/2014
5078	25531^27552-27552^25531	121424	Frank Doornink	02/2024
5079	(17*10^121418-113)/3	121419	Robert Price	06/2021
5080	2^403336-1861469	121417	Enzo Doria	03/2016
5081	27929^22186+22186^27929	121382	Hans Havermann	02/2021
5082	p(24442)#/2-64	121381	Robert Price	04/2017
5083	11^116555-720	121380	Enzo Doria	11/2012
5084	2^403100-461267	121346	Enzo Doria	07/2015
5085	2^403093-112213	121344	Enzo Doria	06/2014
5086	29404^13385+13385^29404	121340	Hans Havermann	02/2021
5087	28106^20745+20745^28106	121332	Hans Havermann	02/2021
5088	(316^48539+1)/317	121330	Eric Chen	10/2017
5089	(23*10^121320-71)/3	121321	Robert Price	07/2020
5090	2^403004+1866361	121317	Enzo Doria	03/2016
5091	2^402953+89	121301	Lelio R Paula	10/2013
5092	2^402944-2788319	121299	Enzo Doria	03/2016
5093	(44*10^121297-719)/9	121298	Robert Price	12/2018
5094	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
5095	2^402828-113183	121264	Enzo Doria	07/2014
5096	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
5097	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
5099	2^402715+1874223	121230	Enzo Doria	06/2016
5098	(35*10^121229-593)/9	121230	Robert Price	07/2018
5100	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
5101	28719^16568+16568^28719	121174	Hans Havermann	02/2021
5102	7*10^121144+9	121145	Robert Price	09/2015
5103	27490^25467+25467^27490	121121	Hans Havermann	02/2021
5104	34575^3182+3182^34575	121106	Hans Havermann	02/2021
5105	5*10^121100-37	121101	Robert Price	11/2021
5106	25592^27467-27467^25592	121078	Frank Doornink	02/2024
5107	29954^10935+10935^29954	120979	Hans Havermann	02/2021
5108	33585^3992+3992^33585	120946	Hans Havermann	02/2021
5109	40296^1003+1003^40296	120941	Hans Havermann	02/2021
5110	2^401725-113251	120932	Enzo Doria	07/2014
5111	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
5112	2^401652+73711	120910	Enzo Doria	04/2016
5113	(2^401632+3)/79	120902	Lelio R Paula	04/2014
5114	40450^973+973^40450	120870	Hans Havermann	01/2021
5115	(8*10^120851-11)/3	120852	Robert Price	07/2023
5116	10^120841+88417	120842	Patrick De Geest	04/2020
5117	10^120841-123456789	120841	Robert Price	02/2020
5118	10^120841-176853	120841	Patrick De Geest	04/2020
5119	2^401406-2791331	120836	Enzo Doria	03/2016
5120	(28^83497+1)/29	120832	Robert Price	07/2013
5121	(22*10^120828+161)/3	120829	Robert Price	05/2019
5122	2^401369+1867367	120825	Enzo Doria	03/2016
5123	(5*10^120821+43)/3	120822	Robert Price	12/2021
5124	26990^27263-27263^26990	120808	Frank Doornink	03/2024
5125	(10^120782+29)/3	120782	Serge Batalov	12/2014
5126	2^401215-1657	120778	Yves Minet	07/2014
5127	2^401159+53	120761	Lelio R Paula	10/2013
5128	27782^22179+22179^27782	120739	Hans Havermann	01/2021
5129	32974^4585+4585^32974	120730	Hans Havermann	02/2021
5130	2^401031-113047	120723	Enzo Doria	07/2014
5131	30598^8813+8813^30598	120713	Hans Havermann	02/2021
5132	(71*10^120703-287)/9	120704	Robert Price	09/2019
5133	25671^27370-27370^25671	120687	Frank Doornink	02/2024
5134	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
5135	34793^2940+2940^34793	120675	Hans Havermann	02/2021
5136	26028^27329-27329^26028	120670	Frank Doornink	03/2024
5137	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5138	(166*10^120654+11)/3	120656	Robert Price	03/2021
5139	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5140	8*10^120637-27	120638	Robert Price	10/2021
5141	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5142	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5143	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5144	9*10^120617-61	120618	Robert Price	06/2021
5145	(29*10^120590-71)/3	120591	Robert Price	07/2021
5146	2^400571-15	120584	Lelio R Paula	10/2013
5147	(10^120574+359)/9	120574	Serge Batalov	12/2014
5148	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5149	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5150	2^400424-216413	120540	Enzo Doria	04/2013
5151	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5152	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5153	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5154	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5155	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5156	2^400166+1874899	120462	Enzo Doria	06/2016
5157	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5158	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5159	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5160	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5161	2^399999+54173	120412	Norman Luhn	08/2023
5162	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5163	2^399966+73759	120402	Enzo Doria	04/2016
5164	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5165	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5167	2^399918-95	120388	Lelio R Paula	04/2013
5166	2^399918+214009	120388	Enzo Doria	10/2023
5168	(28*10^120381-67)/3	120382	Robert Price	10/2020
5169	(49*10^120380-139)/9	120381	Robert Price	03/2019
5170	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
5171	2^399792-1849259	120350	Enzo Doria	08/2015
5172	9*10^120342-7	120343	Robert Price	09/2015
5173	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
5174	(331*10^120332-7)/9	120334	Robert Price	04/2022
5175	(13*10^120306-37)/3	120307	Robert Price	01/2019
5176	(23*10^120299+37)/3	120300	Robert Price	02/2022
5177	25935^27254-27254^25935	120297	Frank Doornink	03/2024
5178	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
5179	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
5180	2^399526-1861721	120270	Enzo Doria	11/2015
5181	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
5182	32016^5687+5687^32016	120217	Hans Havermann	01/2021
5183	(205*10^120212-1)/3	120214	Robert Price	11/2021
5184	2^399322-2798111	120208	Enzo Doria	04/2016
5185	30438^8867+8867^30438	120163	Hans Havermann	02/2021
5186	3^251841-5*2^251841	120159	Jon Grantham	08/2023
5188	72^64693-71^64693	120157	Robert Price	03/2014
5187	(17*10^120156-161)/9	120157	Robert Price	02/2021
5189	2^399111-28489	120145	Enzo Doria	08/2015
5190	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
5191	30254^9333+9333^30254	120110	Hans Havermann	02/2021
5192	30882^7745+7745^30882	120101	Hans Havermann	02/2021
5194	2^398877+105	120074	Donovan Johnson	01/2006
5193	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
5195	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
5196	2^398710+57	120024	Lelio R Paula	04/2013
5197	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
5198	2^398691-115057	120018	Enzo Doria	06/2015
5199	L(574219)	120005	Renaud Lifchitz	03/2004
5200	2^398571+60413	119982	Yves Minet	03/2011
5201	28623^15538+15538^28623	119971	Hans Havermann	02/2021
5202	p(24179)#/2-64	119949	Robert Price	04/2017
5203	2^398448+1872001	119945	Enzo Doria	05/2016
5204	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
5205	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
5206	(191*10^119941-17)/3	119943	Robert Price	11/2021
5207	634^42803+42803^634	119938	Norbert Schneider	07/2019
5208	31083^7220+7220^31083	119935	Hans Havermann	01/2021
5209	(68*10^119931-11)/3	119933	Robert Price	01/2020
5210	8*10^119930-3	119931	Ray Chandler	04/2011
5211	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
5212	(10^119880+179)/9	119880	Serge Batalov	12/2014
5213	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
5214	(10^119836+77)/3	119836	Robert Price	01/2018
5215	26681^27074-27074^26681	119835	Frank Doornink	03/2024
5216	28179^17870+17870^28179	119821	Hans Havermann	02/2021
5217	2^398029+1872527	119819	Enzo Doria	05/2016
5218	33142^4119+4119^33142	119802	Hans Havermann	01/2021
5219	2^397897-113541	119779	Enzo Doria	08/2014
5220	28636^15171+15171^28636	119728	Hans Havermann	02/2021
5221	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
5222	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
5223	(19*10^119716+101)/3	119717	Robert Price	09/2019
5224	29563^11208+11208^29563	119717	Hans Havermann	02/2021
5225	2^397655-933075	119707	Paul Bourdelais	06/2021
5226	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
5227	28243^17308+17308^28243	119701	Hans Havermann	02/2021
5228	77*10^119688+3	119690	Robert Price	06/2020
5229	586*25^85601+3717	119668	Eric Chen	10/2023
5230	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
5231	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
5232	2^397426+73849	119638	Enzo Doria	04/2016
5233	8*10^119509+29	119510	Robert Price	11/2021
5234	2^396933-112723	119489	Enzo Doria	06/2014
5235	11^114738-150	119488	Enzo Doria	10/2012
5236	(4*10^119474+149)/9	119474	Robert Price	04/2018
5237	2^396790-21	119446	Lelio R Paula	04/2013
5238	32061^5300+5300^32061	119405	Hans Havermann	01/2021
5239	(2^396633-7)/5	119398	Lelio R Paula	04/2014
5240	27382^22913+22913^27382	119388	Hans Havermann	03/2021
5241	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
5242	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
5243	(47*10^119354+259)/9	119355	Robert Price	03/2022
5245	105^59050+104	119352	Norbert Schneider	11/2016
5244	126^56824-125	119352	Norbert Schneider	12/2018
5246	2^396469+111546435	119350	Paul Bourdelais	10/2021
5247	139^55690-138	119345	Norbert Schneider	04/2019
5248	790^41179+41179^790	119322	Norbert Schneider	04/2019
5249	2^396374+73729	119321	Enzo Doria	04/2016
5250	88*10^119295+3	119297	Robert Price	05/2020

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Probable Primes Top 10000

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