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 ?
6001	2^409436-112799	123253	Enzo Doria	06/2014
6002	28212^23321+23321^28212	123223	Hans Havermann	03/2021
6003	2^409225+1873787	123189	Enzo Doria	06/2016
6004	2^409174+73009	123174	Enzo Doria	04/2016
6005	(4893*35^79754-31)/34	123148	Eric Chen	05/2025
6006	2^409058-112685	123139	Enzo Doria	06/2014
6007	(13*10^123137-61)/3	123138	Robert Price	11/2018
6008	4*10^123113+21	123114	Robert Price	12/2018
6009	2^408778+77689	123055	Enzo Doria	05/2016
6010	660^43643-43643^660	123054	Norman Luhn	10/2024
6011	2^408690-75	123028	Lelio R Paula	11/2013
6012	28327^22032+22032^28327	123026	Hans Havermann	03/2021
6013	(29*10^122996+673)/9	122997	Robert Price	12/2018
6014	(65*10^122994-101)/9	122995	Robert Price	01/2022
6015	2^408574-2787341	122994	Enzo Doria	03/2016
6016	3*10^122977+37	122978	Robert Price	08/2018
6017	(7*10^122976-67)/3	122977	Robert Price	10/2021
6018	Phi(157825,10)	122961	Maksym Voznyy	06/2015
6019	25493^27902-27902^25493	122948	Frank Doornink	02/2024
6020	26749^27768-27768^26749	122938	Frank Doornink	03/2024
6021	(68*10^122933-419)/9	122934	Robert Price	07/2019
6022	29712^13721+13721^29712	122931	Hans Havermann	03/2021
6023	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
6024	(266*10^122872-17)/3	122874	Robert Price	07/2020
6025	(16*10^122871+77)/3	122872	Robert Price	03/2019
6026	30395^11022+11022^30395	122865	Hans Havermann	03/2021
6027	4*10^122859-69	122860	Robert Price	01/2022
6028	(10^122857+167)/3	122857	Robert Price	05/2021
6029	33331^4852+4852^33331	122856	Hans Havermann	03/2021
6030	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
6031	(19*10^122836-43)/3	122837	Robert Price	05/2019
6032	315^49162-49162^315	122822	Norman Luhn	10/2024
6033	28420^20969+20969^28420	122820	Hans Havermann	03/2021
6034	(16*10^122818+179)/3	122819	Robert Price	11/2021
6035	29865^12934+12934^29865	122797	Hans Havermann	03/2021
6036	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
6037	17^99766+18	122757	Anonymous	09/2024
6038	(32*10^122733-77)/9	122734	Robert Price	06/2018
6039	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
6041	(22*10^122681+161)/3	122682	Robert Price	05/2019
6040	29513^14350+14350^29513	122682	Hans Havermann	03/2021
6042	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
6043	Phi(149534,2^7)	122640	Henri Lifchitz	10/2025
6045	(26*10^122625-131)/3	122626	Robert Price	10/2019
6044	(643*33^80753+3709)/32	122626	Eric Chen	12/2023
6046	27925^24562+24562^27925	122599	Hans Havermann	03/2021
6047	(92365^24691-1)/92364	122599	Anonymous	09/2025
6048	(73*10^122592-1)/9	122593	Robert Price	01/2015
6049	(5*10^122592+91)/3	122593	Robert Price	04/2018
6050	36751^2166+2166^36751	122589	Hans Havermann	03/2021
6051	(85*10^122585-1)/3	122587	Robert Price	02/2020
6052	29368^14931+14931^29368	122585	Hans Havermann	03/2021
6053	2^407179-112075	122574	Enzo Doria	06/2014
6054	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
6055	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
6056	(646*10^122533+11)/9	122535	Robert Price	10/2021
6057	2^407008-1867919	122522	Enzo Doria	04/2016
6058	11^117642-300	122512	Enzo Doria	10/2012
6059	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
6060	2^406949+72197	122504	Enzo Doria	04/2016
6061	(19*10^122501+149)/3	122502	Robert Price	05/2019
6062	28632^18977+18977^28632	122495	Hans Havermann	03/2021
6063	31815^7076+7076^31815	122481	Hans Havermann	03/2021
6064	2^406826-65	122467	Lelio R Paula	11/2013
6065	2^406821-2797363	122466	Enzo Doria	04/2016
6066	(7*10^122456-331)/9	122456	Robert Price	03/2022
6067	2^406758-17	122447	Lelio R Paula	11/2013
6068	29941^12282+12282^29941	122437	Hans Havermann	03/2021
6069	(30^82883-1)/29	122427	Robert Price	12/2011
6070	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
6071	28732^18215+18215^28732	122411	Hans Havermann	03/2021
6072	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
6073	4*10^122377+19	122378	Robert Price	10/2018
6074	28227^21634+21634^28227	122368	Hans Havermann	03/2021
6075	Phi(246362,10)	122365	Makoto Kamada	09/2019
6076	3*10^122345-97	122346	Robert Price	07/2018
6077	97^61575-2	122336	Lelio R Paula	12/2014
6078	2*10^122319+47	122320	Robert Price	12/2021
6079	208^52765+52765^208	122313	Norbert Schneider	11/2020
6081	2^406298+2799109	122308	Enzo Doria	04/2016
6080	2^406296+213691	122308	Enzo Doria	09/2023
6082	7*10^122294+57	122295	Robert Price	06/2019
6083	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
6084	2^406229-1849993	122288	Enzo Doria	08/2015
6085	3*10^122274+7	122275	Robert Price	07/2015
6086	2^406117+1876577	122254	Enzo Doria	07/2016
6087	29308^14835+14835^29308	122253	Hans Havermann	03/2021
6088	28119^22268+22268^28119	122253	Hans Havermann	03/2021
6089	32167^6312+6312^32167	122240	Hans Havermann	03/2021
6090	3^256199-2^256199	122238	Mike Oakes	06/2005
6091	27678^26053+26053^27678	122223	Hans Havermann	03/2021
6092	2^405992-78557	122216	Jorge Menendez	03/2018
6093	(8*10^122203+43)/3	122204	Robert Price	06/2018
6094	(58*10^122170+329)/9	122171	Robert Price	05/2019
6095	2^405774+179149	122151	Enzo Doria	06/2016
6096	2^405693+20417	122126	Enzo Doria	07/2023
6097	(218*10^122109+7)/9	122111	Robert Price	06/2022
6098	29189^15246+15246^29189	122103	Hans Havermann	03/2021
6100	34*10^122082-9	122084	Robert Price	06/2020
6099	33442^4473+4473^33442	122084	Hans Havermann	03/2021
6101	5*10^122082+41	122083	Robert Price	03/2019
6102	31849^6808+6808^31849	122078	Hans Havermann	03/2021
6104	2^405514-3311	122072	Yves Minet	12/2014
6105	2^405514-115511	122072	Enzo Doria	07/2015
6103	23*10^122070-7	122072	Robert Price	02/2020
6106	2^405422-113261	122045	Enzo Doria	07/2014
6107	95^61698-61698^95	122022	Norman Luhn	10/2024
6108	2^405173+71237	121970	Enzo Doria	04/2016
6109	fibonacci(583574)+2	121960	Jon Grantham	08/2023
6110	(154*10^121953+17)/9	121955	Robert Price	06/2022
6111	(34*10^121924+191)/9	121925	Robert Price	08/2021
6112	(2^405016+1)/257	121920	Lelio R Paula	04/2014
6113	28557^18590+18590^28557	121918	Hans Havermann	03/2021
6114	28641^18002+18002^28641	121877	Hans Havermann	03/2021
6115	2^404858+71329	121875	Enzo Doria	04/2016
6116	2^404813-114703	121861	Enzo Doria	04/2015
6117	2^404764+77791	121847	Enzo Doria	05/2016
6118	28830^16841+16841^28830	121847	Hans Havermann	03/2021
6119	(4*10^121825+89)/3	121826	Robert Price	08/2021
6120	317^48694+48694^317	121787	Norbert Schneider	08/2015
6121	2^404536-115259	121778	Enzo Doria	06/2015
6122	2^404501-631	121767	Yves Minet	07/2012
6123	5*10^121764-69	121765	Robert Price	02/2021
6124	(34^79493-3^79493)/31	121741	Robert Price	07/2025
6125	28236^20485+20485^28236	121738	Hans Havermann	02/2021
6126	(382*10^121694-31)/9	121696	Robert Price	06/2022
6127	63^67620+2	121672	Lelio R Paula	08/2015
6128	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
6129	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
6130	(16*10^121633+167)/3	121634	Robert Price	06/2019
6131	29955^11494+11494^29955	121632	Hans Havermann	02/2021
6132	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
6133	31088^8163+8163^31088	121612	Hans Havermann	02/2021
6134	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
6135	(211^52301-1)/210	121560	Anonymous	04/2024
6136	(10^121543-79)/3	121543	Robert Price	01/2018
6137	801^41852-41852^801	121523	Norman Luhn	10/2024
6138	2^403676+76831	121519	Enzo Doria	05/2016
6139	(41^75337-1)/98233421080	121492	Paul Vanderveen	05/2025
6140	715^42564-42564^715	121491	Norman Luhn	10/2024
6141	(7*10^121487+143)/3	121488	Robert Price	03/2018
6142	27965^22086+22086^27965	121484	Hans Havermann	02/2021
6143	(893*10^121470+7)/9	121472	Robert Price	06/2021
6144	(206*10^121462-11)/3	121464	Robert Price	02/2022
6145	26282^27481-27481^26282	121457	Frank Doornink	03/2024
6146	(77*10^121455+67)/9	121456	Robert Price	12/2021
6147	2^403363-113635	121425	Enzo Doria	08/2014
6148	25531^27552-27552^25531	121424	Frank Doornink	02/2024
6149	(17*10^121418-113)/3	121419	Robert Price	06/2021
6150	2^403336-1861469	121417	Enzo Doria	03/2016
6151	27929^22186+22186^27929	121382	Hans Havermann	02/2021
6152	p(24442)#/2-64	121381	Robert Price	04/2017
6153	11^116555-720	121380	Enzo Doria	11/2012
6154	(873^41263+1)/874	121353	Jinyuan Wang	12/2024
6155	2^403100-461267	121346	Enzo Doria	07/2015
6156	2^403093-112213	121344	Enzo Doria	06/2014
6157	29404^13385+13385^29404	121340	Hans Havermann	02/2021
6158	28106^20745+20745^28106	121332	Hans Havermann	02/2021
6159	(316^48539+1)/317	121330	Eric Chen	10/2017
6160	(23*10^121320-71)/3	121321	Robert Price	07/2020
6161	2^403004+1866361	121317	Enzo Doria	03/2016
6162	2^402953+89	121301	Lelio R Paula	10/2013
6163	2^402944-2788319	121299	Enzo Doria	03/2016
6164	(44*10^121297-719)/9	121298	Robert Price	12/2018
6165	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
6166	2^402828-113183	121264	Enzo Doria	07/2014
6167	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
6168	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
6169	282^49477-49477^282	121231	Norman Luhn	10/2024
6171	2^402715+1874223	121230	Enzo Doria	06/2016
6170	(35*10^121229-593)/9	121230	Robert Price	07/2018
6172	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
6173	291^49190-49190^291	121199	Norman Luhn	10/2024
6174	(10^121243)/(121243^10)	121193	Henri Lifchitz	05/2025
6175	28719^16568+16568^28719	121174	Hans Havermann	02/2021
6176	7*10^121144+9	121145	Robert Price	09/2015
6177	27490^25467+25467^27490	121121	Hans Havermann	02/2021
6178	34575^3182+3182^34575	121106	Hans Havermann	02/2021
6179	5*10^121100-37	121101	Robert Price	11/2021
6180	F(579521)/516247738177	121101	Serge Batalov	07/2024
6181	25592^27467-27467^25592	121078	Frank Doornink	02/2024
6182	29954^10935+10935^29954	120979	Hans Havermann	02/2021
6183	33585^3992+3992^33585	120946	Hans Havermann	02/2021
6184	40296^1003+1003^40296	120941	Hans Havermann	02/2021
6185	2^401725-113251	120932	Enzo Doria	07/2014
6186	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
6187	2^401652+73711	120910	Enzo Doria	04/2016
6188	(2^401632+3)/79	120902	Lelio R Paula	04/2014
6189	40450^973+973^40450	120870	Hans Havermann	01/2021
6190	(8*10^120851-11)/3	120852	Robert Price	07/2023
6191	10^120841+88417	120842	Patrick De Geest	04/2020
6192	10^120841-123456789	120841	Robert Price	02/2020
6193	10^120841-176853	120841	Patrick De Geest	04/2020
6194	2^401406-2791331	120836	Enzo Doria	03/2016
6195	(28^83497+1)/29	120832	Robert Price	07/2013
6196	(22*10^120828+161)/3	120829	Robert Price	05/2019
6197	2^401369+1867367	120825	Enzo Doria	03/2016
6198	(5*10^120821+43)/3	120822	Robert Price	12/2021
6199	26990^27263-27263^26990	120808	Frank Doornink	03/2024
6200	(10^120782+29)/3	120782	Serge Batalov	12/2014
6201	2^401215-1657	120778	Yves Minet	07/2014
6202	2^401159+53	120761	Lelio R Paula	10/2013
6203	27782^22179+22179^27782	120739	Hans Havermann	01/2021
6204	242^50649-50649^242	120738	Norman Luhn	09/2024
6205	32974^4585+4585^32974	120730	Hans Havermann	02/2021
6206	2^401031-113047	120723	Enzo Doria	07/2014
6207	30598^8813+8813^30598	120713	Hans Havermann	02/2021
6208	(71*10^120703-287)/9	120704	Robert Price	09/2019
6209	25671^27370-27370^25671	120687	Frank Doornink	02/2024
6210	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
6211	34793^2940+2940^34793	120675	Hans Havermann	02/2021
6212	26028^27329-27329^26028	120670	Frank Doornink	03/2024
6213	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
6214	(166*10^120654+11)/3	120656	Robert Price	03/2021
6215	34066^3481+3481^34066	120652	Hans Havermann	02/2021
6216	8*10^120637-27	120638	Robert Price	10/2021
6217	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
6218	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
6219	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
6220	9*10^120617-61	120618	Robert Price	06/2021
6221	(29*10^120590-71)/3	120591	Robert Price	07/2021
6222	2^400571-15	120584	Lelio R Paula	10/2013
6223	(10^120574+359)/9	120574	Serge Batalov	12/2014
6224	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
6225	27431^24810+24810^27431	120550	Hans Havermann	02/2021
6226	2^400424-216413	120540	Enzo Doria	04/2013
6227	29090^13911+13911^29090	120531	Hans Havermann	02/2021
6228	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
6229	27899^20868+20868^27899	120510	Hans Havermann	02/2021
6230	33740^3729+3729^33740	120506	Hans Havermann	02/2021
6231	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
6232	17228^28437-28437^17228	120466	Norbert Schneider	08/2025
6233	1069^39770-39770^1069	120463	Norbert Schneider	05/2025
6235	2^400166+1874899	120462	Enzo Doria	06/2016
6234	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
6236	2739^35038-35038^2739	120447	Norbert Schneider	05/2025
6237	37078^1771+1771^37078	120438	Hans Havermann	02/2021
6238	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
6239	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
6240	12857^29306-29306^12857	120423	Norbert Schneider	07/2025
6241	2^399999+54173	120412	Norman Luhn	08/2023
6242	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
6243	2^399966+73759	120402	Enzo Doria	04/2016
6244	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
6245	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
6246	2^399918-95	120388	Lelio R Paula	04/2013
6247	2^399918+214009	120388	Enzo Doria	10/2023
6248	(28*10^120381-67)/3	120382	Robert Price	10/2020
6249	(49*10^120380-139)/9	120381	Robert Price	03/2019
6250	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020

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Probable Primes Top 10000

(301969 PRPs in the top)