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	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
5002	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
5003	2^455922+76249	137247	Enzo Doria	05/2016
5004	31310^24171+24171^31310	137241	Hans Havermann	05/2021
5005	14^119741-119741^14	137239	Serge Batalov	04/2016
5006	35014^8297+8297^35014	137218	Hans Havermann	05/2021
5007	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
5009	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
5008	124^65536+57^65536	137195	Serge Batalov	03/2018
5010	2^455689+72677	137177	Enzo Doria	04/2016
5011	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
5012	31287^24128+24128^31287	137116	Hans Havermann	05/2021
5013	(37^87421-1)/36	137093	Robert Price	03/2012
5014	36233^6070+6070^36233	137077	Hans Havermann	05/2021
5015	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
5016	38418^3697+3697^38418	137070	Hans Havermann	04/2021
5017	2^455323-57	137066	Lelio R Paula	09/2017
5018	(56*10^137019+583)/9	137020	Robert Price	08/2021
5019	25017^31148-31148^25017	136997	Frank Doornink	12/2023
5020	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
5021	2^455025-112723	136977	Enzo Doria	06/2014
5022	33876^11039+11039^33876	136959	Hans Havermann	05/2021
5023	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
5024	(251^57059-1)/250	136921	Anonymous	04/2024
5025	35142^7873+7873^35142	136919	Hans Havermann	05/2021
5026	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
5027	66*10^136894+7	136896	Robert Price	07/2020
5028	28766^30697-30697^28766	136875	Frank Doornink	05/2024
5029	2^454675-1777	136871	Yves Minet	10/2011
5030	31676^20931+20931^31676	136866	Hans Havermann	05/2021
5031	3*10^136829+29	136830	Robert Price	05/2018
5032	4*10^136813-57	136814	Robert Price	10/2018
5033	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
5034	fibonacci(654572)-2	136798	Jon Grantham	08/2023
5035	37359^4588+4588^37359	136795	Hans Havermann	05/2021
5036	2^454348-53	136773	Lelio R Paula	09/2017
5037	31^91680-2	136729	Lelio R Paula	05/2017
5038	2^454199-113697	136728	Enzo Doria	09/2014
5039	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5040	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5042	7*10^136716+69	136717	Robert Price	07/2019
5041	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5043	6*10^136692+53	136693	Robert Price	05/2020
5044	(13*10^136687+47)/3	136688	Robert Price	10/2018
5045	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5046	2^453935-2791357	136649	Enzo Doria	01/2016
5047	2^453906-69131	136640	Enzo Doria	11/2015
5048	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5049	2^453791+1873913	136605	Enzo Doria	06/2016
5050	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5051	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5052	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5053	580^49413+49413^580	136550	Norbert Schneider	02/2019
5054	2^453503-2788297	136519	Enzo Doria	11/2015
5055	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5056	(2*10^136484+187)/9	136484	Robert Price	06/2022
5057	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5058	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5059	2^453267-113827	136447	Enzo Doria	09/2014
5060	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5061	2^453102+1877629	136398	Enzo Doria	08/2016
5062	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5063	(62*10^136384-791)/9	136385	Robert Price	06/2019
5064	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5065	(17*10^136354-113)/3	136355	Robert Price	06/2021
5066	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5067	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5068	(25*10^136303+161)/3	136304	Robert Price	09/2019
5069	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5070	(182*10^136291+1)/3	136293	Robert Price	02/2020
5071	(88*10^136234+83)/9	136235	Robert Price	03/2022
5072	23*10^136225-7	136227	Robert Price	02/2020
5073	L(651821)	136223	Henri Lifchitz	09/2008
5074	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5075	2^452460+77701	136205	Enzo Doria	05/2016
5076	2^452440-114755	136199	Enzo Doria	04/2015
5077	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5078	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5079	(47*10^136141+493)/9	136142	Robert Price	03/2019
5080	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5081	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5082	2*10^136057-43	136058	Robert Price	04/2018
5083	2^451971+21563	136057	Enzo Doria	08/2023
5084	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5085	2^451947-22165	136050	Enzo Doria	07/2013
5086	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5087	2^451787-21805	136002	Enzo Doria	07/2013
5088	2^451734-112817	135986	Enzo Doria	06/2014
5089	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5090	2^451705-21879	135977	Enzo Doria	07/2013
5091	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5092	2^451560-112349	135934	Enzo Doria	06/2014
5093	2^451530+45	135925	Lelio R Paula	08/2017
5094	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5095	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5096	(25*10^135906-73)/3	135907	Robert Price	09/2019
5097	2^451450-21743	135900	Enzo Doria	07/2013
5098	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5099	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5100	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5101	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5102	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5103	(77*10^135789+157)/9	135790	Robert Price	05/2022
5104	2^450958+60529	135752	Enzo Doria	08/2023
5105	2^450805+65	135706	Lelio R Paula	08/2017
5106	10^135669+21	135670	Boyan Hu	12/2024
5107	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5108	2*10^135663+69	135664	Robert Price	06/2020
5109	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5110	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5111	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5112	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5113	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5114	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5115	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5116	(76*10^135553-49)/9	135554	Robert Price	07/2022
5117	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5118	(844*10^135527-7)/9	135529	Robert Price	05/2021
5119	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5120	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5121	2^449944-113247	135447	Enzo Doria	07/2014
5122	2^449770-113247	135395	Enzo Doria	07/2014
5123	2^449637-21471	135355	Enzo Doria	07/2013
5124	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5125	2^449571-75	135335	Lelio R Paula	08/2017
5126	(14*10^135301-53)/3	135302	Robert Price	12/2018
5127	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5128	(13*10^135279+437)/9	135280	Robert Price	04/2018
5129	2^449330-35	135262	Lelio R Paula	08/2017
5130	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5131	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5132	(13*10^135184-43)/3	135185	Robert Price	11/2018
5133	2^449049-115309	135178	Enzo Doria	07/2015
5134	(10^135174+191)/3	135174	Robert Price	02/2018
5135	2^449030-15	135172	Lelio R Paula	08/2017
5136	(157*10^135151-1)/3	135153	Robert Price	01/2022
5137	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5138	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5139	(37*10^135099+251)/9	135100	Robert Price	09/2021
5140	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5141	2^448762-351401	135091	Enzo Doria	07/2015
5142	2*10^135083-43	135084	Robert Price	04/2018
5143	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5144	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5145	k(198476)	135054	Robert Price	07/2020
5146	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5147	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5148	5*10^135019+77	135020	Robert Price	12/2018
5149	(10^135011+719)/9	135011	Serge Batalov	12/2014
5150	(197*10^134978+7)/3	134980	Robert Price	12/2020
5151	2^448386-2786261	134978	Enzo Doria	03/2016
5152	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5153	(73*10^134939+143)/9	134940	Robert Price	07/2019
5154	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5155	2^448122+20809	134899	Enzo Doria	08/2023
5156	2^448113-113949	134896	Enzo Doria	11/2014
5157	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5158	2^447888-2786639	134828	Enzo Doria	03/2016
5159	2^447870-396765	134823	Enzo Doria	07/2013
5160	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5161	2^447766-21791	134791	Enzo Doria	07/2013
5162	(19*10^134786-49)/3	134787	Robert Price	05/2019
5163	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5164	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5165	2^447552-1019	134727	Yves Minet	02/2014
5166	(2*10^134720-41)/3	134720	Robert Price	02/2018
5167	(25*10^134695-97)/9	134696	Robert Price	01/2022
5168	2^447437-113569	134692	Enzo Doria	08/2014
5169	2^447426-65	134689	Lelio R Paula	08/2017
5170	2^447357-2797573	134668	Enzo Doria	04/2016
5171	2^447278+93	134645	Lelio R Paula	08/2017
5172	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5173	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5174	2^447094-113193	134589	Enzo Doria	07/2014
5175	3^282041-9934	134568	Enzo Doria	05/2014
5176	2^447019-109039	134567	Enzo Doria	04/2014
5177	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5178	2^446990-22041	134558	Enzo Doria	07/2013
5179	123^64370+122	134528	Karsten Bonath	04/2018
5180	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5181	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5182	2^446782-39701	134495	Enzo Doria	09/2015
5183	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5184	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5185	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5186	2^446494-16485	134409	Enzo Doria	04/2013
5187	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5188	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5189	2^446441+65	134393	Lelio R Paula	08/2017
5190	(10^134385+719)/9	134385	Serge Batalov	12/2014
5191	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5192	(2*10^134364+529)/9	134364	Robert Price	01/2018
5193	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5194	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5195	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5196	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5198	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5197	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5199	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5200	(189^58967-1)/188	134234	Anonymous	06/2024
5201	10^134209+99867	134210	Patrick De Geest	05/2021
5202	10^134209-80000001	134209	Robert Price	04/2021
5203	10^134209-323283	134209	Patrick De Geest	05/2021
5204	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5205	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5206	63^74568+2	134174	Lelio R Paula	06/2017
5207	2^445671-22071	134161	Enzo Doria	07/2013
5208	532^49205+49205^532	134129	Norbert Schneider	02/2019
5209	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5210	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5211	2^445515-113859	134114	Enzo Doria	10/2014
5213	(22*10^134111-37)/3	134112	Robert Price	04/2019
5212	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5214	3*2^445478+5	134103	Jon Grantham	07/2023
5215	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5216	5*2^445380-3	134074	Jon Grantham	07/2023
5217	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5218	(277*10^134059-7)/9	134061	Robert Price	02/2022
5219	2^445328-216917	134058	Enzo Doria	05/2014
5220	2^445202+1874899	134020	Enzo Doria	06/2016
5221	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5222	(35*10^134003-89)/9	134004	Robert Price	02/2022
5223	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5224	(35*10^133979-593)/9	133980	Robert Price	07/2018
5225	2*10^133955+51	133956	Robert Price	05/2018
5226	(49*10^133952+437)/9	133953	Robert Price	09/2021
5227	2^444964-113639	133948	Enzo Doria	08/2014
5228	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5229	10^133902+167841	133903	Patrick De Geest	05/2021
5231	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5230	10^133902-100001	133902	Robert Price	07/2020
5232	2^444784-113859	133894	Enzo Doria	10/2014
5233	(132^63127-1)/131	133864	Anonymous	06/2024
5234	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5235	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5236	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5237	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5238	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5239	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5240	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5241	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5242	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5243	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5244	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5245	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5246	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5247	(266*10^133603+1)/3	133605	Robert Price	04/2020
5248	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5249	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5250	(134*10^133573-11)/3	133575	Robert Price	01/2022

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Probable Primes Top 10000

(301979 PRPs in the top)