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	34015^11134+11134^34015	137647	Hans Havermann	06/2021
5002	2^457240-59939	137643	Enzo Doria	10/2015
5003	(856*10^137633-1)/9	137635	Robert Price	03/2020
5004	36232^6289+6289^36232	137631	Hans Havermann	05/2021
5005	2^457120-21575	137607	Enzo Doria	07/2013
5007	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
5006	30963^27722+27722^30963	137564	Hans Havermann	04/2021
5008	33722^12003+12003^33722	137562	Hans Havermann	06/2021
5009	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
5010	41901^1918+1918^41901	137555	Hans Havermann	06/2021
5011	(7*10^137551-1)/3	137552	Robert Price	08/2022
5012	32930^15021+15021^32930	137539	Hans Havermann	05/2021
5013	31178^25785+25785^31178	137538	Hans Havermann	05/2021
5014	419^52446+52446^419	137525	Norbert Schneider	11/2020
5015	2^456813+214175	137515	Enzo Doria	10/2023
5016	2^456796-113513	137510	Enzo Doria	08/2014
5017	31788^21137+21137^31788	137485	Hans Havermann	04/2021
5018	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
5019	27151^31004-31004^27151	137466	Frank Doornink	01/2024
5020	2^456503-114361	137422	Enzo Doria	01/2015
5021	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
5022	30618^30618-5^5	137352	Serge Batalov	04/2024
5023	36248^6147+6147^36248	137332	Hans Havermann	05/2021
5024	31986^19651+19651^31986	137329	Hans Havermann	05/2021
5025	2^456167+22313	137320	Enzo Doria	09/2023
5026	31817^20656+20656^31817	137292	Hans Havermann	05/2021
5027	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
5028	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
5029	2^455922+76249	137247	Enzo Doria	05/2016
5030	31310^24171+24171^31310	137241	Hans Havermann	05/2021
5031	14^119741-119741^14	137239	Serge Batalov	04/2016
5032	35014^8297+8297^35014	137218	Hans Havermann	05/2021
5033	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
5035	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
5034	124^65536+57^65536	137195	Serge Batalov	03/2018
5036	2^455689+72677	137177	Enzo Doria	04/2016
5037	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
5038	31287^24128+24128^31287	137116	Hans Havermann	05/2021
5039	(37^87421-1)/36	137093	Robert Price	03/2012
5040	36233^6070+6070^36233	137077	Hans Havermann	05/2021
5041	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
5042	38418^3697+3697^38418	137070	Hans Havermann	04/2021
5043	2^455323-57	137066	Lelio R Paula	09/2017
5044	(56*10^137019+583)/9	137020	Robert Price	08/2021
5045	25017^31148-31148^25017	136997	Frank Doornink	12/2023
5046	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
5047	2^455025-112723	136977	Enzo Doria	06/2014
5048	33876^11039+11039^33876	136959	Hans Havermann	05/2021
5049	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
5050	(251^57059-1)/250	136921	Anonymous	04/2024
5051	35142^7873+7873^35142	136919	Hans Havermann	05/2021
5052	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
5053	66*10^136894+7	136896	Robert Price	07/2020
5054	28766^30697-30697^28766	136875	Frank Doornink	05/2024
5055	2^454675-1777	136871	Yves Minet	10/2011
5056	31676^20931+20931^31676	136866	Hans Havermann	05/2021
5057	3*10^136829+29	136830	Robert Price	05/2018
5058	4*10^136813-57	136814	Robert Price	10/2018
5059	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
5060	fibonacci(654572)-2	136798	Jon Grantham	08/2023
5061	37359^4588+4588^37359	136795	Hans Havermann	05/2021
5062	2^454348-53	136773	Lelio R Paula	09/2017
5063	31^91680-2	136729	Lelio R Paula	05/2017
5064	2^454199-113697	136728	Enzo Doria	09/2014
5065	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5066	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5068	7*10^136716+69	136717	Robert Price	07/2019
5067	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5069	6*10^136692+53	136693	Robert Price	05/2020
5070	(13*10^136687+47)/3	136688	Robert Price	10/2018
5071	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5072	2^453935-2791357	136649	Enzo Doria	01/2016
5073	2^453906-69131	136640	Enzo Doria	11/2015
5074	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5075	2^453791+1873913	136605	Enzo Doria	06/2016
5076	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5077	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5078	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5079	580^49413+49413^580	136550	Norbert Schneider	02/2019
5080	2^453503-2788297	136519	Enzo Doria	11/2015
5081	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5082	(2*10^136484+187)/9	136484	Robert Price	06/2022
5083	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5084	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5085	2^453267-113827	136447	Enzo Doria	09/2014
5086	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5087	2^453102+1877629	136398	Enzo Doria	08/2016
5088	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5089	(62*10^136384-791)/9	136385	Robert Price	06/2019
5090	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5091	(17*10^136354-113)/3	136355	Robert Price	06/2021
5092	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5093	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5094	(25*10^136303+161)/3	136304	Robert Price	09/2019
5095	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5096	(182*10^136291+1)/3	136293	Robert Price	02/2020
5097	(88*10^136234+83)/9	136235	Robert Price	03/2022
5098	23*10^136225-7	136227	Robert Price	02/2020
5099	L(651821)	136223	Henri Lifchitz	09/2008
5100	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5101	2^452460+77701	136205	Enzo Doria	05/2016
5102	2^452440-114755	136199	Enzo Doria	04/2015
5103	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5104	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5105	(47*10^136141+493)/9	136142	Robert Price	03/2019
5106	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5107	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5108	2*10^136057-43	136058	Robert Price	04/2018
5109	2^451971+21563	136057	Enzo Doria	08/2023
5110	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5111	2^451947-22165	136050	Enzo Doria	07/2013
5112	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5113	2^451787-21805	136002	Enzo Doria	07/2013
5114	2^451734-112817	135986	Enzo Doria	06/2014
5115	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5116	2^451705-21879	135977	Enzo Doria	07/2013
5117	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5118	2^451560-112349	135934	Enzo Doria	06/2014
5119	2^451530+45	135925	Lelio R Paula	08/2017
5120	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5121	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5122	(25*10^135906-73)/3	135907	Robert Price	09/2019
5123	2^451450-21743	135900	Enzo Doria	07/2013
5124	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5125	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5126	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5127	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5128	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5129	(77*10^135789+157)/9	135790	Robert Price	05/2022
5130	2^450958+60529	135752	Enzo Doria	08/2023
5131	2^450805+65	135706	Lelio R Paula	08/2017
5132	10^135669+21	135670	Boyan Hu	12/2024
5133	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5134	2*10^135663+69	135664	Robert Price	06/2020
5135	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5136	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5137	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5138	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5139	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5140	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5141	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5142	(76*10^135553-49)/9	135554	Robert Price	07/2022
5143	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5144	(844*10^135527-7)/9	135529	Robert Price	05/2021
5145	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5146	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5147	2^449944-113247	135447	Enzo Doria	07/2014
5148	2^449770-113247	135395	Enzo Doria	07/2014
5149	2^449637-21471	135355	Enzo Doria	07/2013
5150	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5151	2^449571-75	135335	Lelio R Paula	08/2017
5152	(14*10^135301-53)/3	135302	Robert Price	12/2018
5153	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5154	(13*10^135279+437)/9	135280	Robert Price	04/2018
5155	2^449330-35	135262	Lelio R Paula	08/2017
5156	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5157	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5158	(13*10^135184-43)/3	135185	Robert Price	11/2018
5159	2^449049-115309	135178	Enzo Doria	07/2015
5160	(10^135174+191)/3	135174	Robert Price	02/2018
5161	2^449030-15	135172	Lelio R Paula	08/2017
5162	(157*10^135151-1)/3	135153	Robert Price	01/2022
5163	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5164	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5165	(37*10^135099+251)/9	135100	Robert Price	09/2021
5166	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5167	2^448762-351401	135091	Enzo Doria	07/2015
5168	2*10^135083-43	135084	Robert Price	04/2018
5169	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5170	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5171	k(198476)	135054	Robert Price	07/2020
5172	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5173	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5174	5*10^135019+77	135020	Robert Price	12/2018
5175	(10^135011+719)/9	135011	Serge Batalov	12/2014
5176	(197*10^134978+7)/3	134980	Robert Price	12/2020
5177	2^448386-2786261	134978	Enzo Doria	03/2016
5178	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5179	(73*10^134939+143)/9	134940	Robert Price	07/2019
5180	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5181	2^448122+20809	134899	Enzo Doria	08/2023
5182	2^448113-113949	134896	Enzo Doria	11/2014
5183	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5184	2^447888-2786639	134828	Enzo Doria	03/2016
5185	2^447870-396765	134823	Enzo Doria	07/2013
5186	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5187	2^447766-21791	134791	Enzo Doria	07/2013
5188	(19*10^134786-49)/3	134787	Robert Price	05/2019
5189	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5190	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5191	2^447552-1019	134727	Yves Minet	02/2014
5192	(2*10^134720-41)/3	134720	Robert Price	02/2018
5193	(25*10^134695-97)/9	134696	Robert Price	01/2022
5194	2^447437-113569	134692	Enzo Doria	08/2014
5195	2^447426-65	134689	Lelio R Paula	08/2017
5196	2^447357-2797573	134668	Enzo Doria	04/2016
5197	2^447278+93	134645	Lelio R Paula	08/2017
5198	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5199	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5200	2^447094-113193	134589	Enzo Doria	07/2014
5201	3^282041-9934	134568	Enzo Doria	05/2014
5202	2^447019-109039	134567	Enzo Doria	04/2014
5203	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5204	2^446990-22041	134558	Enzo Doria	07/2013
5205	123^64370+122	134528	Karsten Bonath	04/2018
5206	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5207	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5208	2^446782-39701	134495	Enzo Doria	09/2015
5209	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5210	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5211	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5212	2^446494-16485	134409	Enzo Doria	04/2013
5213	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5214	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5215	2^446441+65	134393	Lelio R Paula	08/2017
5216	(10^134385+719)/9	134385	Serge Batalov	12/2014
5217	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5218	(2*10^134364+529)/9	134364	Robert Price	01/2018
5219	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5220	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5221	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5222	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5224	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5223	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5225	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5226	(189^58967-1)/188	134234	Anonymous	06/2024
5227	10^134209+99867	134210	Patrick De Geest	05/2021
5228	10^134209-80000001	134209	Robert Price	04/2021
5229	10^134209-323283	134209	Patrick De Geest	05/2021
5230	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5231	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5232	63^74568+2	134174	Lelio R Paula	06/2017
5233	2^445671-22071	134161	Enzo Doria	07/2013
5234	532^49205+49205^532	134129	Norbert Schneider	02/2019
5235	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5236	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5237	2^445515-113859	134114	Enzo Doria	10/2014
5239	(22*10^134111-37)/3	134112	Robert Price	04/2019
5238	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5240	3*2^445478+5	134103	Jon Grantham	07/2023
5241	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5242	5*2^445380-3	134074	Jon Grantham	07/2023
5243	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5244	(277*10^134059-7)/9	134061	Robert Price	02/2022
5245	2^445328-216917	134058	Enzo Doria	05/2014
5246	2^445202+1874899	134020	Enzo Doria	06/2016
5247	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5248	(35*10^134003-89)/9	134004	Robert Price	02/2022
5249	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5250	(35*10^133979-593)/9	133980	Robert Price	07/2018

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Probable Primes Top 10000

(302010 PRPs in the top)