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	2024^41836+2025	138319	Henri Lifchitz	01/2025
5002	28782^31019-31019^28782	138318	Frank Doornink	05/2024
5003	32963^15696+15696^32963	138306	Hans Havermann	05/2021
5004	2^459343-113611	138277	Enzo Doria	08/2014
5005	(28*10^138240+113)/3	138241	Robert Price	03/2020
5006	2^459199+1874393	138233	Enzo Doria	06/2016
5007	33339^14002+14002^33339	138230	Hans Havermann	05/2021
5008	30137^30860-30860^30137	138226	Frank Doornink	05/2024
5009	2^459063-345307	138192	Enzo Doria	06/2015
5010	2*10^138162-43	138163	Robert Price	04/2018
5011	2^458927-112747	138151	Enzo Doria	06/2014
5012	2^458927-69217	138151	Enzo Doria	11/2015
5013	30907^29458+29458^30907	138130	Hans Havermann	05/2021
5014	32882^15837+15837^32882	138094	Hans Havermann	05/2021
5015	39252^3295+3295^39252	138083	Hans Havermann	05/2021
5016	33789^12190+12190^33789	138062	Hans Havermann	06/2021
5017	555555*2^458524+1513	138036	Darren Bedwell	08/2009
5018	28095^31028-31028^28095	138033	Frank Doornink	05/2024
5019	30931^29002+29002^30931	138028	Hans Havermann	05/2021
5020	2^458465+2^32+1	138012	T. D. Noe	06/2007
5021	32206^19275+19275^32206	138003	Hans Havermann	05/2021
5022	2^458321-113053	137969	Enzo Doria	07/2014
5023	6^177298+323	137965	Riley Fisher	03/2023
5024	2^458298+79459	137962	Enzo Doria	06/2016
5025	30254^30789-30789^30254	137959	Frank Doornink	05/2024
5026	2^458248-21815	137947	Enzo Doria	07/2013
5027	2^458194+1876549	137931	Enzo Doria	07/2016
5028	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
5029	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
5030	(793*10^137887+53)/9	137889	Robert Price	01/2022
5031	2^457937+57	137853	Lelio R Paula	09/2017
5032	28714^30921-30921^28714	137849	Frank Doornink	05/2024
5033	(8*10^137845+13)/3	137846	Robert Price	06/2018
5034	2^457822+105	137819	Donovan Johnson	06/2006
5035	2^457754-113711	137798	Enzo Doria	09/2014
5036	11^132315-360	137792	Enzo Doria	09/2012
5037	(2^659318)%L(659318)	137787	Henri Lifchitz	05/2025
5038	32072^19689+19689^32072	137725	Hans Havermann	06/2021
5039	26529^31132-31132^26529	137720	Frank Doornink	03/2024
5040	44592^1225+1225^44592	137707	Hans Havermann	05/2021
5041	28986^30857-30857^28986	137690	Frank Doornink	05/2024
5042	2^457347-37	137676	Lelio R Paula	09/2017
5043	2^457322-2786393	137668	Enzo Doria	10/2015
5044	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
5045	Phi(699340M,10)	137664	Anonymous	03/2025
5046	34015^11134+11134^34015	137647	Hans Havermann	06/2021
5047	2^457240-59939	137643	Enzo Doria	10/2015
5048	(856*10^137633-1)/9	137635	Robert Price	03/2020
5049	36232^6289+6289^36232	137631	Hans Havermann	05/2021
5050	2^457120-21575	137607	Enzo Doria	07/2013
5051	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
5052	30963^27722+27722^30963	137564	Hans Havermann	04/2021
5053	33722^12003+12003^33722	137562	Hans Havermann	06/2021
5054	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
5055	41901^1918+1918^41901	137555	Hans Havermann	06/2021
5056	(7*10^137551-1)/3	137552	Robert Price	08/2022
5057	32930^15021+15021^32930	137539	Hans Havermann	05/2021
5058	31178^25785+25785^31178	137538	Hans Havermann	05/2021
5059	419^52446+52446^419	137525	Norbert Schneider	11/2020
5060	2^456813+214175	137515	Enzo Doria	10/2023
5061	2^456796-113513	137510	Enzo Doria	08/2014
5062	31788^21137+21137^31788	137485	Hans Havermann	04/2021
5063	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
5064	27151^31004-31004^27151	137466	Frank Doornink	01/2024
5065	2^456503-114361	137422	Enzo Doria	01/2015
5066	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
5067	30618^30618-5^5	137352	Serge Batalov	04/2024
5068	36248^6147+6147^36248	137332	Hans Havermann	05/2021
5069	31986^19651+19651^31986	137329	Hans Havermann	05/2021
5070	2^456167+22313	137320	Enzo Doria	09/2023
5071	31817^20656+20656^31817	137292	Hans Havermann	05/2021
5072	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
5073	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
5074	2^455922+76249	137247	Enzo Doria	05/2016
5075	31310^24171+24171^31310	137241	Hans Havermann	05/2021
5076	14^119741-119741^14	137239	Serge Batalov	04/2016
5077	35014^8297+8297^35014	137218	Hans Havermann	05/2021
5078	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
5080	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
5079	124^65536+57^65536	137195	Serge Batalov	03/2018
5081	2^455689+72677	137177	Enzo Doria	04/2016
5082	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
5083	31287^24128+24128^31287	137116	Hans Havermann	05/2021
5084	(37^87421-1)/36	137093	Robert Price	03/2012
5085	36233^6070+6070^36233	137077	Hans Havermann	05/2021
5086	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
5087	38418^3697+3697^38418	137070	Hans Havermann	04/2021
5088	2^455323-57	137066	Lelio R Paula	09/2017
5089	(56*10^137019+583)/9	137020	Robert Price	08/2021
5090	25017^31148-31148^25017	136997	Frank Doornink	12/2023
5091	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
5092	2^455025-112723	136977	Enzo Doria	06/2014
5093	33876^11039+11039^33876	136959	Hans Havermann	05/2021
5094	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
5095	(251^57059-1)/250	136921	Anonymous	04/2024
5096	35142^7873+7873^35142	136919	Hans Havermann	05/2021
5097	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
5098	66*10^136894+7	136896	Robert Price	07/2020
5099	28766^30697-30697^28766	136875	Frank Doornink	05/2024
5100	2^454675-1777	136871	Yves Minet	10/2011
5101	31676^20931+20931^31676	136866	Hans Havermann	05/2021
5102	3*10^136829+29	136830	Robert Price	05/2018
5103	4*10^136813-57	136814	Robert Price	10/2018
5104	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
5105	fibonacci(654572)-2	136798	Jon Grantham	08/2023
5106	37359^4588+4588^37359	136795	Hans Havermann	05/2021
5107	2^454348-53	136773	Lelio R Paula	09/2017
5108	31^91680-2	136729	Lelio R Paula	05/2017
5109	2^454199-113697	136728	Enzo Doria	09/2014
5110	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5111	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5113	7*10^136716+69	136717	Robert Price	07/2019
5112	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5114	6*10^136692+53	136693	Robert Price	05/2020
5115	(13*10^136687+47)/3	136688	Robert Price	10/2018
5116	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5117	2^453935-2791357	136649	Enzo Doria	01/2016
5118	2^453906-69131	136640	Enzo Doria	11/2015
5119	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5120	2^453791+1873913	136605	Enzo Doria	06/2016
5121	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5122	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5123	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5124	580^49413+49413^580	136550	Norbert Schneider	02/2019
5125	2^453503-2788297	136519	Enzo Doria	11/2015
5126	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5127	(2*10^136484+187)/9	136484	Robert Price	06/2022
5128	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5129	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5130	2^453267-113827	136447	Enzo Doria	09/2014
5131	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5132	2^453102+1877629	136398	Enzo Doria	08/2016
5133	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5134	(62*10^136384-791)/9	136385	Robert Price	06/2019
5135	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5136	(17*10^136354-113)/3	136355	Robert Price	06/2021
5137	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5138	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5139	(25*10^136303+161)/3	136304	Robert Price	09/2019
5140	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5141	(182*10^136291+1)/3	136293	Robert Price	02/2020
5142	(88*10^136234+83)/9	136235	Robert Price	03/2022
5143	23*10^136225-7	136227	Robert Price	02/2020
5144	L(651821)	136223	Henri Lifchitz	09/2008
5145	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5146	2^452460+77701	136205	Enzo Doria	05/2016
5147	2^452440-114755	136199	Enzo Doria	04/2015
5148	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5149	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5150	(47*10^136141+493)/9	136142	Robert Price	03/2019
5151	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5152	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5153	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5154	2*10^136057-43	136058	Robert Price	04/2018
5155	2^451971+21563	136057	Enzo Doria	08/2023
5156	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5157	2^451947-22165	136050	Enzo Doria	07/2013
5158	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5159	2^451787-21805	136002	Enzo Doria	07/2013
5160	2^451734-112817	135986	Enzo Doria	06/2014
5161	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5162	2^451705-21879	135977	Enzo Doria	07/2013
5163	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5164	2^451560-112349	135934	Enzo Doria	06/2014
5165	2^451530+45	135925	Lelio R Paula	08/2017
5166	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5167	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5168	(25*10^135906-73)/3	135907	Robert Price	09/2019
5169	2^451450-21743	135900	Enzo Doria	07/2013
5170	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5171	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5172	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5173	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5174	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5175	(77*10^135789+157)/9	135790	Robert Price	05/2022
5176	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5177	2^450958+60529	135752	Enzo Doria	08/2023
5178	2^450805+65	135706	Lelio R Paula	08/2017
5179	10^135669+21	135670	Boyan Hu	12/2024
5180	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5181	2*10^135663+69	135664	Robert Price	06/2020
5182	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5183	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5184	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5185	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5186	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5187	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5189	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5188	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5190	(76*10^135553-49)/9	135554	Robert Price	07/2022
5191	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5192	(844*10^135527-7)/9	135529	Robert Price	05/2021
5193	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5194	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5195	2^449944-113247	135447	Enzo Doria	07/2014
5196	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5197	2^449770-113247	135395	Enzo Doria	07/2014
5198	2^449637-21471	135355	Enzo Doria	07/2013
5199	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5200	2^449571-75	135335	Lelio R Paula	08/2017
5201	(14*10^135301-53)/3	135302	Robert Price	12/2018
5202	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5203	(13*10^135279+437)/9	135280	Robert Price	04/2018
5204	2^449330-35	135262	Lelio R Paula	08/2017
5205	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5206	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5207	(13*10^135184-43)/3	135185	Robert Price	11/2018
5208	2^449049-115309	135178	Enzo Doria	07/2015
5209	(10^135174+191)/3	135174	Robert Price	02/2018
5210	2^449030-15	135172	Lelio R Paula	08/2017
5211	(157*10^135151-1)/3	135153	Robert Price	01/2022
5212	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5213	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5214	(37*10^135099+251)/9	135100	Robert Price	09/2021
5215	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5216	2^448762-351401	135091	Enzo Doria	07/2015
5217	2*10^135083-43	135084	Robert Price	04/2018
5218	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5219	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5220	k(198476)	135054	Robert Price	07/2020
5221	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5222	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5223	5*10^135019+77	135020	Robert Price	12/2018
5224	(10^135011+719)/9	135011	Serge Batalov	12/2014
5225	(197*10^134978+7)/3	134980	Robert Price	12/2020
5226	2^448386-2786261	134978	Enzo Doria	03/2016
5227	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5228	(73*10^134939+143)/9	134940	Robert Price	07/2019
5229	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5230	2^448122+20809	134899	Enzo Doria	08/2023
5231	2^448113-113949	134896	Enzo Doria	11/2014
5232	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5233	2^447888-2786639	134828	Enzo Doria	03/2016
5234	2^447870-396765	134823	Enzo Doria	07/2013
5235	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5236	2^447766-21791	134791	Enzo Doria	07/2013
5237	(19*10^134786-49)/3	134787	Robert Price	05/2019
5238	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5239	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5240	2^447552-1019	134727	Yves Minet	02/2014
5241	(2*10^134720-41)/3	134720	Robert Price	02/2018
5242	(25*10^134695-97)/9	134696	Robert Price	01/2022
5243	2^447437-113569	134692	Enzo Doria	08/2014
5244	2^447426-65	134689	Lelio R Paula	08/2017
5245	2^447357-2797573	134668	Enzo Doria	04/2016
5246	2^447278+93	134645	Lelio R Paula	08/2017
5247	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5248	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5249	2^447094-113193	134589	Enzo Doria	07/2014
5250	3^282041-9934	134568	Enzo Doria	05/2014

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Probable Primes Top 10000

(302281 PRPs in the top)