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 ?
4751	32963^15696+15696^32963	138306	Hans Havermann	05/2021
4752	2^459343-113611	138277	Enzo Doria	08/2014
4753	(28*10^138240+113)/3	138241	Robert Price	03/2020
4754	2^459199+1874393	138233	Enzo Doria	06/2016
4755	33339^14002+14002^33339	138230	Hans Havermann	05/2021
4756	30137^30860-30860^30137	138226	Frank Doornink	05/2024
4757	2^459063-345307	138192	Enzo Doria	06/2015
4758	2*10^138162-43	138163	Robert Price	04/2018
4759	2^458927-112747	138151	Enzo Doria	06/2014
4760	2^458927-69217	138151	Enzo Doria	11/2015
4761	30907^29458+29458^30907	138130	Hans Havermann	05/2021
4762	32882^15837+15837^32882	138094	Hans Havermann	05/2021
4763	39252^3295+3295^39252	138083	Hans Havermann	05/2021
4764	33789^12190+12190^33789	138062	Hans Havermann	06/2021
4765	555555*2^458524+1513	138036	Darren Bedwell	08/2009
4766	28095^31028-31028^28095	138033	Frank Doornink	05/2024
4767	30931^29002+29002^30931	138028	Hans Havermann	05/2021
4768	2^458465+2^32+1	138012	T. D. Noe	06/2007
4769	32206^19275+19275^32206	138003	Hans Havermann	05/2021
4770	2^458321-113053	137969	Enzo Doria	07/2014
4771	6^177298+323	137965	Riley Fisher	03/2023
4772	2^458298+79459	137962	Enzo Doria	06/2016
4773	30254^30789-30789^30254	137959	Frank Doornink	05/2024
4774	2^458248-21815	137947	Enzo Doria	07/2013
4775	2^458194+1876549	137931	Enzo Doria	07/2016
4776	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
4777	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
4778	(793*10^137887+53)/9	137889	Robert Price	01/2022
4779	2^457937+57	137853	Lelio R Paula	09/2017
4780	28714^30921-30921^28714	137849	Frank Doornink	05/2024
4781	(8*10^137845+13)/3	137846	Robert Price	06/2018
4782	2^457822+105	137819	Donovan Johnson	06/2006
4783	2^457754-113711	137798	Enzo Doria	09/2014
4784	11^132315-360	137792	Enzo Doria	09/2012
4785	(2^659318)%L(659318)	137787	Henri Lifchitz	05/2025
4786	32072^19689+19689^32072	137725	Hans Havermann	06/2021
4787	26529^31132-31132^26529	137720	Frank Doornink	03/2024
4788	44592^1225+1225^44592	137707	Hans Havermann	05/2021
4789	28986^30857-30857^28986	137690	Frank Doornink	05/2024
4790	2^457347-37	137676	Lelio R Paula	09/2017
4791	2^457322-2786393	137668	Enzo Doria	10/2015
4792	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
4793	Phi(699340M,10)	137664	Anonymous	03/2025
4794	34015^11134+11134^34015	137647	Hans Havermann	06/2021
4795	2^457240-59939	137643	Enzo Doria	10/2015
4796	(856*10^137633-1)/9	137635	Robert Price	03/2020
4797	36232^6289+6289^36232	137631	Hans Havermann	05/2021
4798	2^457120-21575	137607	Enzo Doria	07/2013
4800	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
4799	30963^27722+27722^30963	137564	Hans Havermann	04/2021
4801	33722^12003+12003^33722	137562	Hans Havermann	06/2021
4802	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
4803	41901^1918+1918^41901	137555	Hans Havermann	06/2021
4804	(7*10^137551-1)/3	137552	Robert Price	08/2022
4805	32930^15021+15021^32930	137539	Hans Havermann	05/2021
4806	31178^25785+25785^31178	137538	Hans Havermann	05/2021
4807	419^52446+52446^419	137525	Norbert Schneider	11/2020
4808	2^456813+214175	137515	Enzo Doria	10/2023
4809	2^456796-113513	137510	Enzo Doria	08/2014
4810	31788^21137+21137^31788	137485	Hans Havermann	04/2021
4811	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
4812	27151^31004-31004^27151	137466	Frank Doornink	01/2024
4813	2^456503-114361	137422	Enzo Doria	01/2015
4814	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
4815	30618^30618-5^5	137352	Serge Batalov	04/2024
4816	36248^6147+6147^36248	137332	Hans Havermann	05/2021
4817	31986^19651+19651^31986	137329	Hans Havermann	05/2021
4818	2^456167+22313	137320	Enzo Doria	09/2023
4819	31817^20656+20656^31817	137292	Hans Havermann	05/2021
4820	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
4821	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
4822	2^455922+76249	137247	Enzo Doria	05/2016
4823	31310^24171+24171^31310	137241	Hans Havermann	05/2021
4824	14^119741-119741^14	137239	Serge Batalov	04/2016
4825	35014^8297+8297^35014	137218	Hans Havermann	05/2021
4826	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
4828	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
4827	124^65536+57^65536	137195	Serge Batalov	03/2018
4829	2^455689+72677	137177	Enzo Doria	04/2016
4830	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
4831	31287^24128+24128^31287	137116	Hans Havermann	05/2021
4832	(37^87421-1)/36	137093	Robert Price	03/2012
4833	36233^6070+6070^36233	137077	Hans Havermann	05/2021
4834	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
4835	38418^3697+3697^38418	137070	Hans Havermann	04/2021
4836	2^455323-57	137066	Lelio R Paula	09/2017
4837	(56*10^137019+583)/9	137020	Robert Price	08/2021
4838	25017^31148-31148^25017	136997	Frank Doornink	12/2023
4839	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
4840	2^455025-112723	136977	Enzo Doria	06/2014
4841	33876^11039+11039^33876	136959	Hans Havermann	05/2021
4842	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
4843	(251^57059-1)/250	136921	Anonymous	04/2024
4844	35142^7873+7873^35142	136919	Hans Havermann	05/2021
4845	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
4846	66*10^136894+7	136896	Robert Price	07/2020
4847	28766^30697-30697^28766	136875	Frank Doornink	05/2024
4848	2^454675-1777	136871	Yves Minet	10/2011
4849	31676^20931+20931^31676	136866	Hans Havermann	05/2021
4850	3*10^136829+29	136830	Robert Price	05/2018
4851	4*10^136813-57	136814	Robert Price	10/2018
4852	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
4853	fibonacci(654572)-2	136798	Jon Grantham	08/2023
4854	37359^4588+4588^37359	136795	Hans Havermann	05/2021
4855	2^454348-53	136773	Lelio R Paula	09/2017
4856	31^91680-2	136729	Lelio R Paula	05/2017
4857	2^454199-113697	136728	Enzo Doria	09/2014
4858	30785^27622+27622^30785	136725	Hans Havermann	05/2021
4859	32973^14014+14014^32973	136725	Hans Havermann	05/2021
4861	7*10^136716+69	136717	Robert Price	07/2019
4860	36002^6273+6273^36002	136717	Hans Havermann	05/2021
4862	6*10^136692+53	136693	Robert Price	05/2020
4863	(13*10^136687+47)/3	136688	Robert Price	10/2018
4864	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
4865	2^453935-2791357	136649	Enzo Doria	01/2016
4866	2^453906-69131	136640	Enzo Doria	11/2015
4867	33232^12915+12915^33232	136620	Hans Havermann	05/2021
4868	2^453791+1873913	136605	Enzo Doria	06/2016
4869	34166^9951+9951^34166	136592	Hans Havermann	05/2021
4870	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
4871	31102^24635+24635^31102	136587	Hans Havermann	05/2021
4872	580^49413+49413^580	136550	Norbert Schneider	02/2019
4873	2^453503-2788297	136519	Enzo Doria	11/2015
4874	34989^7958+7958^34989	136486	Hans Havermann	12/2020
4875	(2*10^136484+187)/9	136484	Robert Price	06/2022
4876	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
4877	31007^25158+25158^31007	136452	Hans Havermann	11/2020
4878	2^453267-113827	136447	Enzo Doria	09/2014
4879	32234^17085+17085^32234	136435	Hans Havermann	12/2020
4880	2^453102+1877629	136398	Enzo Doria	08/2016
4881	31016^24981+24981^31016	136397	Hans Havermann	12/2020
4882	(62*10^136384-791)/9	136385	Robert Price	06/2019
4883	34171^9798+9798^34171	136382	Hans Havermann	12/2020
4884	(17*10^136354-113)/3	136355	Robert Price	06/2021
4885	32756^14541+14541^32756	136350	Hans Havermann	11/2020
4886	32205^17086+17086^32205	136313	Hans Havermann	12/2020
4887	(25*10^136303+161)/3	136304	Robert Price	09/2019
4888	35337^7196+7196^35337	136299	Hans Havermann	12/2020
4889	(182*10^136291+1)/3	136293	Robert Price	02/2020
4890	(88*10^136234+83)/9	136235	Robert Price	03/2022
4891	23*10^136225-7	136227	Robert Price	02/2020
4892	L(651821)	136223	Henri Lifchitz	09/2008
4893	25519^30908-30908^25519	136208	Frank Doornink	02/2024
4894	2^452460+77701	136205	Enzo Doria	05/2016
4895	2^452440-114755	136199	Enzo Doria	04/2015
4896	28625^30558-30558^28625	136190	Frank Doornink	05/2024
4897	32286^16489+16489^32286	136157	Hans Havermann	11/2020
4898	(47*10^136141+493)/9	136142	Robert Price	03/2019
4899	27140^30699-30699^27140	136108	Frank Doornink	01/2024
4900	40392^2339+2339^40392	136082	Hans Havermann	12/2020
4901	2*10^136057-43	136058	Robert Price	04/2018
4902	2^451971+21563	136057	Enzo Doria	08/2023
4903	(2^451956-5)/181	136051	Lelio R Paula	07/2015
4904	2^451947-22165	136050	Enzo Doria	07/2013
4905	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
4906	2^451787-21805	136002	Enzo Doria	07/2013
4907	2^451734-112817	135986	Enzo Doria	06/2014
4908	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
4909	2^451705-21879	135977	Enzo Doria	07/2013
4910	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
4911	2^451560-112349	135934	Enzo Doria	06/2014
4912	2^451530+45	135925	Lelio R Paula	08/2017
4913	26594^30719-30719^26594	135925	Frank Doornink	03/2024
4914	31622^19875+19875^31622	135922	Hans Havermann	11/2020
4915	(25*10^135906-73)/3	135907	Robert Price	09/2019
4916	2^451450-21743	135900	Enzo Doria	07/2013
4917	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
4918	35218^7199+7199^35218	135846	Hans Havermann	11/2020
4919	35661^6446+6446^35661	135844	Hans Havermann	11/2020
4920	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
4921	31869^18248+18248^31869	135801	Hans Havermann	12/2020
4922	(77*10^135789+157)/9	135790	Robert Price	05/2022
4923	2^450958+60529	135752	Enzo Doria	08/2023
4924	2^450805+65	135706	Lelio R Paula	08/2017
4925	10^135669+21	135670	Boyan Hu	12/2024
4926	30761^25728+25728^30761	135669	Hans Havermann	12/2020
4927	2*10^135663+69	135664	Robert Price	06/2020
4928	33962^9867+9867^33962	135651	Hans Havermann	11/2020
4929	34474^8605+8605^34474	135647	Hans Havermann	11/2020
4930	34501^8508+8508^34501	135583	Hans Havermann	12/2020
4931	35487^6614+6614^35487	135577	Hans Havermann	12/2020
4932	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
4933	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
4934	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
4935	(76*10^135553-49)/9	135554	Robert Price	07/2022
4936	5*3^284077+2^284077	135540	Jon Grantham	08/2023
4937	(844*10^135527-7)/9	135529	Robert Price	05/2021
4938	27191^30560-30560^27191	135517	Frank Doornink	01/2024
4939	40387^2260+2260^40387	135463	Hans Havermann	12/2020
4940	2^449944-113247	135447	Enzo Doria	07/2014
4941	2^449770-113247	135395	Enzo Doria	07/2014
4942	2^449637-21471	135355	Enzo Doria	07/2013
4943	26061^30650-30650^26061	135351	Frank Doornink	03/2024
4944	2^449571-75	135335	Lelio R Paula	08/2017
4945	(14*10^135301-53)/3	135302	Robert Price	12/2018
4946	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
4947	(13*10^135279+437)/9	135280	Robert Price	04/2018
4948	2^449330-35	135262	Lelio R Paula	08/2017
4949	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
4950	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
4951	(13*10^135184-43)/3	135185	Robert Price	11/2018
4952	2^449049-115309	135178	Enzo Doria	07/2015
4953	(10^135174+191)/3	135174	Robert Price	02/2018
4954	2^449030-15	135172	Lelio R Paula	08/2017
4955	(157*10^135151-1)/3	135153	Robert Price	01/2022
4956	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
4957	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
4958	(37*10^135099+251)/9	135100	Robert Price	09/2021
4959	32221^15586+15586^32221	135095	Hans Havermann	12/2020
4960	2^448762-351401	135091	Enzo Doria	07/2015
4961	2*10^135083-43	135084	Robert Price	04/2018
4962	31357^20278+20278^31357	135056	Hans Havermann	12/2020
4963	32242^15445+15445^32242	135055	Hans Havermann	12/2020
4964	k(198476)	135054	Robert Price	07/2020
4965	32461^14470+14470^32461	135053	Hans Havermann	12/2020
4966	31353^20288+20288^31353	135045	Hans Havermann	12/2020
4967	5*10^135019+77	135020	Robert Price	12/2018
4968	(10^135011+719)/9	135011	Serge Batalov	12/2014
4969	(197*10^134978+7)/3	134980	Robert Price	12/2020
4970	2^448386-2786261	134978	Enzo Doria	03/2016
4971	26480^30517-30517^26480	134975	Frank Doornink	03/2024
4972	(73*10^134939+143)/9	134940	Robert Price	07/2019
4973	33957^9392+9392^33957	134903	Hans Havermann	12/2020
4974	2^448122+20809	134899	Enzo Doria	08/2023
4975	2^448113-113949	134896	Enzo Doria	11/2014
4976	30958^22755+22755^30958	134887	Hans Havermann	12/2020
4977	2^447888-2786639	134828	Enzo Doria	03/2016
4978	2^447870-396765	134823	Enzo Doria	07/2013
4979	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
4980	2^447766-21791	134791	Enzo Doria	07/2013
4981	(19*10^134786-49)/3	134787	Robert Price	05/2019
4982	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
4983	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
4984	2^447552-1019	134727	Yves Minet	02/2014
4985	(2*10^134720-41)/3	134720	Robert Price	02/2018
4986	(25*10^134695-97)/9	134696	Robert Price	01/2022
4987	2^447437-113569	134692	Enzo Doria	08/2014
4988	2^447426-65	134689	Lelio R Paula	08/2017
4989	2^447357-2797573	134668	Enzo Doria	04/2016
4990	2^447278+93	134645	Lelio R Paula	08/2017
4991	33193^11370+11370^33193	134623	Hans Havermann	12/2020
4992	30736^23979+23979^30736	134619	Hans Havermann	11/2020
4993	2^447094-113193	134589	Enzo Doria	07/2014
4994	3^282041-9934	134568	Enzo Doria	05/2014
4995	2^447019-109039	134567	Enzo Doria	04/2014
4996	31376^19437+19437^31376	134561	Hans Havermann	12/2020
4997	2^446990-22041	134558	Enzo Doria	07/2013
4998	123^64370+122	134528	Karsten Bonath	04/2018
4999	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5000	31251^20158+20158^31251	134519	Hans Havermann	11/2020

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PRP Records

Probable Primes Top 10000

(301737 PRPs in the top)