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	32072^19689+19689^32072	137725	Hans Havermann	06/2021
4752	26529^31132-31132^26529	137720	Frank Doornink	03/2024
4753	44592^1225+1225^44592	137707	Hans Havermann	05/2021
4754	28986^30857-30857^28986	137690	Frank Doornink	05/2024
4755	2^457347-37	137676	Lelio R Paula	09/2017
4756	2^457322-2786393	137668	Enzo Doria	10/2015
4757	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
4758	Phi(699340M,10)	137664	Anonymous	03/2025
4759	34015^11134+11134^34015	137647	Hans Havermann	06/2021
4760	2^457240-59939	137643	Enzo Doria	10/2015
4761	(856*10^137633-1)/9	137635	Robert Price	03/2020
4762	36232^6289+6289^36232	137631	Hans Havermann	05/2021
4763	2^457120-21575	137607	Enzo Doria	07/2013
4765	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
4764	30963^27722+27722^30963	137564	Hans Havermann	04/2021
4766	33722^12003+12003^33722	137562	Hans Havermann	06/2021
4767	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
4768	41901^1918+1918^41901	137555	Hans Havermann	06/2021
4769	(7*10^137551-1)/3	137552	Robert Price	08/2022
4770	32930^15021+15021^32930	137539	Hans Havermann	05/2021
4771	31178^25785+25785^31178	137538	Hans Havermann	05/2021
4772	419^52446+52446^419	137525	Norbert Schneider	11/2020
4773	2^456813+214175	137515	Enzo Doria	10/2023
4774	2^456796-113513	137510	Enzo Doria	08/2014
4775	31788^21137+21137^31788	137485	Hans Havermann	04/2021
4776	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
4777	27151^31004-31004^27151	137466	Frank Doornink	01/2024
4778	2^456503-114361	137422	Enzo Doria	01/2015
4779	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
4780	30618^30618-5^5	137352	Serge Batalov	04/2024
4781	36248^6147+6147^36248	137332	Hans Havermann	05/2021
4782	31986^19651+19651^31986	137329	Hans Havermann	05/2021
4783	2^456167+22313	137320	Enzo Doria	09/2023
4784	31817^20656+20656^31817	137292	Hans Havermann	05/2021
4785	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
4786	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
4787	2^455922+76249	137247	Enzo Doria	05/2016
4788	31310^24171+24171^31310	137241	Hans Havermann	05/2021
4789	14^119741-119741^14	137239	Serge Batalov	04/2016
4790	35014^8297+8297^35014	137218	Hans Havermann	05/2021
4791	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
4793	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
4792	124^65536+57^65536	137195	Serge Batalov	03/2018
4794	2^455689+72677	137177	Enzo Doria	04/2016
4795	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
4796	31287^24128+24128^31287	137116	Hans Havermann	05/2021
4797	(37^87421-1)/36	137093	Robert Price	03/2012
4798	36233^6070+6070^36233	137077	Hans Havermann	05/2021
4799	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
4800	38418^3697+3697^38418	137070	Hans Havermann	04/2021
4801	2^455323-57	137066	Lelio R Paula	09/2017
4802	(56*10^137019+583)/9	137020	Robert Price	08/2021
4803	25017^31148-31148^25017	136997	Frank Doornink	12/2023
4804	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
4805	2^455025-112723	136977	Enzo Doria	06/2014
4806	33876^11039+11039^33876	136959	Hans Havermann	05/2021
4807	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
4808	(251^57059-1)/250	136921	Anonymous	04/2024
4809	35142^7873+7873^35142	136919	Hans Havermann	05/2021
4810	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
4811	66*10^136894+7	136896	Robert Price	07/2020
4812	28766^30697-30697^28766	136875	Frank Doornink	05/2024
4813	2^454675-1777	136871	Yves Minet	10/2011
4814	31676^20931+20931^31676	136866	Hans Havermann	05/2021
4815	3*10^136829+29	136830	Robert Price	05/2018
4816	4*10^136813-57	136814	Robert Price	10/2018
4817	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
4818	fibonacci(654572)-2	136798	Jon Grantham	08/2023
4819	37359^4588+4588^37359	136795	Hans Havermann	05/2021
4820	2^454348-53	136773	Lelio R Paula	09/2017
4821	31^91680-2	136729	Lelio R Paula	05/2017
4822	2^454199-113697	136728	Enzo Doria	09/2014
4823	30785^27622+27622^30785	136725	Hans Havermann	05/2021
4824	32973^14014+14014^32973	136725	Hans Havermann	05/2021
4826	7*10^136716+69	136717	Robert Price	07/2019
4825	36002^6273+6273^36002	136717	Hans Havermann	05/2021
4827	6*10^136692+53	136693	Robert Price	05/2020
4828	(13*10^136687+47)/3	136688	Robert Price	10/2018
4829	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
4830	2^453935-2791357	136649	Enzo Doria	01/2016
4831	2^453906-69131	136640	Enzo Doria	11/2015
4832	33232^12915+12915^33232	136620	Hans Havermann	05/2021
4833	2^453791+1873913	136605	Enzo Doria	06/2016
4834	34166^9951+9951^34166	136592	Hans Havermann	05/2021
4835	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
4836	31102^24635+24635^31102	136587	Hans Havermann	05/2021
4837	580^49413+49413^580	136550	Norbert Schneider	02/2019
4838	2^453503-2788297	136519	Enzo Doria	11/2015
4839	34989^7958+7958^34989	136486	Hans Havermann	12/2020
4840	(2*10^136484+187)/9	136484	Robert Price	06/2022
4841	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
4842	31007^25158+25158^31007	136452	Hans Havermann	11/2020
4843	2^453267-113827	136447	Enzo Doria	09/2014
4844	32234^17085+17085^32234	136435	Hans Havermann	12/2020
4845	2^453102+1877629	136398	Enzo Doria	08/2016
4846	31016^24981+24981^31016	136397	Hans Havermann	12/2020
4847	(62*10^136384-791)/9	136385	Robert Price	06/2019
4848	34171^9798+9798^34171	136382	Hans Havermann	12/2020
4849	(17*10^136354-113)/3	136355	Robert Price	06/2021
4850	32756^14541+14541^32756	136350	Hans Havermann	11/2020
4851	32205^17086+17086^32205	136313	Hans Havermann	12/2020
4852	(25*10^136303+161)/3	136304	Robert Price	09/2019
4853	35337^7196+7196^35337	136299	Hans Havermann	12/2020
4854	(182*10^136291+1)/3	136293	Robert Price	02/2020
4855	(88*10^136234+83)/9	136235	Robert Price	03/2022
4856	23*10^136225-7	136227	Robert Price	02/2020
4857	L(651821)	136223	Henri Lifchitz	09/2008
4858	25519^30908-30908^25519	136208	Frank Doornink	02/2024
4859	2^452460+77701	136205	Enzo Doria	05/2016
4860	2^452440-114755	136199	Enzo Doria	04/2015
4861	28625^30558-30558^28625	136190	Frank Doornink	05/2024
4862	32286^16489+16489^32286	136157	Hans Havermann	11/2020
4863	(47*10^136141+493)/9	136142	Robert Price	03/2019
4864	27140^30699-30699^27140	136108	Frank Doornink	01/2024
4865	40392^2339+2339^40392	136082	Hans Havermann	12/2020
4866	2*10^136057-43	136058	Robert Price	04/2018
4867	2^451971+21563	136057	Enzo Doria	08/2023
4868	(2^451956-5)/181	136051	Lelio R Paula	07/2015
4869	2^451947-22165	136050	Enzo Doria	07/2013
4870	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
4871	2^451787-21805	136002	Enzo Doria	07/2013
4872	2^451734-112817	135986	Enzo Doria	06/2014
4873	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
4874	2^451705-21879	135977	Enzo Doria	07/2013
4875	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
4876	2^451560-112349	135934	Enzo Doria	06/2014
4877	2^451530+45	135925	Lelio R Paula	08/2017
4878	26594^30719-30719^26594	135925	Frank Doornink	03/2024
4879	31622^19875+19875^31622	135922	Hans Havermann	11/2020
4880	(25*10^135906-73)/3	135907	Robert Price	09/2019
4881	2^451450-21743	135900	Enzo Doria	07/2013
4882	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
4883	35218^7199+7199^35218	135846	Hans Havermann	11/2020
4884	35661^6446+6446^35661	135844	Hans Havermann	11/2020
4885	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
4886	31869^18248+18248^31869	135801	Hans Havermann	12/2020
4887	(77*10^135789+157)/9	135790	Robert Price	05/2022
4888	2^450958+60529	135752	Enzo Doria	08/2023
4889	2^450805+65	135706	Lelio R Paula	08/2017
4890	10^135669+21	135670	Boyan Hu	12/2024
4891	30761^25728+25728^30761	135669	Hans Havermann	12/2020
4892	2*10^135663+69	135664	Robert Price	06/2020
4893	33962^9867+9867^33962	135651	Hans Havermann	11/2020
4894	34474^8605+8605^34474	135647	Hans Havermann	11/2020
4895	34501^8508+8508^34501	135583	Hans Havermann	12/2020
4896	35487^6614+6614^35487	135577	Hans Havermann	12/2020
4897	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
4898	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
4899	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
4900	(76*10^135553-49)/9	135554	Robert Price	07/2022
4901	5*3^284077+2^284077	135540	Jon Grantham	08/2023
4902	(844*10^135527-7)/9	135529	Robert Price	05/2021
4903	27191^30560-30560^27191	135517	Frank Doornink	01/2024
4904	40387^2260+2260^40387	135463	Hans Havermann	12/2020
4905	2^449944-113247	135447	Enzo Doria	07/2014
4906	2^449770-113247	135395	Enzo Doria	07/2014
4907	2^449637-21471	135355	Enzo Doria	07/2013
4908	26061^30650-30650^26061	135351	Frank Doornink	03/2024
4909	2^449571-75	135335	Lelio R Paula	08/2017
4910	(14*10^135301-53)/3	135302	Robert Price	12/2018
4911	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
4912	(13*10^135279+437)/9	135280	Robert Price	04/2018
4913	2^449330-35	135262	Lelio R Paula	08/2017
4914	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
4915	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
4916	(13*10^135184-43)/3	135185	Robert Price	11/2018
4917	2^449049-115309	135178	Enzo Doria	07/2015
4918	(10^135174+191)/3	135174	Robert Price	02/2018
4919	2^449030-15	135172	Lelio R Paula	08/2017
4920	(157*10^135151-1)/3	135153	Robert Price	01/2022
4921	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
4922	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
4923	(37*10^135099+251)/9	135100	Robert Price	09/2021
4924	32221^15586+15586^32221	135095	Hans Havermann	12/2020
4925	2^448762-351401	135091	Enzo Doria	07/2015
4926	2*10^135083-43	135084	Robert Price	04/2018
4927	31357^20278+20278^31357	135056	Hans Havermann	12/2020
4928	32242^15445+15445^32242	135055	Hans Havermann	12/2020
4929	k(198476)	135054	Robert Price	07/2020
4930	32461^14470+14470^32461	135053	Hans Havermann	12/2020
4931	31353^20288+20288^31353	135045	Hans Havermann	12/2020
4932	5*10^135019+77	135020	Robert Price	12/2018
4933	(10^135011+719)/9	135011	Serge Batalov	12/2014
4934	(197*10^134978+7)/3	134980	Robert Price	12/2020
4935	2^448386-2786261	134978	Enzo Doria	03/2016
4936	26480^30517-30517^26480	134975	Frank Doornink	03/2024
4937	(73*10^134939+143)/9	134940	Robert Price	07/2019
4938	33957^9392+9392^33957	134903	Hans Havermann	12/2020
4939	2^448122+20809	134899	Enzo Doria	08/2023
4940	2^448113-113949	134896	Enzo Doria	11/2014
4941	30958^22755+22755^30958	134887	Hans Havermann	12/2020
4942	2^447888-2786639	134828	Enzo Doria	03/2016
4943	2^447870-396765	134823	Enzo Doria	07/2013
4944	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
4945	2^447766-21791	134791	Enzo Doria	07/2013
4946	(19*10^134786-49)/3	134787	Robert Price	05/2019
4947	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
4948	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
4949	2^447552-1019	134727	Yves Minet	02/2014
4950	(2*10^134720-41)/3	134720	Robert Price	02/2018
4951	(25*10^134695-97)/9	134696	Robert Price	01/2022
4952	2^447437-113569	134692	Enzo Doria	08/2014
4953	2^447426-65	134689	Lelio R Paula	08/2017
4954	2^447357-2797573	134668	Enzo Doria	04/2016
4955	2^447278+93	134645	Lelio R Paula	08/2017
4956	33193^11370+11370^33193	134623	Hans Havermann	12/2020
4957	30736^23979+23979^30736	134619	Hans Havermann	11/2020
4958	2^447094-113193	134589	Enzo Doria	07/2014
4959	3^282041-9934	134568	Enzo Doria	05/2014
4960	2^447019-109039	134567	Enzo Doria	04/2014
4961	31376^19437+19437^31376	134561	Hans Havermann	12/2020
4962	2^446990-22041	134558	Enzo Doria	07/2013
4963	123^64370+122	134528	Karsten Bonath	04/2018
4964	30100^29461+29461^30100	134525	Hans Havermann	11/2020
4965	31251^20158+20158^31251	134519	Hans Havermann	11/2020
4966	2^446782-39701	134495	Enzo Doria	09/2015
4967	31817^16858+16858^31817	134485	Hans Havermann	12/2020
4968	32448^13937+13937^32448	134471	Hans Havermann	12/2020
4969	5^192321+3^192321-1	134427	Jon Grantham	08/2023
4970	2^446494-16485	134409	Enzo Doria	04/2013
4971	30042^29785+29785^30042	134408	Hans Havermann	12/2020
4972	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
4973	2^446441+65	134393	Lelio R Paula	08/2017
4974	(10^134385+719)/9	134385	Serge Batalov	12/2014
4975	30043^29688+29688^30043	134370	Hans Havermann	12/2020
4976	(2*10^134364+529)/9	134364	Robert Price	01/2018
4977	34657^7512+7512^34657	134323	Hans Havermann	11/2020
4978	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
4979	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
4980	42035^1564+1564^42035	134270	Hans Havermann	12/2020
4982	(2^446022-7)/339	134264	Lelio R Paula	07/2015
4981	30621^24248+24248^30621	134264	Hans Havermann	12/2020
4983	30341^26562+26562^30341	134237	Hans Havermann	11/2020
4984	(189^58967-1)/188	134234	Anonymous	06/2024
4985	10^134209+99867	134210	Patrick De Geest	05/2021
4986	10^134209-80000001	134209	Robert Price	04/2021
4987	10^134209-323283	134209	Patrick De Geest	05/2021
4988	29976^29953+29953^29976	134186	Hans Havermann	12/2020
4989	35038^6755+6755^35038	134183	Hans Havermann	12/2020
4990	63^74568+2	134174	Lelio R Paula	06/2017
4991	2^445671-22071	134161	Enzo Doria	07/2013
4992	532^49205+49205^532	134129	Norbert Schneider	02/2019
4993	36453^4780+4780^36453	134127	Hans Havermann	04/2021
4994	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
4995	2^445515-113859	134114	Enzo Doria	10/2014
4997	(22*10^134111-37)/3	134112	Robert Price	04/2019
4996	31083^20636+20636^31083	134112	Hans Havermann	04/2021
4998	3*2^445478+5	134103	Jon Grantham	07/2023
4999	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5000	5*2^445380-3	134074	Jon Grantham	07/2023

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Probable Primes Top 10000

(301692 PRPs in the top)