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	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
4752	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
4753	2^363769+5711	109506	Lelio R Paula	04/2017
4754	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
4755	p(22245)#/2-8	109462	Robert Price	01/2017
4756	2^363556+55	109442	Lelio R Paula	01/2012
4757	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
4758	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
4759	2^363406+1871569	109397	Enzo Doria	05/2016
4760	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
4761	(2^363349+7)/9	109378	Lelio R Paula	01/2014
4762	3^229236+100	109374	Lelio R Paula	03/2017
4763	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
4764	2^363268-58695	109355	Lelio R Paula	04/2017
4765	2^363191-112321	109332	Enzo Doria	06/2014
4766	26231^14718+14718^26231	109327	Hans Havermann	10/2020
4767	25461^19672+19672^25461	109326	Hans Havermann	10/2020
4768	4*10^109316-63	109317	Robert Price	10/2018
4769	2^363120+3	109311	Donovan Johnson	04/2006
4770	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
4771	2^363042-114641	109287	Enzo Doria	04/2015
4772	2^363020-112793	109280	Enzo Doria	06/2014
4773	(85*10^109253+203)/9	109254	Robert Price	09/2020
4774	24990^23431+23431^24990	109202	Hans Havermann	10/2020
4775	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
4776	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
4777	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
4778	25060^22737+22737^25060	109180	Hans Havermann	10/2020
4779	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
4780	5^156181+38	109166	Lelio R Paula	02/2017
4781	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
4782	25138^21993+21993^25138	109157	Hans Havermann	10/2020
4783	4*10^109142+91	109143	Robert Price	08/2018
4784	3^228750+68	109142	Lelio R Paula	03/2017
4785	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
4786	(23*10^109113+61)/3	109114	Robert Price	01/2022
4787	2*10^109100-49	109101	Robert Price	09/2020
4788	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
4789	65^60167-64^60167	109078	Robert Price	08/2013
4790	7*3^228589-2	109066	Lelio R Paula	09/2014
4791	24874^24243+24243^24874	109063	Hans Havermann	11/2020
4792	(17*10^109059-161)/9	109060	Robert Price	02/2021
4793	29158^5495+5495^29158	109050	Hans Havermann	11/2020
4794	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
4795	2*7^129008+9	109025	Lelio R Paula	11/2014
4796	88*10^109022+7	109024	Robert Price	03/2020
4797	28194^7337+7337^28194	108985	Hans Havermann	10/2020
4798	(5*10^108960+91)/3	108961	Robert Price	04/2018
4799	2^361957+76367	108960	Enzo Doria	05/2016
4800	2^361873-1411	108935	Yves Minet	01/2013
4801	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
4802	115^52842-114	108892	Norbert Schneider	07/2018
4803	13^97745-24	108883	Lelio R Paula	03/2017
4804	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
4805	17^88475+8	108864	Lelio R Paula	04/2017
4806	2^361567+51	108843	Lelio R Paula	01/2012
4807	2^361563-109501	108842	Enzo Doria	04/2014
4808	12^100852+83	108838	Lelio R Paula	03/2017
4809	2^361497+767	108822	Lelio R Paula	01/2012
4810	28019^7630+7630^28019	108785	Hans Havermann	10/2020
4811	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
4812	2^361280-112349	108757	Enzo Doria	06/2014
4813	2^361271-5955	108754	Lelio R Paula	04/2017
4814	12^100757+19	108736	Lelio R Paula	03/2017
4815	25368^19333+19333^25368	108735	Hans Havermann	11/2020
4816	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
4817	2^361153-111546435	108718	Paul Bourdelais	10/2021
4818	14^94849-61	108710	Lelio R Paula	05/2017
4819	27267^9700+9700^27267	108708	Hans Havermann	11/2020
4820	(19^85009-5^85009)/14	108705	Robert Price	07/2013
4821	24832^23853+23853^24832	108704	Hans Havermann	11/2020
4822	27502^8963+8963^27502	108701	Hans Havermann	11/2020
4823	25807^16278+16278^25807	108689	Hans Havermann	11/2020
4824	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
4825	2^360973+1299	108664	Lelio R Paula	04/2017
4826	2^360959-109101	108660	Enzo Doria	04/2014
4827	6*5^155454+7	108659	Lelio R Paula	11/2014
4828	10^108656+79	108657	Lelio R Paula	02/2017
4829	10^108656-50001	108656	Patrick De Geest	03/2017
4830	2^360918-35	108648	Lelio R Paula	01/2012
4831	4*10^108646-47	108647	Robert Price	10/2021
4832	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
4833	3*10^108624-49	108625	Robert Price	07/2018
4834	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
4835	(134*10^108610+7)/3	108612	Robert Price	02/2020
4836	2*10^108609+29	108610	Robert Price	02/2021
4837	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
4838	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
4839	2^360706-458903	108584	Enzo Doria	04/2015
4840	31112^3087+3087^31112	108567	Hans Havermann	11/2020
4841	2^360641-113185	108564	Enzo Doria	07/2014
4842	(29*10^108559-71)/3	108560	Robert Price	07/2021
4843	2^360618+75019	108557	Enzo Doria	04/2016
4844	(14*10^108545-221)/9	108546	Robert Price	04/2018
4845	(44*10^108544-233)/9	108545	Robert Price	01/2019
4846	3*5^155286+2	108541	Lelio R Paula	11/2014
4847	7^128422+4	108530	Lelio R Paula	11/2014
4848	7^128421-80	108529	Lelio R Paula	03/2017
4849	2^360497+53807	108521	Yves Minet	07/2010
4850	2^360468-4559	108512	Yves Minet	03/2019
4851	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
4852	2^360366+1459	108481	Lelio R Paula	09/2011
4853	2^360364-1499	108481	Yves Minet	05/2013
4854	25662^16871+16871^25662	108477	Hans Havermann	10/2020
4855	25009^21748+21748^25009	108475	Hans Havermann	10/2020
4856	14^94642-23	108472	Lelio R Paula	05/2017
4857	(197*10^108446-11)/3	108448	Robert Price	03/2020
4858	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
4859	4*10^108412+9	108413	Robert Price	05/2015
4860	(259*10^108409-1)/3	108411	Robert Price	12/2020
4861	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
4862	133^51042-132	108406	Norbert Schneider	02/2019
4863	2^360093-351103	108399	Enzo Doria	06/2015
4864	2^360042+723	108384	Lelio R Paula	01/2012
4865	85^56164-2	108364	Lelio R Paula	10/2013
4866	2^359937-29323	108352	Enzo Doria	07/2015
4867	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
4868	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
4869	2^359898-19997	108341	Enzo Doria	06/2013
4870	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
4871	2*5^154948-7	108305	Lelio R Paula	11/2014
4872	10^108303+13	108304	Lelio R Paula	02/2017
4873	10^108303-207959	108303	Patrick De Geest	03/2017
4874	7*10^108300+69	108301	Robert Price	07/2019
4875	2^359730+753	108290	Lelio R Paula	12/2011
4876	(8*10^108273+13)/3	108274	Robert Price	06/2018
4877	2^359650-19797	108266	Enzo Doria	06/2013
4878	91^55259-90^55259	108255	Robert Price	07/2015
4879	10^108251+85749	108252	Patrick De Geest	02/2021
4880	10^108251-50000000001	108251	Robert Price	12/2020
4881	10^108251-252081	108251	Patrick De Geest	02/2021
4882	4*10^108238-71	108239	Robert Price	12/2018
4883	3^226845+68	108233	Lelio R Paula	03/2017
4884	31836^2509+2509^31836	108227	Hans Havermann	10/2020
4885	5^154822-12866	108216	Enzo Doria	05/2014
4886	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
4887	2^359454-177	108207	Lelio R Paula	12/2011
4888	(19*10^108184+191)/3	108185	Robert Price	05/2019
4889	6^139022-59	108181	Lelio R Paula	02/2017
4890	(19*10^108176-43)/3	108177	Robert Price	05/2019
4891	2^359352-179	108176	Lelio R Paula	12/2011
4892	2^359338-1858781	108172	Enzo Doria	04/2016
4893	12^100230-97	108167	Lelio R Paula	03/2017
4894	27028^10043+10043^27028	108163	Hans Havermann	11/2020
4895	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
4896	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
4897	26583^11702+11702^26583	108147	Hans Havermann	11/2020
4898	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
4899	6^138956-59	108129	Lelio R Paula	02/2017
4900	2^359184+30285	108126	Lelio R Paula	04/2017
4901	13^97059+10	108119	Lelio R Paula	03/2017
4902	2^359137-81	108112	Lelio R Paula	12/2011
4904	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
4903	2^359110-11655	108103	Lelio R Paula	04/2017
4905	2^359069-933075	108091	Paul Bourdelais	06/2021
4906	26227^13222+13222^26227	108090	Hans Havermann	10/2020
4907	8*6^138875+5	108067	Lelio R Paula	11/2014
4908	2^358987-216919	108066	Enzo Doria	05/2014
4909	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
4910	39^67918-67918^39	108062	Norbert Schneider	02/2017
4911	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
4912	25282^18767+18767^25282	108040	Hans Havermann	11/2020
4913	2^358785-16933	108006	Enzo Doria	05/2013
4914	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
4915	6^138770-77	107985	Lelio R Paula	02/2017
4916	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
4917	10^107976+19	107977	Lelio R Paula	02/2017
4918	10^107976-202103	107976	Patrick De Geest	03/2017
4919	2^358684+75781	107975	Enzo Doria	04/2016
4920	24928^21411+21411^24928	107955	Hans Havermann	10/2020
4921	99^54094+2	107952	Lelio R Paula	06/2013
4922	(2^358583-9)/391	107942	Lelio R Paula	12/2013
4923	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
4924	2^358538+55	107931	Lelio R Paula	12/2011
4925	2^358517-109009	107925	Enzo Doria	03/2014
4926	26395^12258+12258^26395	107914	Hans Havermann	10/2020
4927	3^226159+104	107906	Lelio R Paula	03/2017
4928	2^358310-11655	107863	Lelio R Paula	03/2017
4929	(68*10^107852-329)/9	107853	Robert Price	03/2021
4930	2^358275-112987	107852	Enzo Doria	07/2014
4931	3^226038+4	107848	Tyler NeSmith	01/2021
4932	2^358233-20005	107839	Enzo Doria	06/2013
4933	2^358194+175	107828	Lelio R Paula	12/2011
4934	107^53125-106	107812	Norbert Schneider	12/2016
4935	(25*10^107804+161)/3	107805	Robert Price	09/2019
4936	3^225922-2	107793	Lelio R Paula	10/2013
4937	12^99874-95	107783	Lelio R Paula	03/2017
4938	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
4939	2^358030-171	107778	Lelio R Paula	12/2011
4940	11^103488-4170	107772	Enzo Doria	12/2012
4941	2^357930-4547	107748	Yves Minet	03/2019
4942	2^357911-20089	107742	Enzo Doria	06/2013
4943	2^357885+12857	107735	Yves Minet	07/2010
4944	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
4945	7^127473+40	107728	Lelio R Paula	03/2017
4946	5*2^357850+9	107725	Lelio R Paula	09/2014
4947	2^357786-291191	107705	Enzo Doria	06/2015
4948	28907^5320+5320^28907	107705	Hans Havermann	10/2020
4949	18^85798-23	107700	Lelio R Paula	04/2017
4950	3*10^107697+61	107698	Robert Price	09/2020
4951	(14*10^107694-83)/3	107695	Robert Price	12/2018
4952	2^357688-1854269	107675	Enzo Doria	09/2015
4953	2^357671-112225	107670	Enzo Doria	06/2014
4954	34323^1370+1370^34323	107662	Hans Havermann	11/2020
4955	2^357618-21005	107654	Enzo Doria	06/2013
4956	2^357615-17505	107653	Enzo Doria	05/2013
4957	26350^12171+12171^26350	107649	Hans Havermann	11/2020
4958	(30^72871-1)/29	107638	Robert Price	12/2011
4959	25021^20026+20026^25021	107631	Hans Havermann	11/2020
4960	2^357521+1870217	107625	Enzo Doria	05/2016
4961	2^357477-1203	107612	Lelio R Paula	03/2017
4962	26008^13693+13693^26008	107583	Hans Havermann	10/2020
4963	25432^16991+16991^25432	107583	Hans Havermann	10/2020
4964	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
4965	5^153894-18	107568	Lelio R Paula	02/2017
4966	2^357324-69059	107566	Enzo Doria	11/2015
4967	467^40296+40296^467	107563	Norbert Schneider	03/2019
4968	29446^4495+4495^29446	107559	Hans Havermann	10/2020
4969	(8*10^107556-149)/3	107557	Robert Price	12/2021
4970	2^357283-869688105	107553	Lelio R Paula	01/2017
4971	2^357280-16805	107552	Enzo Doria	05/2013
4972	10^107547+481719	107548	Patrick De Geest	03/2017
4973	10^107547-47	107547	Lelio R Paula	02/2017
4974	17^87396-32	107537	Lelio R Paula	04/2017
4975	(746*10^107505+1)/9	107507	Robert Price	03/2020
4976	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
4977	2^357081+107	107493	Lelio R Paula	12/2011
4978	2^357058-3911	107486	Yves Minet	04/2017
4979	3^225274+64	107484	Lelio R Paula	03/2017
4980	5*10^107482-57	107483	Robert Price	03/2021
4981	18^85619-95	107476	Lelio R Paula	04/2017
4982	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
4983	3^225248-130	107471	Lelio R Paula	03/2017
4984	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
4985	27029^9448+9448^27029	107450	Hans Havermann	11/2020
4986	2^356935-18085	107449	Enzo Doria	05/2013
4987	55396^87+87^55396	107442	Hans Havermann	10/2020
4988	(14*10^107439-137)/3	107440	Robert Price	04/2021
4989	10^107409+37	107410	Lelio R Paula	02/2017
4990	10^107409-329633	107409	Patrick De Geest	03/2017
4991	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
4992	2^356787-109027	107404	Enzo Doria	04/2014
4993	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
4994	3*10^107389+77	107390	Robert Price	09/2018
4995	5^153622-42	107378	Lelio R Paula	02/2017
4996	2^356699-97305	107378	Lelio R Paula	03/2017
4997	2^356654+85	107364	Lelio R Paula	11/2011
4998	2^356641-19921	107360	Enzo Doria	06/2013
4999	5*10^107355+11	107356	Robert Price	08/2019
5000	2^356623-465	107355	Lelio R Paula	03/2017

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Probable Primes Top 10000

(288949 PRPs in the top)