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	2^419328-1859939	126231	Enzo Doria	03/2016
4752	2^419282-1851507	126217	Enzo Doria	08/2015
4753	(133*10^126212+17)/3	126214	Robert Price	11/2021
4754	2^419251+1866143	126208	Enzo Doria	03/2016
4755	11^121185+2	126202	Robert Price	05/2014
4756	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
4757	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
4758	2^418851+23	126087	Robert Price	09/2015
4759	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
4760	2^418829+167	126081	Lelio R Paula	01/2012
4761	31037^11530+11530^31037	126067	Hans Havermann	03/2021
4762	4*10^126064-69	126065	Robert Price	01/2022
4763	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
4764	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
4765	(35*10^126048-323)/9	126049	Robert Price	10/2021
4766	33016^6551+6551^33016	126000	Hans Havermann	03/2021
4767	2^418548-111546435	125996	Paul Bourdelais	10/2021
4768	25134^28625-28625^25134	125958	Frank Doornink	12/2023
4769	34736^4227+4227^34736	125954	Hans Havermann	03/2021
4770	26197^28502-28502^26197	125930	Frank Doornink	03/2024
4771	2^418319-109501	125927	Enzo Doria	04/2014
4772	2^418316-112373	125926	Enzo Doria	06/2014
4773	40398^1309+1309^40398	125919	Hans Havermann	03/2021
4774	(8*10^125894-29)/3	125895	Robert Price	07/2018
4775	(26*10^125886-413)/9	125887	Robert Price	05/2018
4776	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
4777	55*10^125847+9	125849	Robert Price	03/2022
4778	4*10^125832+57	125833	Robert Price	05/2022
4779	2^417968+1869811	125821	Enzo Doria	06/2016
4780	2^417902+63	125802	Lelio R Paula	09/2015
4781	(10^125792-91)/9	125792	Serge Batalov	12/2014
4782	30438^13573+13573^30438	125791	Hans Havermann	03/2021
4783	32867^6714+6714^32867	125782	Hans Havermann	03/2021
4784	31155^10892+10892^31155	125777	Hans Havermann	03/2021
4785	(35*10^125754-593)/9	125755	Robert Price	07/2018
4786	30455^13464+13464^30455	125754	Hans Havermann	03/2021
4787	(32*10^125751-77)/9	125752	Robert Price	06/2018
4788	2^417704+77011	125742	Enzo Doria	05/2016
4789	29755^16816+16816^29755	125737	Hans Havermann	03/2021
4790	(22*10^125734+203)/9	125735	Robert Price	10/2021
4791	29918^15915+15915^29918	125710	Hans Havermann	03/2021
4792	(10^125706+149)/3	125706	Serge Batalov	12/2014
4793	28531^25368+25368^28531	125659	Hans Havermann	03/2021
4794	2^417419-115309	125656	Enzo Doria	07/2015
4795	(46*10^125642+593)/9	125643	Robert Price	04/2022
4796	2^417315+213953	125625	Enzo Doria	10/2023
4797	2^417300+77281	125620	Enzo Doria	05/2016
4798	30638^12537+12537^30638	125561	Hans Havermann	03/2021
4799	2^417095-1657	125559	Yves Minet	07/2014
4800	30162^14525+14525^30162	125538	Hans Havermann	03/2021
4801	(56*10^125535+583)/9	125536	Robert Price	08/2021
4802	(23*10^125517-179)/3	125518	Robert Price	06/2022
4803	9*10^125516+29	125517	Robert Price	03/2022
4804	(88*10^125492-637)/9	125493	Robert Price	11/2020
4805	28958^21525+21525^28958	125474	Hans Havermann	02/2021
4808	2^416773-25	125462	Lelio R Paula	09/2015
4806	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
4807	26078^28409-28409^26078	125462	Frank Doornink	03/2024
4809	33889^5032+5032^33889	125449	Hans Havermann	03/2021
4810	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
4811	(2861^36481+1)/(2861^191+1)	125438	Martin Hopf	12/2023
4812	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
4813	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
4814	2^416641-2*416641+1	125422	Robert Price	05/2018
4815	33392^5697+5697^33392	125409	Hans Havermann	03/2021
4816	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
4817	2^416530+1870429	125389	Enzo Doria	05/2016
4818	(56*10^125385+691)/9	125386	Robert Price	05/2019
4819	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
4820	31074^10837+10837^31074	125381	Hans Havermann	03/2021
4821	33745^5194+5194^33745	125380	Hans Havermann	03/2021
4822	2^416490+1875109	125376	Enzo Doria	09/2016
4823	28360^26331+26331^28360	125365	Hans Havermann	03/2021
4824	2^416416-114929	125354	Enzo Doria	05/2015
4825	25805^28412-28412^25805	125346	Frank Doornink	03/2024
4826	(77*10^125330-293)/9	125331	Robert Price	09/2019
4827	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
4828	2^416134+1865899	125269	Enzo Doria	03/2016
4829	153^57337-152	125264	Norbert Schneider	12/2018
4830	(599*10^125224+13)/9	125226	Robert Price	02/2022
4831	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
4832	30054^14657+14657^30054	125207	Hans Havermann	03/2021
4833	(23^91943-1)/22	125201	Robert Price	01/2012
4834	2^415884-933075	125194	Paul Bourdelais	06/2021
4835	43125^27010-106	125185	Enzo Doria	08/2012
4836	(38*10^125166+349)/9	125167	Robert Price	10/2018
4837	10^125166-5001	125166	Robert Price	12/2021
4838	2^415765-112603	125158	Enzo Doria	06/2014
4839	8*10^125088-13	125089	Robert Price	08/2019
4840	(25*10^125076-13)/3	125077	Robert Price	09/2019
4841	(11*10^125054+73)/3	125055	Robert Price	08/2021
4842	(29*10^125021-113)/3	125022	Robert Price	10/2019
4843	2^415290-113591	125015	Enzo Doria	08/2014
4844	2^415276-460919	125011	Enzo Doria	06/2015
4845	2^415259+77243	125006	Enzo Doria	05/2016
4846	(67*10^124990+77)/9	124991	Robert Price	10/2021
4847	2^415144-3683	124971	Yves Minet	10/2011
4848	2^415092+111546435	124956	Paul Bourdelais	10/2021
4849	31936^8173+8173^31936	124946	Hans Havermann	03/2021
4850	27458^28145-28145^27458	124927	Frank Doornink	03/2024
4851	5^178715-4	124916	Tyler NeSmith	07/2021
4852	29767^15700+15700^29767	124900	Hans Havermann	03/2021
4853	2^414874+79	124890	Lelio R Paula	01/2015
4854	25292^28361-28361^25292	124874	Frank Doornink	01/2024
4855	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
4856	2^414618+79459	124813	Enzo Doria	06/2016
4857	(61*10^124809-1)/3	124811	Robert Price	01/2020
4858	(29*10^124765-71)/3	124766	Robert Price	07/2021
4859	2^414432-1846709	124757	Enzo Doria	07/2015
4860	2*10^124751-51	124752	Robert Price	04/2018
4861	(56*10^124735+367)/9	124736	Robert Price	06/2019
4862	27362^28111-28111^27362	124733	Frank Doornink	03/2024
4863	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
4864	(23*10^124690+37)/3	124691	Robert Price	02/2022
4865	56*10^124656-3	124658	Robert Price	03/2020
4866	(7*10^124648+197)/3	124649	Robert Price	07/2018
4868	2^414032-5	124637	Henri Lifchitz	07/2006
4867	2^414032+1872331	124637	Enzo Doria	05/2016
4869	37373^2158+2158^37373	124604	Hans Havermann	03/2021
4870	29811^15112+15112^29811	124590	Hans Havermann	03/2021
4871	2^413781-2023	124561	Riley Fisher	09/2023
4872	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
4873	29757^15296+15296^29757	124521	Hans Havermann	03/2021
4874	35056^3561+3561^35056	124504	Hans Havermann	03/2021
4875	40588^1167+1167^40588	124487	Hans Havermann	02/2021
4876	(85*10^124485-49)/9	124486	Robert Price	12/2020
4877	64^68909-63^68909	124463	Robert Price	07/2013
4878	35016^3581+3581^35016	124448	Hans Havermann	03/2021
4879	2^413387+76253	124442	Enzo Doria	04/2016
4880	28749^21298+21298^28749	124436	Hans Havermann	03/2021
4881	2^413352+524287	124432	Paul Underwood	09/2018
4882	287117#+391613	124424	Nicolas PALAU	01/2017
4883	(4*10^124420+83)/3	124421	Robert Price	02/2018
4884	34578^3965+3965^34578	124421	Hans Havermann	03/2021
4885	(68*10^124392-329)/9	124393	Robert Price	03/2021
4886	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
4887	10^124383+58407	124384	Patrick De Geest	08/2021
4889	10^124383-8000001	124383	Robert Price	04/2021
4888	10^124383-5801	124383	Patrick De Geest	08/2021
4890	26091^28154-28154^26091	124342	Frank Doornink	03/2024
4891	(41*10^124335-383)/9	124336	Robert Price	11/2018
4892	(304*10^124329-43)/9	124331	Robert Price	02/2020
4893	34716^3811+3811^34716	124320	Hans Havermann	03/2021
4894	26892^28063-28063^26892	124309	Frank Doornink	03/2024
4895	2^412868-120599	124286	Paul Bourdelais	02/2012
4896	10^124248+899089	124249	Patrick De Geest	05/2021
4898	10^124248-1000001	124248	Robert Price	08/2020
4897	10^124248-501903	124248	Patrick De Geest	05/2021
4899	45^75145-2	124231	Lelio R Paula	08/2015
4900	29901^14272+14272^29901	124224	Hans Havermann	03/2021
4901	2^412645-112213	124219	Enzo Doria	06/2014
4902	29837^14500+14500^29837	124163	Hans Havermann	03/2021
4903	28074^26455+26455^28074	124158	Hans Havermann	03/2021
4904	2^412285+213317	124111	Enzo Doria	09/2023
4905	2^412248+74611	124100	Enzo Doria	04/2016
4906	(22*10^124096-13)/9	124097	Robert Price	06/2018
4907	(455*10^124093+31)/9	124095	Robert Price	06/2021
4908	2^412192-3329	124083	Yves Minet	12/2014
4909	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
4911	(25*10^124076-67)/3	124077	Robert Price	06/2019
4910	28132^25735+25735^28132	124077	Hans Havermann	03/2021
4912	F(593689)	124074	Henri Lifchitz	01/2005
4913	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
4914	26372^28057-28057^26372	124045	Frank Doornink	03/2024
4915	27528^27937-27937^27528	124034	Frank Doornink	03/2024
4916	35364^3215+3215^35364	124028	Hans Havermann	03/2021
4918	(266*10^124022-11)/3	124024	Robert Price	04/2020
4917	29987^13674+13674^29987	124024	Hans Havermann	03/2021
4919	2^411932-111546435	124004	Paul Bourdelais	10/2021
4920	2^411884-113279	123990	Enzo Doria	07/2014
4921	(2^411832+1)/257	123972	Lelio R Paula	05/2014
4922	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
4923	(26*10^123970-89)/9	123971	Robert Price	06/2018
4924	2^411790-1853531	123962	Enzo Doria	08/2015
4925	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
4926	(101*10^123950+7)/9	123952	Robert Price	02/2022
4927	2^411711-113257	123938	Enzo Doria	07/2014
4928	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
4929	36289^2598+2598^36289	123914	Hans Havermann	03/2021
4930	(11*10^123899-179)/3	123900	Robert Price	09/2018
4931	32276^6879+6879^32276	123860	Hans Havermann	02/2021
4932	2^411325-351103	123822	Enzo Doria	06/2015
4933	(646*10^123817+11)/9	123819	Robert Price	10/2021
4934	30738^10643+10643^30738	123784	Hans Havermann	03/2021
4935	31074^9607+9607^31074	123755	Hans Havermann	03/2021
4936	2^411052+1872481	123739	Enzo Doria	05/2016
4937	34365^3986+3986^34365	123733	Hans Havermann	03/2021
4938	2^410997+39	123723	Lelio R Paula	05/2014
4939	(649^43987-1)/648	123700	Michael Stocker	05/2020
4940	(148*10^123688-1)/3	123690	Robert Price	03/2020
4941	36825^2284+2284^36825	123684	Hans Havermann	03/2021
4942	29582^15171+15171^29582	123683	Hans Havermann	03/2021
4943	10^123671+3593037	123672	Paul Bourdelais	10/2021
4944	8*10^123657+87	123658	Robert Price	10/2019
4945	30505^11302+11302^30505	123642	Hans Havermann	03/2021
4946	29956^13401+13401^29956	123633	Hans Havermann	03/2021
4947	155^56438+154	123618	Norbert Schneider	01/2019
4948	2^410596-39	123602	Lelio R Paula	05/2014
4949	(41*10^123600-221)/9	123601	Robert Price	10/2021
4950	28995^18302+18302^28995	123592	Hans Havermann	03/2021
4951	28302^23269+23269^28302	123589	Hans Havermann	03/2021
4952	2^410540-115079	123585	Enzo Doria	06/2015
4953	(7*10^123563+107)/3	123564	Robert Price	02/2018
4954	9*10^123549+89	123550	Robert Price	11/2019
4955	(197*10^123545+7)/3	123547	Robert Price	12/2020
4956	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
4957	2^410342+212449	123526	Enzo Doria	08/2023
4958	(29*10^123510+277)/9	123511	Robert Price	11/2021
4959	28118^24687+24687^28118	123508	Hans Havermann	03/2021
4960	39994^1225+1225^39994	123507	Hans Havermann	03/2021
4961	2^410206-113081	123485	Enzo Doria	07/2014
4962	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
4963	28974^18215+18215^28974	123442	Hans Havermann	03/2021
4964	28901^18618+18618^28901	123406	Hans Havermann	03/2021
4965	2^409909-189	123395	Enzo Doria	05/2014
4966	2^409896-109043	123391	Enzo Doria	04/2014
4967	2^409890+75409	123390	Enzo Doria	04/2016
4968	81254^33+33^81254	123386	Hans Havermann	03/2021
4969	33463^4854+4854^33463	123348	Hans Havermann	03/2021
4970	34061^4182+4182^34061	123348	Hans Havermann	03/2021
4971	133^58076-2	123345	Lelio R Paula	10/2017
4972	F(590041)	123311	Henri Lifchitz	01/2005
4973	(82*10^123299+377)/9	123300	Robert Price	03/2022
4974	2^409566-113501	123292	Enzo Doria	08/2014
4975	2^409533+77747	123282	Enzo Doria	05/2016
4976	2^409436-112799	123253	Enzo Doria	06/2014
4977	28212^23321+23321^28212	123223	Hans Havermann	03/2021
4978	2^409225+1873787	123189	Enzo Doria	06/2016
4979	2^409174+73009	123174	Enzo Doria	04/2016
4980	2^409058-112685	123139	Enzo Doria	06/2014
4981	(13*10^123137-61)/3	123138	Robert Price	11/2018
4982	4*10^123113+21	123114	Robert Price	12/2018
4983	2^408778+77689	123055	Enzo Doria	05/2016
4984	2^408690-75	123028	Lelio R Paula	11/2013
4985	28327^22032+22032^28327	123026	Hans Havermann	03/2021
4986	(29*10^122996+673)/9	122997	Robert Price	12/2018
4987	(65*10^122994-101)/9	122995	Robert Price	01/2022
4988	2^408574-2787341	122994	Enzo Doria	03/2016
4989	3*10^122977+37	122978	Robert Price	08/2018
4990	(7*10^122976-67)/3	122977	Robert Price	10/2021
4991	Phi(157825,10)	122961	Maksym Voznyy	06/2015
4992	25493^27902-27902^25493	122948	Frank Doornink	02/2024
4993	26749^27768-27768^26749	122938	Frank Doornink	03/2024
4994	(68*10^122933-419)/9	122934	Robert Price	07/2019
4995	29712^13721+13721^29712	122931	Hans Havermann	03/2021
4996	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
4997	(266*10^122872-17)/3	122874	Robert Price	07/2020
4998	(16*10^122871+77)/3	122872	Robert Price	03/2019
4999	30395^11022+11022^30395	122865	Hans Havermann	03/2021
5000	4*10^122859-69	122860	Robert Price	01/2022

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