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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(35*10^125754-593)/9	125755	Robert Price	07/2018
4752	30455^13464+13464^30455	125754	Hans Havermann	03/2021
4753	(32*10^125751-77)/9	125752	Robert Price	06/2018
4754	2^417704+77011	125742	Enzo Doria	05/2016
4755	29755^16816+16816^29755	125737	Hans Havermann	03/2021
4756	(22*10^125734+203)/9	125735	Robert Price	10/2021
4757	29918^15915+15915^29918	125710	Hans Havermann	03/2021
4758	(10^125706+149)/3	125706	Serge Batalov	12/2014
4759	28531^25368+25368^28531	125659	Hans Havermann	03/2021
4760	2^417419-115309	125656	Enzo Doria	07/2015
4761	(46*10^125642+593)/9	125643	Robert Price	04/2022
4762	2^417315+213953	125625	Enzo Doria	10/2023
4763	2^417300+77281	125620	Enzo Doria	05/2016
4764	30638^12537+12537^30638	125561	Hans Havermann	03/2021
4765	2^417095-1657	125559	Yves Minet	07/2014
4766	30162^14525+14525^30162	125538	Hans Havermann	03/2021
4767	(56*10^125535+583)/9	125536	Robert Price	08/2021
4768	(23*10^125517-179)/3	125518	Robert Price	06/2022
4769	9*10^125516+29	125517	Robert Price	03/2022
4770	(88*10^125492-637)/9	125493	Robert Price	11/2020
4771	28958^21525+21525^28958	125474	Hans Havermann	02/2021
4774	2^416773-25	125462	Lelio R Paula	09/2015
4772	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
4773	26078^28409-28409^26078	125462	Frank Doornink	03/2024
4775	33889^5032+5032^33889	125449	Hans Havermann	03/2021
4776	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
4777	(2861^36481+1)/(2861^191+1)	125438	Martin Hopf	12/2023
4778	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
4779	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
4780	2^416641-2*416641+1	125422	Robert Price	05/2018
4781	33392^5697+5697^33392	125409	Hans Havermann	03/2021
4782	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
4783	2^416530+1870429	125389	Enzo Doria	05/2016
4784	(56*10^125385+691)/9	125386	Robert Price	05/2019
4785	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
4786	31074^10837+10837^31074	125381	Hans Havermann	03/2021
4787	33745^5194+5194^33745	125380	Hans Havermann	03/2021
4788	2^416490+1875109	125376	Enzo Doria	09/2016
4789	28360^26331+26331^28360	125365	Hans Havermann	03/2021
4790	2^416416-114929	125354	Enzo Doria	05/2015
4791	25805^28412-28412^25805	125346	Frank Doornink	03/2024
4792	(77*10^125330-293)/9	125331	Robert Price	09/2019
4793	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
4794	2^416134+1865899	125269	Enzo Doria	03/2016
4795	153^57337-152	125264	Norbert Schneider	12/2018
4796	(599*10^125224+13)/9	125226	Robert Price	02/2022
4797	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
4798	30054^14657+14657^30054	125207	Hans Havermann	03/2021
4799	(23^91943-1)/22	125201	Robert Price	01/2012
4800	2^415884-933075	125194	Paul Bourdelais	06/2021
4801	43125^27010-106	125185	Enzo Doria	08/2012
4802	(38*10^125166+349)/9	125167	Robert Price	10/2018
4803	10^125166-5001	125166	Robert Price	12/2021
4804	2^415765-112603	125158	Enzo Doria	06/2014
4805	8*10^125088-13	125089	Robert Price	08/2019
4806	(25*10^125076-13)/3	125077	Robert Price	09/2019
4807	(11*10^125054+73)/3	125055	Robert Price	08/2021
4808	(29*10^125021-113)/3	125022	Robert Price	10/2019
4809	2^415290-113591	125015	Enzo Doria	08/2014
4810	2^415276-460919	125011	Enzo Doria	06/2015
4811	2^415259+77243	125006	Enzo Doria	05/2016
4812	(67*10^124990+77)/9	124991	Robert Price	10/2021
4813	2^415144-3683	124971	Yves Minet	10/2011
4814	2^415092+111546435	124956	Paul Bourdelais	10/2021
4815	31936^8173+8173^31936	124946	Hans Havermann	03/2021
4816	27458^28145-28145^27458	124927	Frank Doornink	03/2024
4817	5^178715-4	124916	Tyler NeSmith	07/2021
4818	29767^15700+15700^29767	124900	Hans Havermann	03/2021
4819	2^414874+79	124890	Lelio R Paula	01/2015
4820	25292^28361-28361^25292	124874	Frank Doornink	01/2024
4821	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
4822	2^414618+79459	124813	Enzo Doria	06/2016
4823	(61*10^124809-1)/3	124811	Robert Price	01/2020
4824	(29*10^124765-71)/3	124766	Robert Price	07/2021
4825	2^414432-1846709	124757	Enzo Doria	07/2015
4826	2*10^124751-51	124752	Robert Price	04/2018
4827	(56*10^124735+367)/9	124736	Robert Price	06/2019
4828	27362^28111-28111^27362	124733	Frank Doornink	03/2024
4829	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
4830	(23*10^124690+37)/3	124691	Robert Price	02/2022
4831	56*10^124656-3	124658	Robert Price	03/2020
4832	(7*10^124648+197)/3	124649	Robert Price	07/2018
4834	2^414032-5	124637	Henri Lifchitz	07/2006
4833	2^414032+1872331	124637	Enzo Doria	05/2016
4835	37373^2158+2158^37373	124604	Hans Havermann	03/2021
4836	29811^15112+15112^29811	124590	Hans Havermann	03/2021
4837	2^413781-2023	124561	Riley Fisher	09/2023
4838	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
4839	29757^15296+15296^29757	124521	Hans Havermann	03/2021
4840	35056^3561+3561^35056	124504	Hans Havermann	03/2021
4841	40588^1167+1167^40588	124487	Hans Havermann	02/2021
4842	(85*10^124485-49)/9	124486	Robert Price	12/2020
4843	64^68909-63^68909	124463	Robert Price	07/2013
4844	35016^3581+3581^35016	124448	Hans Havermann	03/2021
4845	2^413387+76253	124442	Enzo Doria	04/2016
4846	28749^21298+21298^28749	124436	Hans Havermann	03/2021
4847	2^413352+524287	124432	Paul Underwood	09/2018
4848	287117#+391613	124424	Nicolas PALAU	01/2017
4849	(4*10^124420+83)/3	124421	Robert Price	02/2018
4850	34578^3965+3965^34578	124421	Hans Havermann	03/2021
4851	(68*10^124392-329)/9	124393	Robert Price	03/2021
4852	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
4853	10^124383+58407	124384	Patrick De Geest	08/2021
4855	10^124383-8000001	124383	Robert Price	04/2021
4854	10^124383-5801	124383	Patrick De Geest	08/2021
4856	26091^28154-28154^26091	124342	Frank Doornink	03/2024
4857	(41*10^124335-383)/9	124336	Robert Price	11/2018
4858	(304*10^124329-43)/9	124331	Robert Price	02/2020
4859	34716^3811+3811^34716	124320	Hans Havermann	03/2021
4860	26892^28063-28063^26892	124309	Frank Doornink	03/2024
4861	2^412868-120599	124286	Paul Bourdelais	02/2012
4862	10^124248+899089	124249	Patrick De Geest	05/2021
4864	10^124248-1000001	124248	Robert Price	08/2020
4863	10^124248-501903	124248	Patrick De Geest	05/2021
4865	45^75145-2	124231	Lelio R Paula	08/2015
4866	29901^14272+14272^29901	124224	Hans Havermann	03/2021
4867	2^412645-112213	124219	Enzo Doria	06/2014
4868	29837^14500+14500^29837	124163	Hans Havermann	03/2021
4869	28074^26455+26455^28074	124158	Hans Havermann	03/2021
4870	2^412285+213317	124111	Enzo Doria	09/2023
4871	2^412248+74611	124100	Enzo Doria	04/2016
4872	(22*10^124096-13)/9	124097	Robert Price	06/2018
4873	(455*10^124093+31)/9	124095	Robert Price	06/2021
4874	2^412192-3329	124083	Yves Minet	12/2014
4875	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
4877	(25*10^124076-67)/3	124077	Robert Price	06/2019
4876	28132^25735+25735^28132	124077	Hans Havermann	03/2021
4878	F(593689)	124074	Henri Lifchitz	01/2005
4879	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
4880	26372^28057-28057^26372	124045	Frank Doornink	03/2024
4881	27528^27937-27937^27528	124034	Frank Doornink	03/2024
4882	35364^3215+3215^35364	124028	Hans Havermann	03/2021
4884	(266*10^124022-11)/3	124024	Robert Price	04/2020
4883	29987^13674+13674^29987	124024	Hans Havermann	03/2021
4885	2^411932-111546435	124004	Paul Bourdelais	10/2021
4886	2^411884-113279	123990	Enzo Doria	07/2014
4887	(2^411832+1)/257	123972	Lelio R Paula	05/2014
4888	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
4889	(26*10^123970-89)/9	123971	Robert Price	06/2018
4890	2^411790-1853531	123962	Enzo Doria	08/2015
4891	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
4892	(101*10^123950+7)/9	123952	Robert Price	02/2022
4893	2^411711-113257	123938	Enzo Doria	07/2014
4894	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
4895	36289^2598+2598^36289	123914	Hans Havermann	03/2021
4896	(11*10^123899-179)/3	123900	Robert Price	09/2018
4897	32276^6879+6879^32276	123860	Hans Havermann	02/2021
4898	2^411325-351103	123822	Enzo Doria	06/2015
4899	(646*10^123817+11)/9	123819	Robert Price	10/2021
4900	30738^10643+10643^30738	123784	Hans Havermann	03/2021
4901	31074^9607+9607^31074	123755	Hans Havermann	03/2021
4902	2^411052+1872481	123739	Enzo Doria	05/2016
4903	34365^3986+3986^34365	123733	Hans Havermann	03/2021
4904	2^410997+39	123723	Lelio R Paula	05/2014
4905	(649^43987-1)/648	123700	Michael Stocker	05/2020
4906	(148*10^123688-1)/3	123690	Robert Price	03/2020
4907	36825^2284+2284^36825	123684	Hans Havermann	03/2021
4908	29582^15171+15171^29582	123683	Hans Havermann	03/2021
4909	10^123671+3593037	123672	Paul Bourdelais	10/2021
4910	8*10^123657+87	123658	Robert Price	10/2019
4911	30505^11302+11302^30505	123642	Hans Havermann	03/2021
4912	29956^13401+13401^29956	123633	Hans Havermann	03/2021
4913	155^56438+154	123618	Norbert Schneider	01/2019
4914	2^410596-39	123602	Lelio R Paula	05/2014
4915	(41*10^123600-221)/9	123601	Robert Price	10/2021
4916	28995^18302+18302^28995	123592	Hans Havermann	03/2021
4917	28302^23269+23269^28302	123589	Hans Havermann	03/2021
4918	2^410540-115079	123585	Enzo Doria	06/2015
4919	(7*10^123563+107)/3	123564	Robert Price	02/2018
4920	9*10^123549+89	123550	Robert Price	11/2019
4921	(197*10^123545+7)/3	123547	Robert Price	12/2020
4922	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
4923	2^410342+212449	123526	Enzo Doria	08/2023
4924	(29*10^123510+277)/9	123511	Robert Price	11/2021
4925	28118^24687+24687^28118	123508	Hans Havermann	03/2021
4926	39994^1225+1225^39994	123507	Hans Havermann	03/2021
4927	2^410206-113081	123485	Enzo Doria	07/2014
4928	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
4929	28974^18215+18215^28974	123442	Hans Havermann	03/2021
4930	28901^18618+18618^28901	123406	Hans Havermann	03/2021
4931	2^409909-189	123395	Enzo Doria	05/2014
4932	2^409896-109043	123391	Enzo Doria	04/2014
4933	2^409890+75409	123390	Enzo Doria	04/2016
4934	81254^33+33^81254	123386	Hans Havermann	03/2021
4935	33463^4854+4854^33463	123348	Hans Havermann	03/2021
4936	34061^4182+4182^34061	123348	Hans Havermann	03/2021
4937	133^58076-2	123345	Lelio R Paula	10/2017
4938	F(590041)	123311	Henri Lifchitz	01/2005
4939	(82*10^123299+377)/9	123300	Robert Price	03/2022
4940	2^409566-113501	123292	Enzo Doria	08/2014
4941	2^409533+77747	123282	Enzo Doria	05/2016
4942	2^409436-112799	123253	Enzo Doria	06/2014
4943	28212^23321+23321^28212	123223	Hans Havermann	03/2021
4944	2^409225+1873787	123189	Enzo Doria	06/2016
4945	2^409174+73009	123174	Enzo Doria	04/2016
4946	2^409058-112685	123139	Enzo Doria	06/2014
4947	(13*10^123137-61)/3	123138	Robert Price	11/2018
4948	4*10^123113+21	123114	Robert Price	12/2018
4949	2^408778+77689	123055	Enzo Doria	05/2016
4950	2^408690-75	123028	Lelio R Paula	11/2013
4951	28327^22032+22032^28327	123026	Hans Havermann	03/2021
4952	(29*10^122996+673)/9	122997	Robert Price	12/2018
4953	(65*10^122994-101)/9	122995	Robert Price	01/2022
4954	2^408574-2787341	122994	Enzo Doria	03/2016
4955	3*10^122977+37	122978	Robert Price	08/2018
4956	(7*10^122976-67)/3	122977	Robert Price	10/2021
4957	Phi(157825,10)	122961	Maksym Voznyy	06/2015
4958	25493^27902-27902^25493	122948	Frank Doornink	02/2024
4959	26749^27768-27768^26749	122938	Frank Doornink	03/2024
4960	(68*10^122933-419)/9	122934	Robert Price	07/2019
4961	29712^13721+13721^29712	122931	Hans Havermann	03/2021
4962	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
4963	(266*10^122872-17)/3	122874	Robert Price	07/2020
4964	(16*10^122871+77)/3	122872	Robert Price	03/2019
4965	30395^11022+11022^30395	122865	Hans Havermann	03/2021
4966	4*10^122859-69	122860	Robert Price	01/2022
4967	(10^122857+167)/3	122857	Robert Price	05/2021
4968	33331^4852+4852^33331	122856	Hans Havermann	03/2021
4969	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
4970	(19*10^122836-43)/3	122837	Robert Price	05/2019
4971	28420^20969+20969^28420	122820	Hans Havermann	03/2021
4972	(16*10^122818+179)/3	122819	Robert Price	11/2021
4973	29865^12934+12934^29865	122797	Hans Havermann	03/2021
4974	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
4975	(32*10^122733-77)/9	122734	Robert Price	06/2018
4976	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
4978	(22*10^122681+161)/3	122682	Robert Price	05/2019
4977	29513^14350+14350^29513	122682	Hans Havermann	03/2021
4979	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
4980	(26*10^122625-131)/3	122626	Robert Price	10/2019
4981	(643*33^80753+3709)/32	122626	Eric Chen	12/2023
4982	27925^24562+24562^27925	122599	Hans Havermann	03/2021
4983	(73*10^122592-1)/9	122593	Robert Price	01/2015
4984	(5*10^122592+91)/3	122593	Robert Price	04/2018
4985	36751^2166+2166^36751	122589	Hans Havermann	03/2021
4986	(85*10^122585-1)/3	122587	Robert Price	02/2020
4987	29368^14931+14931^29368	122585	Hans Havermann	03/2021
4988	2^407179-112075	122574	Enzo Doria	06/2014
4989	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
4990	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
4991	(646*10^122533+11)/9	122535	Robert Price	10/2021
4992	2^407008-1867919	122522	Enzo Doria	04/2016
4993	11^117642-300	122512	Enzo Doria	10/2012
4994	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
4995	2^406949+72197	122504	Enzo Doria	04/2016
4996	(19*10^122501+149)/3	122502	Robert Price	05/2019
4997	28632^18977+18977^28632	122495	Hans Havermann	03/2021
4998	31815^7076+7076^31815	122481	Hans Havermann	03/2021
4999	2^406826-65	122467	Lelio R Paula	11/2013
5000	2^406821-2797363	122466	Enzo Doria	04/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295036 PRPs in the top)