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	40055^1638+1638^40055	128750	Hans Havermann	04/2021
4752	(923^43411-1)/922	128720	Tom Wu	07/2024
4753	11^123594-240	128710	Enzo Doria	09/2012
4754	2^427504-21503	128692	Enzo Doria	07/2013
4755	37727^2574+2574^37727	128673	Hans Havermann	04/2021
4756	29686^21591+21591^29686	128668	Hans Havermann	04/2021
4757	10^128668-70000000001	128668	Robert Price	08/2021
4758	10^128668-350729	128668	Alfred Reich	08/2024
4759	2^427420+91	128667	Lelio R Paula	05/2017
4760	8*10^128651-37	128652	Robert Price	03/2022
4761	(68*10^128645-257)/9	128646	Robert Price	07/2019
4762	2^427269-113635	128621	Enzo Doria	08/2014
4763	2^427130+1877569	128579	Enzo Doria	08/2016
4764	2^427068+20011	128561	Enzo Doria	06/2023
4765	2^427016-115349	128545	Enzo Doria	07/2015
4766	(4*10^128510+137)/3	128511	Robert Price	03/2018
4767	2^426889-112879	128507	Enzo Doria	06/2014
4768	2^426804+1869931	128481	Enzo Doria	05/2016
4769	2^426750+77635	128465	Enzo Doria	05/2016
4770	27708^28913-28913^27708	128450	Frank Doornink	03/2024
4771	36988^2969+2969^36988	128445	Hans Havermann	03/2021
4772	36664^3185+3185^36664	128439	Hans Havermann	03/2021
4773	32618^8649+8649^32618	128416	Hans Havermann	04/2021
4774	28883^27874+27874^28883	128391	Hans Havermann	04/2021
4775	2^426425-91	128367	Lelio R Paula	05/2017
4776	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
4777	2^426352+74971	128345	Enzo Doria	04/2016
4778	(199*10^128343-7)/3	128345	Robert Price	05/2020
4779	4*10^128343-21	128344	Robert Price	09/2018
4780	(65*10^128338+493)/9	128339	Robert Price	08/2021
4781	35632^3997+3997^35632	128337	Hans Havermann	04/2021
4782	2^426300-1863689	128330	Enzo Doria	03/2016
4783	2^426293+1881017	128327	Enzo Doria	11/2016
4784	(88*10^128324-637)/9	128325	Robert Price	11/2020
4785	(491*10^128285+31)/9	128287	Robert Price	04/2022
4786	39103^1908+1908^39103	128281	Hans Havermann	04/2021
4787	2^426043+35	128252	Robert Price	11/2015
4788	(4*10^128244-19)/3	128245	Robert Price	03/2018
4789	26220^29021-29021^26220	128234	Frank Doornink	03/2024
4790	35489^4102+4102^35489	128222	Hans Havermann	04/2021
4791	34721^4926+4926^34721	128208	Hans Havermann	04/2021
4792	(305*10^128198+1)/9	128200	Robert Price	02/2020
4793	2^425808-459959	128181	Enzo Doria	06/2015
4794	30632^15291+15291^30632	128178	Hans Havermann	04/2021
4795	U(623603)	128177	Serge Batalov	07/2024
4796	35981^3648+3648^35981	128167	Hans Havermann	04/2021
4797	2^425627-113605	128127	Enzo Doria	08/2014
4798	(4*10^128109+119)/3	128110	Robert Price	12/2021
4799	(22*10^128094+53)/3	128095	Robert Price	07/2019
4800	(86*10^128086-221)/9	128087	Robert Price	09/2019
4801	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
4802	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
4803	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
4804	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
4805	2^425205+4911	128000	Marek Hubal	02/2017
4806	29241^23836+23836^29241	127995	Hans Havermann	04/2021
4807	2^425118-113663	127974	Enzo Doria	08/2014
4808	(86*10^127967-329)/9	127968	Robert Price	01/2020
4809	2^425061+1869761	127957	Enzo Doria	05/2016
4810	746^44541+44541^746	127955	Norbert Schneider	07/2019
4811	30236^17043+17043^30236	127946	Hans Havermann	03/2021
4812	2^424938+212419	127920	Enzo Doria	08/2023
4813	2^424918-21141	127914	Enzo Doria	07/2013
4814	(62*10^127903+91)/9	127904	Robert Price	07/2021
4815	2^424864-29489	127897	Enzo Doria	08/2015
4816	30438^15893+15893^30438	127877	Hans Havermann	02/2021
4817	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
4818	28929^26258+26258^28929	127845	Hans Havermann	03/2021
4819	30563^15220+15220^30563	127828	Hans Havermann	03/2021
4820	2^424632-2786639	127827	Enzo Doria	03/2016
4821	10^127821-700001	127821	Robert Price	08/2021
4822	2^424577-113755	127811	Enzo Doria	09/2014
4823	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
4824	(56*10^127752+691)/9	127753	Robert Price	05/2019
4825	11^122629-720	127705	Enzo Doria	11/2012
4826	22*10^127645+3	127647	Robert Price	01/2020
4827	28715^27844+27844^28715	127631	Hans Havermann	03/2021
4828	(56*10^127612+187)/9	127613	Robert Price	10/2021
4829	(5*36^81995+821)/7	127609	Eric Chen	01/2021
4830	4*10^127562-39	127563	Robert Price	09/2020
4831	32595^8186+8186^32595	127547	Hans Havermann	03/2021
4832	2^423696-21429	127546	Enzo Doria	07/2013
4833	2^423664-1864559	127536	Enzo Doria	03/2016
4834	37889^2322+2322^37889	127530	Hans Havermann	03/2021
4835	37668^2429+2429^37668	127523	Hans Havermann	03/2021
4836	3^267267-4	127519	Henri Lifchitz	10/2014
4837	fibonacci(610144)-2	127513	Jon Grantham	08/2023
4838	26253^28852-28852^26253	127503	Frank Doornink	03/2024
4839	(103*10^127491+17)/3	127493	Robert Price	08/2020
4840	29376^21869+21869^29376	127487	Hans Havermann	03/2021
4841	31186^12241+12241^31186	127483	Hans Havermann	02/2021
4842	(19^99689+5^99689)/24	127477	Robert Price	09/2013
4843	27069^28754-28754^27069	127452	Frank Doornink	01/2024
4844	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
4845	30594^14645+14645^30594	127446	Hans Havermann	03/2021
4846	2^423328-21537	127435	Enzo Doria	07/2013
4847	(67*10^127413-7)/3	127415	Robert Price	01/2020
4848	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
4849	(2*10^127407+73)/3	127407	Robert Price	09/2020
4850	(2^423165-7)/25	127384	Lelio R Paula	05/2015
4851	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
4852	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
4853	29512^20647+20647^29512	127341	Hans Havermann	03/2021
4854	2^422987-3001935	127332	Paul Bourdelais	07/2023
4855	(112*10^127324+17)/3	127326	Robert Price	03/2020
4856	29565^20252+20252^29565	127321	Hans Havermann	03/2021
4857	fibonacci(609165)-3	127308	Jon Grantham	08/2023
4859	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
4858	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
4860	(16*10^127259+197)/3	127260	Robert Price	04/2019
4861	(26*10^127240+61)/3	127241	Robert Price	10/2019
4862	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
4863	2^422515-114997	127190	Enzo Doria	06/2015
4864	5*10^127179-3	127180	Robert Price	07/2015
4865	31678^10343+10343^31678	127176	Hans Havermann	03/2021
4866	(44*10^127169-233)/9	127170	Robert Price	01/2019
4867	34947^4352+4352^34947	127162	Hans Havermann	03/2021
4868	6*10^127158+19	127159	Robert Price	11/2021
4869	30469^14902+14902^30469	127155	Hans Havermann	03/2021
4870	5*10^127153+77	127154	Robert Price	12/2018
4871	29941^17620+17620^29941	127130	Hans Havermann	02/2021
4872	31607^10516+10516^31607	127119	Hans Havermann	03/2021
4873	(19*10^127118-97)/3	127119	Robert Price	10/2021
4874	(29*10^127111+691)/9	127112	Robert Price	08/2021
4875	736^44335+44335^736	127104	Norbert Schneider	07/2019
4876	33040^7023+7023^33040	127090	Hans Havermann	03/2021
4877	(4*10^127081+167)/9	127081	Robert Price	03/2022
4878	29748^18661+18661^29748	127052	Hans Havermann	03/2021
4879	27905^28578-28578^27905	127049	Frank Doornink	03/2024
4880	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
4881	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
4882	(14*10^127014-137)/3	127015	Robert Price	04/2021
4883	31436^10965+10965^31436	127002	Hans Havermann	03/2021
4884	28905^24758+24758^28905	127001	Hans Havermann	03/2021
4885	2^421860-113285	126993	Enzo Doria	07/2014
4886	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
4887	(2^421827-7)/11	126982	Lelio R Paula	05/2015
4888	26268^28729-28729^26268	126966	Frank Doornink	03/2024
4889	11^121910-840	126957	Enzo Doria	12/2012
4890	(56*10^126935+187)/9	126936	Robert Price	10/2021
4891	28915^24538+24538^28915	126933	Hans Havermann	03/2021
4892	(29*10^126928-77)/3	126929	Robert Price	02/2020
4893	(259*10^126919-1)/3	126921	Robert Price	12/2020
4894	10^126919+204567	126920	Patrick De Geest	05/2021
4895	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
4896	10^126919-100001	126919	Robert Price	07/2020
4897	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
4898	2^421534-3001935	126895	Paul Bourdelais	07/2023
4899	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
4900	(5*10^126871-119)/3	126872	Robert Price	03/2018
4901	331^50339-10004	126846	Enzo Doria	07/2012
4902	2^421363-2790757	126843	Enzo Doria	03/2016
4903	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
4904	37938^2203+2203^37938	126828	Hans Havermann	03/2021
4905	(13*10^126819+77)/9	126820	Robert Price	07/2022
4906	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
4908	(14*10^126784-83)/3	126785	Robert Price	12/2018
4907	2^421169-3001935	126785	Paul Bourdelais	07/2023
4909	2^421161-286183	126783	Enzo Doria	06/2015
4910	26733^28628-28628^26733	126738	Frank Doornink	03/2024
4911	(106*10^126726+17)/3	126728	Robert Price	04/2021
4912	30718^13347+13347^30718	126724	Hans Havermann	03/2021
4913	2^420939-113935	126716	Enzo Doria	10/2014
4914	11*23^93048+356	126708	Eric Chen	08/2023
4915	177^56363-2	126703	Lelio R Paula	10/2017
4916	2^420741-113659	126656	Enzo Doria	08/2014
4917	2^420694-21	126642	Lelio R Paula	05/2017
4918	(13*10^126638+437)/9	126639	Robert Price	04/2018
4919	(167*10^126637-17)/3	126639	Robert Price	03/2020
4920	4*10^126625+87	126626	Robert Price	08/2018
4921	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
4922	7*10^126600-99	126601	Robert Price	06/2019
4923	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
4924	2^420424-59189	126561	Enzo Doria	10/2015
4925	28717^25534+25534^28717	126560	Hans Havermann	03/2021
4926	(86*10^126542+103)/9	126543	Robert Price	12/2021
4927	(19*10^126517-7)/3	126518	Robert Price	12/2023
4928	28922^23655+23655^28922	126503	Hans Havermann	03/2021
4929	2^420126+71893	126471	Enzo Doria	04/2016
4930	25982^28643-28643^25982	126450	Frank Doornink	03/2024
4931	(43*10^126441+47)/9	126442	Robert Price	12/2018
4932	8*10^126408+71	126409	Robert Price	05/2022
4933	2^419866+1877059	126393	Enzo Doria	07/2016
4934	29315^20484+20484^29315	126390	Hans Havermann	03/2021
4935	29433^19676+19676^29433	126384	Hans Havermann	03/2021
4936	F(604711)	126377	Henri Lifchitz	02/2005
4937	2^419757+72707	126360	Enzo Doria	04/2016
4938	2^419720-21569	126349	Enzo Doria	07/2013
4939	2^419637+29	126324	Henri Lifchitz	02/2006
4940	31004^11865+11865^31004	126319	Hans Havermann	03/2021
4941	2^419612+1876741	126316	Enzo Doria	07/2016
4942	2^419520+2793271	126289	Enzo Doria	03/2016
4943	(2^419447-5)/369	126264	Lelio R Paula	05/2014
4944	2^419328-1859939	126231	Enzo Doria	03/2016
4945	2^419282-1851507	126217	Enzo Doria	08/2015
4946	(133*10^126212+17)/3	126214	Robert Price	11/2021
4947	2^419251+1866143	126208	Enzo Doria	03/2016
4948	11^121185+2	126202	Robert Price	05/2014
4949	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
4950	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
4951	2^418851+23	126087	Robert Price	09/2015
4952	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
4953	2^418829+167	126081	Lelio R Paula	01/2012
4954	31037^11530+11530^31037	126067	Hans Havermann	03/2021
4955	4*10^126064-69	126065	Robert Price	01/2022
4956	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
4957	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
4958	(35*10^126048-323)/9	126049	Robert Price	10/2021
4959	33016^6551+6551^33016	126000	Hans Havermann	03/2021
4960	2^418548-111546435	125996	Paul Bourdelais	10/2021
4961	25134^28625-28625^25134	125958	Frank Doornink	12/2023
4962	34736^4227+4227^34736	125954	Hans Havermann	03/2021
4963	26197^28502-28502^26197	125930	Frank Doornink	03/2024
4964	2^418319-109501	125927	Enzo Doria	04/2014
4965	2^418316-112373	125926	Enzo Doria	06/2014
4966	40398^1309+1309^40398	125919	Hans Havermann	03/2021
4967	(8*10^125894-29)/3	125895	Robert Price	07/2018
4968	(26*10^125886-413)/9	125887	Robert Price	05/2018
4969	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
4970	55*10^125847+9	125849	Robert Price	03/2022
4971	4*10^125832+57	125833	Robert Price	05/2022
4972	2^417968+1869811	125821	Enzo Doria	06/2016
4973	2^417902+63	125802	Lelio R Paula	09/2015
4974	(10^125792-91)/9	125792	Serge Batalov	12/2014
4975	30438^13573+13573^30438	125791	Hans Havermann	03/2021
4976	32867^6714+6714^32867	125782	Hans Havermann	03/2021
4977	31155^10892+10892^31155	125777	Hans Havermann	03/2021
4978	(35*10^125754-593)/9	125755	Robert Price	07/2018
4979	30455^13464+13464^30455	125754	Hans Havermann	03/2021
4980	(32*10^125751-77)/9	125752	Robert Price	06/2018
4981	2^417704+77011	125742	Enzo Doria	05/2016
4982	29755^16816+16816^29755	125737	Hans Havermann	03/2021
4983	(22*10^125734+203)/9	125735	Robert Price	10/2021
4984	29918^15915+15915^29918	125710	Hans Havermann	03/2021
4985	(10^125706+149)/3	125706	Serge Batalov	12/2014
4986	28531^25368+25368^28531	125659	Hans Havermann	03/2021
4987	2^417419-115309	125656	Enzo Doria	07/2015
4988	(46*10^125642+593)/9	125643	Robert Price	04/2022
4989	2^417315+213953	125625	Enzo Doria	10/2023
4990	2^417300+77281	125620	Enzo Doria	05/2016
4991	30638^12537+12537^30638	125561	Hans Havermann	03/2021
4992	2^417095-1657	125559	Yves Minet	07/2014
4993	30162^14525+14525^30162	125538	Hans Havermann	03/2021
4994	(56*10^125535+583)/9	125536	Robert Price	08/2021
4995	(23*10^125517-179)/3	125518	Robert Price	06/2022
4996	9*10^125516+29	125517	Robert Price	03/2022
4997	(88*10^125492-637)/9	125493	Robert Price	11/2020
4998	28958^21525+21525^28958	125474	Hans Havermann	02/2021
4999	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
5000	26078^28409-28409^26078	125462	Frank Doornink	03/2024

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295765 PRPs in the top)