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 (> 30000)	Who ?	When ?
5751	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
5752	19^60321+82	77136	Lelio R Paula	03/2015
5753	5*2^256233-3	77135	Lelio R Paula	06/2014
5754	3*2^256149+7	77110	Lelio R Paula	06/2014
5755	3^161594-106	77100	Lelio R Paula	02/2015
5756	2^256114-185	77098	Lelio R Paula	03/2012
5757	8^85349-85349^8	77078	Norbert Schneider	05/2017
5758	2^256043-2786377	77077	Enzo Doria	03/2016
5759	2^255973+1869947	77056	Enzo Doria	05/2016
5760	12^71393-43	77046	Lelio R Paula	02/2015
5761	15^65490+44	77023	Lelio R Paula	02/2015
5762	(3^161411-7)/940	77010	Lelio R Paula	10/2012
5764	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
5763	(570^27943-1)/569	77005	Serge Batalov	12/2016
5765	2^255750-75	76989	Lelio R Paula	03/2012
5766	3*6^98926-5	76980	Lelio R Paula	10/2014
5767	18^61320-1433	76974	Enzo Doria	03/2013
5768	6^98916-17093	76972	Enzo Doria	02/2013
5769	2^255659-110131	76962	Enzo Doria	04/2014
5770	12^71303+91	76949	Lelio R Paula	02/2015
5771	18^61298+59	76946	Lelio R Paula	02/2015
5772	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
5773	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
5774	18^61290-11	76936	Lelio R Paula	02/2015
5776	63^42752-2	76926	Lelio R Paula	08/2013
5775	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
5777	2^255517+56387	76919	Yves Minet	02/2011
5778	2^255499-112567	76913	Enzo Doria	06/2014
5779	2^255492+345	76911	Lelio R Paula	06/2013
5780	10^76875+217591	76876	Patrick De Geest	05/2013
5782	10^76875-53	76875	Robert Price	05/2011
5781	11^73819-5880	76875	Enzo Doria	01/2013
5783	2^255313+18915	76857	Lelio R Paula	06/2013
5784	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
5785	2^255296+5775	76852	Lelio R Paula	06/2013
5786	14^67052-29	76851	Lelio R Paula	02/2015
5787	(8*10^76840+43)/3	76841	Robert Price	10/2017
5788	(7*10^76818-313)/9	76818	Robert Price	11/2016
5789	10^76801+69	76802	Robert Price	03/2011
5790	10^76801-80943	76801	Patrick De Geest	06/2013
5791	2^255105+57	76795	Lelio R Paula	03/2012
5792	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
5793	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
5794	2^255055+1869353	76780	Enzo Doria	05/2016
5795	17^62396-90	76776	Lelio R Paula	03/2015
5796	7^90833-60	76763	Lelio R Paula	02/2015
5797	13^68901-56	76752	Lelio R Paula	03/2015
5798	2^254961+1869917	76751	Enzo Doria	05/2016
5799	9*5^109791-8	76742	Lelio R Paula	10/2014
5800	82^40089+40089^82	76723	Serge Batalov	02/2012
5801	2^254861-2790013	76721	Enzo Doria	03/2016
5802	10^76705+13	76706	Robert Price	01/2011
5803	10^76705-94077	76705	Patrick De Geest	06/2013
5804	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
5805	2^254758-110405	76690	Enzo Doria	05/2014
5806	2^254716-3779	76678	Yves Minet	04/2017
5807	2^254708-110507	76675	Enzo Doria	05/2014
5808	(47*10^76672+133)/9	76673	Robert Price	04/2017
5809	2^254670-112901	76664	Enzo Doria	06/2014
5810	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
5811	2^254598-113183	76642	Enzo Doria	07/2014
5812	19^59932+22	76639	Lelio R Paula	01/2015
5813	2^254569-112213	76633	Enzo Doria	06/2014
5814	2*5^109626+9	76626	Lelio R Paula	10/2014
5815	2^254521+1872527	76619	Enzo Doria	05/2016
5816	(76*10^76615+167)/9	76616	Robert Price	08/2016
5817	25^54799-24^54799	76606	Robert Price	07/2012
5818	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
5819	12^70961-85	76580	Lelio R Paula	02/2015
5820	7^90590-38	76558	Lelio R Paula	02/2015
5821	2^254304+5227	76554	Lelio R Paula	06/2013
5822	(76*10^76547-211)/9	76548	Robert Price	10/2017
5823	18^60979-5363	76546	Enzo Doria	03/2013
5824	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
5825	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
5826	(7*10^76536-313)/9	76536	Robert Price	11/2016
5828	2^254239-27	76534	Lelio R Paula	03/2012
5827	2^254238-1841	76534	Yves Minet	03/2013
5829	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
5830	2^254189-112225	76519	Enzo Doria	06/2014
5831	18^60938-1397	76494	Enzo Doria	03/2013
5832	2^254075-2788417	76485	Enzo Doria	03/2016
5833	7*10^76483-23	76484	Robert Price	04/2016
5834	2^254042-112913	76475	Enzo Doria	06/2014
5835	14^66723-37	76474	Lelio R Paula	02/2015
5836	2^254037-110305	76473	Enzo Doria	05/2014
5837	2^253931-111109	76441	Enzo Doria	05/2014
5838	2^253926-1167	76440	Lelio R Paula	05/2013
5839	(49*10^76438-13)/9	76439	Robert Price	07/2015
5840	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
5841	10^76374+31	76375	Robert Price	03/2011
5842	10^76374-222159	76374	Patrick De Geest	05/2013
5843	2^253561-110533	76330	Enzo Doria	05/2014
5844	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
5845	9*5^109182+2	76316	Lelio R Paula	10/2014
5846	11^73279-3690	76313	Enzo Doria	12/2012
5847	(598*10^76309-31)/9	76311	Robert Price	02/2017
5848	11^73274-24000	76308	Enzo Doria	12/2012
5849	7^90291-6	76305	Theodore Burton	11/2005
5850	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
5851	6^98025+145	76279	Lelio R Paula	01/2015
5852	2^253355+1155	76268	Lelio R Paula	05/2013
5853	(73*10^76262+413)/9	76263	Robert Price	10/2017
5854	2^253292-71219	76249	Enzo Doria	04/2016
5855	7^90221-36	76246	Lelio R Paula	02/2015
5856	18^60727-3473	76229	Enzo Doria	03/2013
5857	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
5858	(8*10^76220-83)/3	76221	Robert Price	10/2017
5859	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
5860	11^73163-2010	76192	Enzo Doria	12/2012
5861	2^253060+54615	76179	Lelio R Paula	05/2013
5862	2^253029+1869761	76170	Enzo Doria	05/2016
5863	2^252955-111007	76148	Enzo Doria	05/2014
5864	2*5^108931+7	76140	Lelio R Paula	10/2014
5865	(86*10^76128+121)/9	76129	Robert Price	03/2017
5866	22154*29^52050+9	76123	Curtis Bright	05/2015
5867	3^159530-112358	76116	Enzo Doria	06/2014
5868	11^73089-48	76115	Lelio R Paula	02/2015
5869	86^39337-85	76098	Norbert Schneider	10/2015
5870	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
5871	6^97783+77	76090	Lelio R Paula	01/2015
5872	2^252712-105	76074	Lelio R Paula	03/2012
5873	(10^76069-19)/9	76069	Robert Price	10/2017
5875	131^35927+2	76068	Lelio R Paula	05/2013
5874	(41*10^76067+373)/9	76068	Robert Price	04/2017
5876	2^252683-139	76066	Lelio R Paula	03/2012
5877	137^35597-136	76061	Norbert Schneider	05/2015
5878	3^159413+106	76060	Lelio R Paula	01/2015
5879	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
5880	(2^252557-9)/71	76026	Lelio R Paula	07/2012
5881	(85*10^76021-103)/9	76022	Robert Price	10/2017
5882	11^72989+80	76011	Lelio R Paula	02/2015
5883	2^252449-459523	75995	Enzo Doria	05/2015
5884	20^58408+73	75991	Lelio R Paula	01/2015
5885	2^252418-1421	75986	Yves Minet	01/2013
5886	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
5887	2^252365-110689	75970	Enzo Doria	05/2014
5888	11^72949-1020	75969	Enzo Doria	11/2012
5889	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
5890	2^252261-110595	75939	Enzo Doria	05/2014
5891	7^89853+76	75935	Lelio R Paula	01/2015
5892	3^159132+56	75926	Lelio R Paula	01/2015
5893	730^26513+26513^730	75916	Norbert Schneider	11/2016
5894	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
5895	5^108596-14846	75906	Enzo Doria	02/2013
5896	5^108560-14846	75881	Enzo Doria	02/2013
5897	2^252051-110359	75875	Enzo Doria	05/2014
5898	2^251971-110509	75851	Enzo Doria	05/2014
5899	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
5900	99655!6-2	75811	Robert Price	07/2017
5901	14*10^75798+1089	75800	Jens K. Andersen	11/2007
5902	2^251784-455	75795	Yves Minet	03/2012
5903	2^251780-1289	75794	Yves Minet	01/2013
5904	2^251760-215609	75788	Paul Bourdelais	03/2013
5905	99^37973+2	75781	Lelio R Paula	05/2013
5906	(185*10^75777+7)/3	75779	Robert Price	02/2017
5907	5*2^251690+3	75767	Lelio R Paula	06/2014
5908	6^97366+95	75766	Lelio R Paula	01/2015
5909	s(23010)	75760	Hans Havermann	11/2017
5910	8*6^97337-7	75744	Lelio R Paula	10/2014
5911	2^251588-111677	75736	Enzo Doria	05/2014
5912	5^108346-13256	75731	Enzo Doria	02/2013
5913	(31^50777+1)/32	75726	Robert Price	07/2013
5914	(10^75707+77)/3	75707	Robert Price	01/2017
5915	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
5916	2^251466+193	75699	Lelio R Paula	03/2012
5917	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
5918	2^251422-109991	75686	Enzo Doria	04/2014
5919	4*5^108245-3	75661	Lelio R Paula	10/2014
5920	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
5921	12^70066+95	75614	Lelio R Paula	02/2015
5922	-E20534/2063	75607	Thomas Ritschel	02/2017
5923	19^59120-50	75600	Lelio R Paula	01/2015
5924	18^60222-4697	75596	Enzo Doria	03/2013
5925	18^60211-4355	75582	Enzo Doria	03/2013
5926	7*2^251014-9	75564	Lelio R Paula	06/2014
5927	6^97101-25	75560	Lelio R Paula	01/2015
5928	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
5929	3^158331-140	75544	Lelio R Paula	01/2015
5931	(37^48157-1)/36	75519	Robert Price	03/2012
5930	(19*10^75518-43)/3	75519	Robert Price	10/2017
5932	2^250868-4229	75519	Yves Minet	08/2018
5933	10^75516+31467	75517	Patrick De Geest	03/2016
5935	10^75516-10^2256-1	75516	Serge Batalov	01/2011
5934	10^75516-66591	75516	Patrick De Geest	03/2016
5936	2^250851-187	75514	Lelio R Paula	03/2012
5937	(43*10^75498-7)/9	75499	Robert Price	12/2014
5938	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
5939	4*5^107971-3	75470	Lelio R Paula	10/2014
5940	(25*10^75465+71)/3	75466	Robert Price	01/2017
5941	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
5942	(182*10^75456+1)/3	75458	Robert Price	02/2017
5943	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
5944	10^75441+13	75442	Robert Price	01/2011
5945	10^75441-9923	75441	Patrick De Geest	05/2013
5946	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
5947	5*7^89231-6	75410	Lelio R Paula	10/2014
5949	2^250503-16995	75409	Lelio R Paula	05/2013
5948	11^72411-28	75409	Lelio R Paula	02/2015
5950	3*5^107860-8	75392	Lelio R Paula	10/2014
5951	(34*10^75387-403)/9	75388	Robert Price	10/2017
5953	2^250426+29835	75386	Lelio R Paula	05/2013
5952	8*3^157999-7	75386	Lelio R Paula	05/2014
5954	(88*10^75381-43)/9	75382	Robert Price	11/2015
5955	2^250382-111755	75373	Enzo Doria	05/2014
5956	2^250374-2798051	75371	Eric Chen	03/2016
5957	(22*10^75368-1)/3	75369	Robert Price	12/2014
5958	(19*10^75338+119)/3	75339	Robert Price	02/2017
5959	2^250223-1859167	75325	Enzo Doria	03/2016
5960	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
5961	3^157831-98	75305	Lelio R Paula	01/2015
5962	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
5963	92^38335-91	75282	Norbert Schneider	01/2016
5964	2^250020+18915	75264	Lelio R Paula	05/2013
5965	2^250002+8193	75259	Lelio R Paula	05/2013
5966	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
5967	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
5968	(5*10^75244+91)/3	75245	Robert Price	11/2016
5969	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
5970	14^65644+67	75237	Lelio R Paula	01/2015
5971	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
5972	129^35638+2	75218	Lelio R Paula	05/2013
5973	2^249853-110475	75214	Enzo Doria	05/2014
5974	2^249762+75409	75186	Enzo Doria	04/2016
5975	565^27318+27318^565	75181	Norbert Schneider	12/2016
5976	(2^249741-7)/685	75177	Lelio R Paula	06/2012
5977	2^249726-112181	75176	Enzo Doria	06/2014
5978	2^249721+11715	75174	Lelio R Paula	05/2013
5979	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
5980	2^249658-47355	75155	Lelio R Paula	05/2013
5981	155^34311+2	75153	Lelio R Paula	05/2013
5982	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
5983	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
5984	2^249522+8415	75114	Lelio R Paula	05/2013
5985	2^249489-110911	75104	Enzo Doria	05/2014
5986	(28*10^75078+131)/3	75079	Robert Price	02/2017
5987	(206*10^75073-17)/9	75075	Robert Price	03/2017
5988	2^249368-110573	75068	Enzo Doria	05/2014
5989	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
5990	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
5991	(26*10^75055-173)/3	75056	Robert Price	10/2017
5992	2^249272+193	75039	Lelio R Paula	03/2012
5993	14^65468+43	75035	Lelio R Paula	01/2015
5994	37^47844+36	75030	Norbert Schneider	05/2014
5995	(52*10^75027-7)/9	75028	Robert Price	12/2014
5996	20^57653+89	75009	Lelio R Paula	01/2015
5997	2^249061-1868353	74975	Enzo Doria	04/2016
5998	7^88713+2*3^88713	74972	Mike Oakes	07/2010
5999	2*6^96313+5	74947	Lelio R Paula	10/2014
6000	(8*10^74944+49)/3	74945	Robert Price	03/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)