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 ?
6001	2^255659-110131	76962	Enzo Doria	04/2014
6002	12^71303+91	76949	Lelio R Paula	02/2015
6003	18^61298+59	76946	Lelio R Paula	02/2015
6004	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
6005	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
6006	18^61290-11	76936	Lelio R Paula	02/2015
6008	63^42752-2	76926	Lelio R Paula	08/2013
6007	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
6009	2^255517+56387	76919	Yves Minet	02/2011
6010	2^255499-112567	76913	Enzo Doria	06/2014
6011	2^255492+345	76911	Lelio R Paula	06/2013
6012	10^76875+217591	76876	Patrick De Geest	05/2013
6014	10^76875-53	76875	Robert Price	05/2011
6013	11^73819-5880	76875	Enzo Doria	01/2013
6015	2^255313+18915	76857	Lelio R Paula	06/2013
6016	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
6017	2^255296+5775	76852	Lelio R Paula	06/2013
6018	14^67052-29	76851	Lelio R Paula	02/2015
6019	(8*10^76840+43)/3	76841	Robert Price	10/2017
6020	(7*10^76818-313)/9	76818	Robert Price	11/2016
6021	10^76801+69	76802	Robert Price	03/2011
6022	10^76801-80943	76801	Patrick De Geest	06/2013
6023	2^255105+57	76795	Lelio R Paula	03/2012
6024	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
6025	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
6026	2^255055+1869353	76780	Enzo Doria	05/2016
6027	17^62396-90	76776	Lelio R Paula	03/2015
6028	7^90833-60	76763	Lelio R Paula	02/2015
6029	13^68901-56	76752	Lelio R Paula	03/2015
6030	2^254961+1869917	76751	Enzo Doria	05/2016
6031	9*5^109791-8	76742	Lelio R Paula	10/2014
6032	82^40089+40089^82	76723	Serge Batalov	02/2012
6033	2^254861-2790013	76721	Enzo Doria	03/2016
6034	10^76705+13	76706	Robert Price	01/2011
6035	10^76705-94077	76705	Patrick De Geest	06/2013
6036	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
6037	2^254758-110405	76690	Enzo Doria	05/2014
6038	2^254716-3779	76678	Yves Minet	04/2017
6039	2^254708-110507	76675	Enzo Doria	05/2014
6040	(47*10^76672+133)/9	76673	Robert Price	04/2017
6041	2^254670-112901	76664	Enzo Doria	06/2014
6042	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
6043	2^254598-113183	76642	Enzo Doria	07/2014
6044	19^59932+22	76639	Lelio R Paula	01/2015
6045	2^254569-112213	76633	Enzo Doria	06/2014
6046	2*5^109626+9	76626	Lelio R Paula	10/2014
6047	2^254521+1872527	76619	Enzo Doria	05/2016
6048	(76*10^76615+167)/9	76616	Robert Price	08/2016
6049	25^54799-24^54799	76606	Robert Price	07/2012
6050	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
6051	12^70961-85	76580	Lelio R Paula	02/2015
6052	7^90590-38	76558	Lelio R Paula	02/2015
6053	2^254304+5227	76554	Lelio R Paula	06/2013
6054	(76*10^76547-211)/9	76548	Robert Price	10/2017
6055	18^60979-5363	76546	Enzo Doria	03/2013
6056	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
6057	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
6058	(7*10^76536-313)/9	76536	Robert Price	11/2016
6060	2^254239-27	76534	Lelio R Paula	03/2012
6059	2^254238-1841	76534	Yves Minet	03/2013
6061	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
6062	2^254189-112225	76519	Enzo Doria	06/2014
6063	18^60938-1397	76494	Enzo Doria	03/2013
6064	2^254075-2788417	76485	Enzo Doria	03/2016
6065	7*10^76483-23	76484	Robert Price	04/2016
6066	2^254042-112913	76475	Enzo Doria	06/2014
6067	14^66723-37	76474	Lelio R Paula	02/2015
6068	2^254037-110305	76473	Enzo Doria	05/2014
6069	2^253931-111109	76441	Enzo Doria	05/2014
6070	2^253926-1167	76440	Lelio R Paula	05/2013
6071	(49*10^76438-13)/9	76439	Robert Price	07/2015
6072	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
6073	10^76374+31	76375	Robert Price	03/2011
6074	10^76374-222159	76374	Patrick De Geest	05/2013
6075	2^253561-110533	76330	Enzo Doria	05/2014
6076	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
6077	9*5^109182+2	76316	Lelio R Paula	10/2014
6078	11^73279-3690	76313	Enzo Doria	12/2012
6079	(598*10^76309-31)/9	76311	Robert Price	02/2017
6080	11^73274-24000	76308	Enzo Doria	12/2012
6081	7^90291-6	76305	Theodore Burton	11/2005
6082	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
6083	6^98025+145	76279	Lelio R Paula	01/2015
6084	2^253355+1155	76268	Lelio R Paula	05/2013
6085	(73*10^76262+413)/9	76263	Robert Price	10/2017
6086	2^253292-71219	76249	Enzo Doria	04/2016
6087	7^90221-36	76246	Lelio R Paula	02/2015
6088	18^60727-3473	76229	Enzo Doria	03/2013
6089	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
6090	(8*10^76220-83)/3	76221	Robert Price	10/2017
6091	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
6092	11^73163-2010	76192	Enzo Doria	12/2012
6093	2^253060+54615	76179	Lelio R Paula	05/2013
6094	2^253029+1869761	76170	Enzo Doria	05/2016
6095	2^252955-111007	76148	Enzo Doria	05/2014
6096	2*5^108931+7	76140	Lelio R Paula	10/2014
6097	(86*10^76128+121)/9	76129	Robert Price	03/2017
6098	22154*29^52050+9	76123	Curtis Bright	05/2015
6099	3^159530-112358	76116	Enzo Doria	06/2014
6100	11^73089-48	76115	Lelio R Paula	02/2015
6101	86^39337-85	76098	Norbert Schneider	10/2015
6102	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
6103	6^97783+77	76090	Lelio R Paula	01/2015
6104	2^252712-105	76074	Lelio R Paula	03/2012
6105	(10^76069-19)/9	76069	Robert Price	10/2017
6107	131^35927+2	76068	Lelio R Paula	05/2013
6106	(41*10^76067+373)/9	76068	Robert Price	04/2017
6108	2^252683-139	76066	Lelio R Paula	03/2012
6109	137^35597-136	76061	Norbert Schneider	05/2015
6110	3^159413+106	76060	Lelio R Paula	01/2015
6111	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
6112	(2^252557-9)/71	76026	Lelio R Paula	07/2012
6113	(85*10^76021-103)/9	76022	Robert Price	10/2017
6114	11^72989+80	76011	Lelio R Paula	02/2015
6115	99877!6-36	75996	Robert Price	11/2018
6116	2^252449-459523	75995	Enzo Doria	05/2015
6117	20^58408+73	75991	Lelio R Paula	01/2015
6118	2^252418-1421	75986	Yves Minet	01/2013
6119	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
6120	2^252365-110689	75970	Enzo Doria	05/2014
6121	11^72949-1020	75969	Enzo Doria	11/2012
6122	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
6123	2^252261-110595	75939	Enzo Doria	05/2014
6124	7^89853+76	75935	Lelio R Paula	01/2015
6125	3^159132+56	75926	Lelio R Paula	01/2015
6126	730^26513+26513^730	75916	Norbert Schneider	11/2016
6127	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
6128	5^108596-14846	75906	Enzo Doria	02/2013
6129	5^108560-14846	75881	Enzo Doria	02/2013
6130	2^252051-110359	75875	Enzo Doria	05/2014
6131	2^251971-110509	75851	Enzo Doria	05/2014
6132	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
6133	99655!6-2	75811	Robert Price	07/2017
6134	14*10^75798+1089	75800	Jens K. Andersen	11/2007
6135	2^251784-455	75795	Yves Minet	03/2012
6136	2^251780-1289	75794	Yves Minet	01/2013
6137	2^251760-215609	75788	Paul Bourdelais	03/2013
6138	99^37973+2	75781	Lelio R Paula	05/2013
6139	(185*10^75777+7)/3	75779	Robert Price	02/2017
6140	5*2^251690+3	75767	Lelio R Paula	06/2014
6141	6^97366+95	75766	Lelio R Paula	01/2015
6142	s(23010)	75760	Hans Havermann	11/2017
6143	8*6^97337-7	75744	Lelio R Paula	10/2014
6144	2^251588-111677	75736	Enzo Doria	05/2014
6145	5^108346-13256	75731	Enzo Doria	02/2013
6146	(31^50777+1)/32	75726	Robert Price	07/2013
6147	(10^75707+77)/3	75707	Robert Price	01/2017
6148	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
6149	2^251466+193	75699	Lelio R Paula	03/2012
6150	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
6151	2^251422-109991	75686	Enzo Doria	04/2014
6152	4*5^108245-3	75661	Lelio R Paula	10/2014
6153	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
6154	12^70066+95	75614	Lelio R Paula	02/2015
6155	-E20534/2063	75607	Thomas Ritschel	02/2017
6156	19^59120-50	75600	Lelio R Paula	01/2015
6157	18^60222-4697	75596	Enzo Doria	03/2013
6158	18^60211-4355	75582	Enzo Doria	03/2013
6159	7*2^251014-9	75564	Lelio R Paula	06/2014
6160	6^97101-25	75560	Lelio R Paula	01/2015
6161	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
6162	3^158331-140	75544	Lelio R Paula	01/2015
6164	(37^48157-1)/36	75519	Robert Price	03/2012
6165	(19*10^75518-43)/3	75519	Robert Price	10/2017
6163	2^250868-4229	75519	Yves Minet	08/2018
6166	10^75516+31467	75517	Patrick De Geest	03/2016
6168	10^75516-10^2256-1	75516	Serge Batalov	01/2011
6167	10^75516-66591	75516	Patrick De Geest	03/2016
6169	2^250851-187	75514	Lelio R Paula	03/2012
6170	(43*10^75498-7)/9	75499	Robert Price	12/2014
6171	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
6172	4*5^107971-3	75470	Lelio R Paula	10/2014
6173	(25*10^75465+71)/3	75466	Robert Price	01/2017
6174	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
6175	(182*10^75456+1)/3	75458	Robert Price	02/2017
6176	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
6177	10^75441+13	75442	Robert Price	01/2011
6178	10^75441-9923	75441	Patrick De Geest	05/2013
6179	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
6180	5*7^89231-6	75410	Lelio R Paula	10/2014
6182	2^250503-16995	75409	Lelio R Paula	05/2013
6181	11^72411-28	75409	Lelio R Paula	02/2015
6183	3*5^107860-8	75392	Lelio R Paula	10/2014
6184	(34*10^75387-403)/9	75388	Robert Price	10/2017
6186	2^250426+29835	75386	Lelio R Paula	05/2013
6185	8*3^157999-7	75386	Lelio R Paula	05/2014
6187	(88*10^75381-43)/9	75382	Robert Price	11/2015
6188	2^250382-111755	75373	Enzo Doria	05/2014
6189	2^250374-2798051	75371	Eric Chen	03/2016
6190	(22*10^75368-1)/3	75369	Robert Price	12/2014
6191	(19*10^75338+119)/3	75339	Robert Price	02/2017
6192	2^250223-1859167	75325	Enzo Doria	03/2016
6193	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
6194	3^157831-98	75305	Lelio R Paula	01/2015
6195	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
6196	92^38335-91	75282	Norbert Schneider	01/2016
6197	2^250020+18915	75264	Lelio R Paula	05/2013
6198	2^250002+8193	75259	Lelio R Paula	05/2013
6199	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
6200	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
6201	(5*10^75244+91)/3	75245	Robert Price	11/2016
6202	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
6203	14^65644+67	75237	Lelio R Paula	01/2015
6204	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
6205	129^35638+2	75218	Lelio R Paula	05/2013
6206	2^249853-110475	75214	Enzo Doria	05/2014
6207	2^249762+75409	75186	Enzo Doria	04/2016
6208	565^27318+27318^565	75181	Norbert Schneider	12/2016
6209	(2^249741-7)/685	75177	Lelio R Paula	06/2012
6210	2^249726-112181	75176	Enzo Doria	06/2014
6211	2^249721+11715	75174	Lelio R Paula	05/2013
6212	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
6213	2^249658-47355	75155	Lelio R Paula	05/2013
6214	155^34311+2	75153	Lelio R Paula	05/2013
6215	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
6216	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
6217	2^249522+8415	75114	Lelio R Paula	05/2013
6218	2^249489-110911	75104	Enzo Doria	05/2014
6219	(28*10^75078+131)/3	75079	Robert Price	02/2017
6220	(206*10^75073-17)/9	75075	Robert Price	03/2017
6221	2^249368-110573	75068	Enzo Doria	05/2014
6222	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
6223	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
6224	(26*10^75055-173)/3	75056	Robert Price	10/2017
6225	2^249272+193	75039	Lelio R Paula	03/2012
6226	14^65468+43	75035	Lelio R Paula	01/2015
6227	37^47844+36	75030	Norbert Schneider	05/2014
6228	(52*10^75027-7)/9	75028	Robert Price	12/2014
6229	20^57653+89	75009	Lelio R Paula	01/2015
6230	2^249061-1868353	74975	Enzo Doria	04/2016
6231	7^88713+2*3^88713	74972	Mike Oakes	07/2010
6232	2*6^96313+5	74947	Lelio R Paula	10/2014
6233	(8*10^74944+49)/3	74945	Robert Price	03/2016
6234	300^30247+30247^300	74926	Norbert Schneider	11/2014
6235	2^248866-171	74917	Lelio R Paula	03/2012
6236	6*5^107168-7	74908	Lelio R Paula	10/2014
6237	11^71926+78	74904	Lelio R Paula	02/2015
6238	2^248824+1869391	74904	Enzo Doria	05/2016
6239	2^248816+1111	74902	Lelio R Paula	01/2011
6240	V(388219)	74890	Serge Batalov	03/2015
6241	2*F(358297)-1	74880	Henri Lifchitz	12/2009
6242	(22*10^74874-31)/9	74875	Robert Price	04/2015
6243	11^71892-76800000	74868	Enzo Doria	01/2013
6244	9*5^107107-4	74866	Lelio R Paula	10/2014
6245	2^248678-710111	74860	Paul Bourdelais	03/2013
6246	(14*10^74858+211)/9	74859	Robert Price	11/2017
6247	13^67194+12	74851	Lelio R Paula	01/2015
6248	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
6249	11^71867-3090	74842	Enzo Doria	12/2012
6250	2^248609+262145	74839	Lelio R Paula	05/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)