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 ?
6001	5^112070-54	78334	Lelio R Paula	02/2015
6002	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
6003	2^260182-113453	78323	Enzo Doria	07/2014
6004	f(16405)	78319	Robert Price	09/2017
6005	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
6006	10^78288+9^(78288+1)	78289	Robert Price	08/2016
6007	10^78288+39109	78289	Patrick De Geest	12/2016
6008	10^78288-216299	78288	Patrick De Geest	12/2016
6009	5^111997+36	78283	Lelio R Paula	02/2015
6010	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
6011	(88*10^78242-7)/9	78243	Robert Price	11/2014
6012	2*6^100547+7	78242	Lelio R Paula	10/2014
6013	2^259860-111089	78226	Enzo Doria	05/2014
6014	37^49875-2	78215	Lelio R Paula	09/2013
6015	(13*10^78213+401)/9	78214	Robert Price	10/2017
6016	7*5^111893-4	78211	Lelio R Paula	10/2014
6017	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
6018	7^92511-6	78181	Theodore Burton	11/2005
6019	(3^163859-4)/253	78179	Lelio R Paula	10/2012
6020	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
6021	3*10^78146+17	78147	Robert Price	03/2017
6022	(576^28307+1)/577	78137	Richard Fischer	01/2018
6023	2^259503+74333	78119	Enzo Doria	04/2016
6024	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
6026	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
6025	6^100379+13	78111	Lelio R Paula	03/2015
6027	2^259469-109909	78108	Enzo Doria	04/2014
6028	15^66413-26	78108	Lelio R Paula	02/2015
6029	7^92410-9266	78096	Mike Oakes	02/2010
6030	2^259398+75799	78087	Enzo Doria	04/2016
6031	2^259394+1876189	78086	Enzo Doria	07/2016
6032	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
6033	5*2^259344-7	78072	Lelio R Paula	06/2014
6034	14^68097-87	78048	Lelio R Paula	02/2015
6035	2^259233-475573	78037	Paul Bourdelais	03/2013
6036	181^34554-2	78012	Lelio R Paula	10/2017
6037	3^163500-28	78010	Robert Price	12/2013
6038	(65*10^77992+691)/9	77993	Robert Price	08/2016
6039	2^259013-112591	77971	Enzo Doria	06/2014
6040	7*10^77969-11	77970	Robert Price	10/2017
6041	6^100193-100193^6	77966	Norbert Schneider	04/2017
6042	2^258863-110235	77926	Enzo Doria	05/2014
6043	2^258852+1605	77923	Lelio R Paula	06/2013
6044	(11*10^77909+49)/3	77910	Robert Price	05/2016
6045	2*7^92187-9	77908	Lelio R Paula	10/2014
6046	2^258763-110155	77896	Enzo Doria	04/2014
6047	2^258694-110387	77875	Enzo Doria	05/2014
6048	11^74773-94	77869	Lelio R Paula	02/2015
6049	6^100067+125	77868	Lelio R Paula	03/2015
6050	15^66205+8	77864	Lelio R Paula	07/2014
6051	5^111373-18136	77847	Enzo Doria	05/2014
6052	2^258524-109877	77824	Enzo Doria	04/2014
6053	6^100002-16643	77817	Enzo Doria	02/2013
6054	(13*10^77811+347)/9	77812	Robert Price	10/2017
6055	65^42916+28	77803	Lelio R Paula	01/2016
6056	(89*10^77781-17)/9	77782	Robert Price	11/2015
6057	2^258382-110405	77781	Enzo Doria	05/2014
6058	5^111278-14996	77780	Enzo Doria	02/2013
6059	14^67862+61	77779	Lelio R Paula	02/2015
6060	10^77777+48483	77778	Patrick De Geest	11/2010
6061	10^77777-183243	77777	Patrick De Geest	11/2010
6062	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
6063	337^30756-10002	77740	Enzo Doria	07/2012
6064	10^77726+99	77727	Robert Price	03/2011
6065	10^77726-85947	77726	Patrick De Geest	06/2013
6066	89^39870-2	77723	Lelio R Paula	08/2013
6067	7^91966-32	77721	Lelio R Paula	02/2015
6068	35^50327+2	77709	Lelio R Paula	05/2013
6069	24^56298+23	77704	Norbert Schneider	12/2016
6070	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
6071	2^258079+179	77690	Lelio R Paula	03/2012
6072	2^258062-113111	77685	Enzo Doria	07/2014
6073	80^40807-79	77660	Norbert Schneider	03/2015
6074	(10^77637+359)/9	77637	Serge Batalov	12/2014
6075	2^257862-165	77625	Lelio R Paula	03/2012
6076	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
6077	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
6078	6^99728+71	77604	Lelio R Paula	01/2015
6079	2^257778-112767	77599	Enzo Doria	06/2014
6080	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
6081	2^257729-73	77585	Lelio R Paula	03/2012
6082	2^257689-63	77573	Lelio R Paula	03/2012
6083	(47*10^77572+493)/9	77573	Robert Price	11/2017
6084	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
6085	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
6086	2^257636-110235	77557	Enzo Doria	05/2014
6087	(23*10^77556+97)/3	77557	Robert Price	02/2017
6088	2^257621-110071	77552	Enzo Doria	04/2014
6089	2^257567-64875	77536	Lelio R Paula	06/2013
6090	2*7^91674+9	77474	Lelio R Paula	10/2014
6091	(17*10^77427-47)/3	77428	Robert Price	05/2017
6092	10^77418+841683	77419	Patrick De Geest	06/2013
6093	10^77418-33	77418	Robert Price	05/2011
6094	19^60539-36	77415	Lelio R Paula	03/2015
6095	37401!!-1024	77397	Robert Price	11/2015
6096	11^74313-18750	77390	Enzo Doria	12/2012
6098	2^257044-112883	77378	Enzo Doria	06/2014
6097	8*10^77377+51	77378	Robert Price	05/2017
6099	2*7^91553+9	77372	Lelio R Paula	10/2014
6100	713^27118+27118^713	77371	Norbert Schneider	12/2016
6101	2^256920-111155	77341	Enzo Doria	05/2014
6102	2^256896-6555	77334	Lelio R Paula	06/2013
6103	(52*10^77322-7)/9	77323	Robert Price	12/2014
6104	2^256849-112939	77320	Enzo Doria	06/2014
6105	(4*10^77309-31)/9	77309	Erik Branger	05/2011
6106	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
6107	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
6108	5*3^161923-4	77258	Lelio R Paula	06/2014
6109	2^256552-1499	77230	Yves Minet	05/2013
6110	2^256460-112757	77203	Enzo Doria	06/2014
6111	2^256398+23299	77184	Yves Minet	02/2011
6112	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
6113	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
6114	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
6115	21^58348-2	77149	Lelio R Paula	08/2013
6116	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
6117	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
6118	19^60321+82	77136	Lelio R Paula	03/2015
6119	5*2^256233-3	77135	Lelio R Paula	06/2014
6120	3*2^256149+7	77110	Lelio R Paula	06/2014
6121	3^161594-106	77100	Lelio R Paula	02/2015
6122	2^256114-185	77098	Lelio R Paula	03/2012
6123	8^85349-85349^8	77078	Norbert Schneider	05/2017
6124	2^256043-2786377	77077	Enzo Doria	03/2016
6125	2^255973+1869947	77056	Enzo Doria	05/2016
6126	12^71393-43	77046	Lelio R Paula	02/2015
6127	15^65490+44	77023	Lelio R Paula	02/2015
6128	(3^161411-7)/940	77010	Lelio R Paula	10/2012
6130	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
6129	(570^27943-1)/569	77005	Serge Batalov	12/2016
6131	2^255750-75	76989	Lelio R Paula	03/2012
6132	3*6^98926-5	76980	Lelio R Paula	10/2014
6133	18^61320-1433	76974	Enzo Doria	03/2013
6134	6^98916-17093	76972	Enzo Doria	02/2013
6135	2^255659-110131	76962	Enzo Doria	04/2014
6136	12^71303+91	76949	Lelio R Paula	02/2015
6137	18^61298+59	76946	Lelio R Paula	02/2015
6138	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
6139	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
6140	18^61290-11	76936	Lelio R Paula	02/2015
6142	63^42752-2	76926	Lelio R Paula	08/2013
6141	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
6143	2^255517+56387	76919	Yves Minet	02/2011
6144	2^255499-112567	76913	Enzo Doria	06/2014
6145	2^255492+345	76911	Lelio R Paula	06/2013
6146	10^76875+217591	76876	Patrick De Geest	05/2013
6148	10^76875-53	76875	Robert Price	05/2011
6147	11^73819-5880	76875	Enzo Doria	01/2013
6149	2^255313+18915	76857	Lelio R Paula	06/2013
6150	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
6151	2^255296+5775	76852	Lelio R Paula	06/2013
6152	14^67052-29	76851	Lelio R Paula	02/2015
6153	(8*10^76840+43)/3	76841	Robert Price	10/2017
6154	(7*10^76818-313)/9	76818	Robert Price	11/2016
6155	10^76801+69	76802	Robert Price	03/2011
6156	10^76801-80943	76801	Patrick De Geest	06/2013
6157	2^255105+57	76795	Lelio R Paula	03/2012
6158	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
6159	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
6160	2^255055+1869353	76780	Enzo Doria	05/2016
6161	17^62396-90	76776	Lelio R Paula	03/2015
6162	7^90833-60	76763	Lelio R Paula	02/2015
6163	13^68901-56	76752	Lelio R Paula	03/2015
6164	2^254961+1869917	76751	Enzo Doria	05/2016
6165	9*5^109791-8	76742	Lelio R Paula	10/2014
6166	82^40089+40089^82	76723	Serge Batalov	02/2012
6167	2^254861-2790013	76721	Enzo Doria	03/2016
6168	10^76705+13	76706	Robert Price	01/2011
6169	10^76705-94077	76705	Patrick De Geest	06/2013
6170	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
6171	2^254758-110405	76690	Enzo Doria	05/2014
6172	2^254716-3779	76678	Yves Minet	04/2017
6173	2^254708-110507	76675	Enzo Doria	05/2014
6174	(47*10^76672+133)/9	76673	Robert Price	04/2017
6175	2^254670-112901	76664	Enzo Doria	06/2014
6176	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
6177	2^254598-113183	76642	Enzo Doria	07/2014
6178	19^59932+22	76639	Lelio R Paula	01/2015
6179	2^254569-112213	76633	Enzo Doria	06/2014
6180	2*5^109626+9	76626	Lelio R Paula	10/2014
6181	2^254521+1872527	76619	Enzo Doria	05/2016
6182	(76*10^76615+167)/9	76616	Robert Price	08/2016
6183	25^54799-24^54799	76606	Robert Price	07/2012
6184	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
6185	12^70961-85	76580	Lelio R Paula	02/2015
6186	7^90590-38	76558	Lelio R Paula	02/2015
6187	2^254304+5227	76554	Lelio R Paula	06/2013
6188	(76*10^76547-211)/9	76548	Robert Price	10/2017
6189	18^60979-5363	76546	Enzo Doria	03/2013
6190	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
6192	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
6191	(7*10^76536-313)/9	76536	Robert Price	11/2016
6194	2^254239-27	76534	Lelio R Paula	03/2012
6193	2^254238-1841	76534	Yves Minet	03/2013
6195	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
6196	2^254189-112225	76519	Enzo Doria	06/2014
6197	18^60938-1397	76494	Enzo Doria	03/2013
6198	2^254075-2788417	76485	Enzo Doria	03/2016
6199	7*10^76483-23	76484	Robert Price	04/2016
6200	2^254042-112913	76475	Enzo Doria	06/2014
6201	14^66723-37	76474	Lelio R Paula	02/2015
6202	2^254037-110305	76473	Enzo Doria	05/2014
6203	2^253931-111109	76441	Enzo Doria	05/2014
6204	2^253926-1167	76440	Lelio R Paula	05/2013
6205	(49*10^76438-13)/9	76439	Robert Price	07/2015
6206	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
6207	10^76374+31	76375	Robert Price	03/2011
6208	10^76374-222159	76374	Patrick De Geest	05/2013
6209	2^253561-110533	76330	Enzo Doria	05/2014
6210	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
6211	9*5^109182+2	76316	Lelio R Paula	10/2014
6212	11^73279-3690	76313	Enzo Doria	12/2012
6213	(598*10^76309-31)/9	76311	Robert Price	02/2017
6214	11^73274-24000	76308	Enzo Doria	12/2012
6215	7^90291-6	76305	Theodore Burton	11/2005
6216	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
6217	6^98025+145	76279	Lelio R Paula	01/2015
6218	2^253355+1155	76268	Lelio R Paula	05/2013
6219	(73*10^76262+413)/9	76263	Robert Price	10/2017
6220	2^253292-71219	76249	Enzo Doria	04/2016
6221	7^90221-36	76246	Lelio R Paula	02/2015
6222	18^60727-3473	76229	Enzo Doria	03/2013
6223	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
6224	(8*10^76220-83)/3	76221	Robert Price	10/2017
6225	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
6226	11^73163-2010	76192	Enzo Doria	12/2012
6227	2^253060+54615	76179	Lelio R Paula	05/2013
6228	2^253029+1869761	76170	Enzo Doria	05/2016
6229	2^252955-111007	76148	Enzo Doria	05/2014
6230	2*5^108931+7	76140	Lelio R Paula	10/2014
6231	(86*10^76128+121)/9	76129	Robert Price	03/2017
6232	22154*29^52050+9	76123	Curtis Bright	05/2015
6233	3^159530-112358	76116	Enzo Doria	06/2014
6234	11^73089-48	76115	Lelio R Paula	02/2015
6235	86^39337-85	76098	Norbert Schneider	10/2015
6236	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
6237	6^97783+77	76090	Lelio R Paula	01/2015
6238	2^252712-105	76074	Lelio R Paula	03/2012
6239	(10^76069-19)/9	76069	Robert Price	10/2017
6241	131^35927+2	76068	Lelio R Paula	05/2013
6240	(41*10^76067+373)/9	76068	Robert Price	04/2017
6242	2^252683-139	76066	Lelio R Paula	03/2012
6243	137^35597-136	76061	Norbert Schneider	05/2015
6244	3^159413+106	76060	Lelio R Paula	01/2015
6245	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
6246	(2^252557-9)/71	76026	Lelio R Paula	07/2012
6247	(85*10^76021-103)/9	76022	Robert Price	10/2017
6248	11^72989+80	76011	Lelio R Paula	02/2015
6249	99877!6-36	75996	Robert Price	11/2018
6250	2^252449-459523	75995	Enzo Doria	05/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)