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) !!!

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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 ?
8001	2^206892-112817	62281	Enzo Doria	06/2014
8002	(7*10^62278+113)/3	62279	Robert Price	10/2017
8003	3^130523+46	62276	Lelio R Paula	04/2013
8004	2^206872-113453	62275	Enzo Doria	07/2014
8005	2^206840-93	62266	Lelio R Paula	08/2011
8006	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
8007	96^31406+95	62256	Norbert Schneider	03/2016
8008	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
8009	2^206765-941683	62243	Paul Bourdelais	11/2012
8010	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
8011	2^206755-1579	62240	Yves Minet	03/2013
8012	11^59764-5820	62238	Enzo Doria	01/2013
8013	5*10^62233+3	62234	Dmitry Domanov	11/2010
8014	8*3^130421+7	62228	Lelio R Paula	04/2014
8015	19^48661+10	62226	Lelio R Paula	05/2013
8016	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
8017	2^206705-112635	62225	Enzo Doria	06/2014
8018	3^130403+8680	62219	Lelio R Paula	04/2013
8019	11^59740-7110	62213	Enzo Doria	01/2013
8021	2^206596-167	62192	Lelio R Paula	08/2011
8020	2^206597+18915	62192	Lelio R Paula	02/2013
8022	6^79918+137	62189	Lelio R Paula	04/2013
8023	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
8024	2^206574+613	62185	Jason Earls	04/2008
8025	3^130328+80	62183	Lelio R Paula	04/2013
8026	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
8027	2^206550+76819	62178	Enzo Doria	05/2016
8028	11^59703-24	62175	Lelio R Paula	05/2013
8029	2^206524+75781	62170	Enzo Doria	04/2016
8030	2^206506+427	62165	Henri Lifchitz	01/2005
8031	2^206465+7695	62153	Lelio R Paula	02/2013
8032	2^206464-1649	62152	Yves Minet	03/2013
8033	5^88917+56	62151	Lelio R Paula	04/2013
8034	2^206444-111569	62146	Enzo Doria	05/2014
8035	5^88908-42	62145	Lelio R Paula	04/2013
8036	18^49495-29	62130	Lelio R Paula	05/2013
8037	3*6^79842-5	62130	Lelio R Paula	09/2014
8038	7*10^62127-17	62128	Robert Price	01/2017
8039	2^206373+8415	62125	Lelio R Paula	02/2013
8040	20^47745-9583	62118	Enzo Doria	03/2013
8041	41^38516-2	62118	Lelio R Paula	08/2013
8042	2^206332-58695	62113	Lelio R Paula	09/2011
8043	11^59639-1260	62108	Enzo Doria	11/2012
8044	2^206232-15893	62083	Enzo Doria	04/2013
8045	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
8046	2^206206+75799	62075	Enzo Doria	04/2016
8047	(74*10^62072+43)/9	62073	Robert Price	10/2015
8048	2^206194-185	62071	Lelio R Paula	08/2011
8049	6^79757-103	62064	Lelio R Paula	04/2013
8050	p(13285)#/2-64	62063	Robert Price	04/2017
8051	(29*10^62030-41)/3	62031	Robert Price	07/2016
8052	20^47675-81	62027	Lelio R Paula	06/2013
8053	3^129972+98	62013	Lelio R Paula	04/2013
8054	2^205962+3	62001	Donovan Johnson	02/2006
8055	2^205933-205933^2	61993	Henri Lifchitz	05/2005
8056	(68*10^61991+7)/3	61993	Robert Price	03/2016
8057	20^47641-663	61983	Enzo Doria	03/2013
8058	3^129861+2660	61960	Lelio R Paula	04/2013
8059	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
8060	18^49354-97	61953	Lelio R Paula	05/2013
8061	(209*10^61947-17)/3	61949	Robert Price	05/2017
8062	14*10^61937+1089	61939	Jens K. Andersen	11/2007
8063	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
8064	20^47600+63	61930	Lelio R Paula	06/2013
8065	(16384!+1185)/(3579*10705361)	61926	Makoto Morimoto	09/2017
8066	44117!3+243	61918	Robert Price	09/2014
8067	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
8068	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
8069	20^47575-81	61897	Lelio R Paula	06/2013
8070	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
8071	87^31909+86	61889	Norbert Schneider	10/2015
8072	2^205568+141	61883	Lelio R Paula	08/2011
8073	10^61868+58927	61869	Patrick De Geest	12/2012
8074	10^61868-39	61868	Robert Price	05/2011
8076	5^88505-88	61863	Lelio R Paula	04/2013
8075	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
8077	13^55528-98	61856	Lelio R Paula	05/2013
8078	(55^35543-1)/54	61856	Paul Bourdelais	08/2017
8079	30535!2-8	61844	Robert Price	06/2015
8080	11^59371-1200	61829	Enzo Doria	11/2012
8081	7*2^205370-5	61824	Lelio R Paula	04/2014
8082	(47*10^61821+403)/9	61822	Robert Price	04/2017
8083	2^205275+7695	61794	Lelio R Paula	02/2013
8084	2^205269+12915	61793	Lelio R Paula	02/2013
8085	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
8086	19^48309+40	61776	Lelio R Paula	05/2013
8087	(424*10^61770-1)/9	61772	Robert Price	11/2017
8088	2^205192-4079	61769	Yves Minet	06/2011
8089	2^205184+16095	61767	Lelio R Paula	09/2011
8090	20^47472-3423	61763	Enzo Doria	03/2013
8091	(17*10^61760-89)/9	61761	Robert Price	11/2017
8092	2^205149-1795	61757	Lelio R Paula	09/2011
8093	2^205110-17	61745	Lelio R Paula	08/2011
8094	(373^24007+1)/374	61737	Eric Chen	10/2017
8095	(2^205025-7)/25	61718	Lelio R Paula	03/2012
8096	27^43117-26^43117	61717	Robert Price	08/2012
8097	2^205016+37	61716	Lelio R Paula	08/2011
8098	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
8099	1263^19898+19898^1263	61712	Serge Batalov	05/2014
8100	135^28963-134	61701	Norbert Schneider	04/2015
8101	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
8102	(7*10^61696+167)/3	61696	Robert Kinser	10/2017
8103	(46*10^61693+17)/9	61694	Robert Price	06/2015
8104	((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768	61684	Phil Carmody	09/2004
8105	1850^18879+18879^1850	61681	Serge Batalov	05/2014
8106	2^204891-1005	61679	Lelio R Paula	09/2011
8107	151^28306-2	61679	Lelio R Paula	10/2017
8108	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
8109	15937^7408+7408^15937	61672	Hans Havermann	02/2017
8110	5^88216-12	61661	Lelio R Paula	04/2013
8111	18185^2454+2454^18185	61645	Hans Havermann	01/2017
8113	2^204767-15865	61642	Enzo Doria	04/2013
8112	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
8114	7*2^204751-9	61638	Lelio R Paula	04/2014
8115	4*10^61625+21	61626	Robert Price	08/2016
8116	15369^10226+10226^15369	61626	Hans Havermann	02/2017
8117	2^204702-18125	61622	Enzo Doria	05/2013
8118	5*3^129146+8	61620	Lelio R Paula	04/2014
8119	2^204673+129	61613	Lelio R Paula	08/2011
8120	18^49079+97	61608	Lelio R Paula	05/2013
8121	106^30416+105	61602	Norbert Schneider	12/2016
8122	2^204590-33	61588	Lelio R Paula	08/2011
8123	2^204586-111975	61587	Enzo Doria	06/2014
8124	2^204580-16077	61585	Enzo Doria	04/2013
8125	2^204574-16041	61583	Enzo Doria	04/2013
8126	15^52358+56	61578	Lelio R Paula	05/2013
8127	(28*10^61574+11)/3	61575	Robert Price	11/2015
8128	2^204516-17493	61566	Enzo Doria	05/2013
8129	4*5^88076-3	61564	Lelio R Paula	09/2014
8130	11^59110-2520	61557	Enzo Doria	12/2012
8131	2^204477-58695	61554	Lelio R Paula	09/2011
8132	12^57026-73	61542	Lelio R Paula	05/2013
8133	(257^25537+1)/258	61541	Richard Fischer	04/2018
8134	17^50013+90	61539	Lelio R Paula	05/2013
8135	56^35201-55^35201	61538	Robert Price	10/2013
8136	8*7^72810+5	61533	Lelio R Paula	09/2014
8138	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
8137	43867!3-6561	61531	Robert Price	11/2015
8141	10^61525+9^(61525-1)	61526	Robert Price	03/2016
8139	10^61525+62257	61526	Patrick De Geest	12/2016
8140	14821^14166+14166^14821	61526	Hans Havermann	01/2017
8143	12^57010-85	61525	Lelio R Paula	05/2013
8142	10^61525-213579	61525	Patrick De Geest	12/2016
8144	2^204332-99	61511	Lelio R Paula	08/2011
8145	2^204323-2221	61508	Yves Minet	08/2013
8147	2^204317-195	61506	Lelio R Paula	08/2011
8146	3^128910-86	61506	Lelio R Paula	04/2013
8148	2^204318+74539	61506	Enzo Doria	04/2016
8149	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
8150	2^204297-1036093	61500	Paul Bourdelais	11/2012
8151	3^128880+58	61492	Lelio R Paula	04/2013
8152	2^204216-111677	61476	Enzo Doria	05/2014
8153	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
8154	2^204129+204129	61449	Henri Lifchitz	04/2002
8155	3^128787+2^(128787-1)	61448	Robert Price	05/2016
8156	11^58999-78	61442	Lelio R Paula	05/2013
8157	2^204083-111967	61436	Enzo Doria	05/2014
8158	(45^37159+1)/46	61431	Robert Price	11/2013
8159	677^21702+21702^677	61430	Norbert Schneider	06/2016
8160	14837^13810+13810^14837	61429	Hans Havermann	02/2017
8161	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
8162	11^58976-1740	61418	Enzo Doria	11/2012
8163	2^204016-16085	61415	Enzo Doria	04/2013
8164	V(379967)	61393	Serge Batalov	03/2015
8165	43777!3-3^43777	61392	Robert Price	08/2015
8166	7^72642+88	61390	Lelio R Paula	04/2013
8167	3^128656+32	61385	Lelio R Paula	04/2013
8168	2^203916-17493	61385	Enzo Doria	05/2013
8169	6^78880+23	61381	Lelio R Paula	04/2013
8170	(388*10^61374-1)/9	61376	Robert Price	11/2017
8171	2^203877-111799	61374	Enzo Doria	05/2014
8172	2^203867-1615	61371	Lelio R Paula	10/2011
8173	4*10^61367+19	61368	Robert Price	04/2016
8174	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
8175	L(293659)/76528122719	61361	Serge Batalov	07/2017
8176	2^203825-15805	61358	Enzo Doria	04/2013
8177	2^203816-15825	61355	Enzo Doria	04/2013
8178	5*10^61348+59	61349	Robert Price	09/2016
8179	21^46395-2	61345	Lelio R Paula	08/2013
8180	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
8181	7*6^78826+5	61340	Lelio R Paula	09/2014
8182	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
8183	2^203706-111	61322	Lelio R Paula	08/2011
8184	17567^3094+3094^17567	61318	Hans Havermann	02/2017
8185	2^203689-31	61317	Thomas Masser	10/2005
8186	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014
8187	2^203642+39	61303	Lelio R Paula	08/2011
8188	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012
8189	11^58849-6040	61285	Enzo Doria	02/2013
8190	43694!3-3	61264	Robert Price	10/2014
8191	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
8192	2^203490+12909	61257	Lelio R Paula	10/2011
8193	(16*10^61251-31)/3	61252	Robert Price	03/2016
8194	20^47077-5703	61249	Enzo Doria	03/2013
8195	2^203434-113081	61240	Enzo Doria	07/2014
8197	5^87606+4	61234	Wojciech Florek	11/2005
8196	2^203412-167	61234	Lelio R Paula	08/2011
8199	2^203402+1089	61231	Lelio R Paula	10/2011
8198	(8*10^61230+67)/3	61231	Robert Price	01/2017
8200	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
8201	1265^19732+19732^1265	61211	Serge Batalov	05/2014
8202	2^203330+145	61209	Lelio R Paula	08/2011
8203	6^78647-137	61200	Lelio R Paula	04/2013
8204	85^31718+84	61198	Norbert Schneider	10/2015
8205	11^58763-270	61196	Enzo Doria	07/2012
8206	2^203285-112321	61195	Enzo Doria	06/2014
8207	2^203253-995143	61186	Paul Bourdelais	11/2012
8208	15319^9862+9862^15319	61184	Hans Havermann	07/2016
8209	7^72395-44	61181	Lelio R Paula	04/2013
8210	(49*10^61167-67)/9	61168	Robert Price	08/2017
8211	5*2^203176-7	61163	Lelio R Paula	04/2014
8212	(26*10^61156-413)/9	61157	Robert Price	10/2017
8214	7^72358+54	61150	Lelio R Paula	04/2013
8213	2^203133-111775	61150	Enzo Doria	05/2014
8215	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
8216	2^203112-18009	61143	Enzo Doria	05/2013
8217	43607!3+729	61129	Robert Price	09/2014
8218	2^203065-114853	61129	Enzo Doria	05/2015
8219	3^128111+196	61125	Lelio R Paula	04/2013
8220	128^29007+29007^128	61124	Serge Batalov	05/2014
8221	4*10^61119+49	61120	Robert Price	08/2017
8222	22355*2^203009-3	61117	Donovan Johnson	03/2004
8223	2^203018+33	61115	Lelio R Paula	08/2011
8224	2^203017-1615	61115	Lelio R Paula	10/2011
8225	16697^4570+4570^16697	61110	Hans Havermann	12/2016
8226	2^202998-17241	61109	Enzo Doria	05/2013
8227	20^46964+93	61102	Lelio R Paula	06/2013
8228	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
8229	20^46960-5463	61097	Enzo Doria	03/2013
8230	(11*10^61095+49)/3	61096	Robert Price	05/2016
8231	2^202934-5955	61090	Lelio R Paula	10/2011
8232	19^47772-68	61089	Lelio R Paula	05/2013
8233	2^202877-499423	61073	Paul Bourdelais	03/2013
8234	2^202763-17125	61038	Enzo Doria	05/2013
8235	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
8236	14788^13355+13355^14788	61011	Hans Havermann	12/2016
8237	16069^6258+6258^16069	61005	Hans Havermann	12/2016
8238	5^87276-14336	61004	Enzo Doria	02/2013
8239	50^35899-49^35899	60992	Robert Price	12/2012
8240	2^202599-3049	60989	Yves Minet	10/2014
8241	2^202535-111571	60970	Enzo Doria	05/2014
8242	(13*10^60966+107)/3	60967	Robert Price	11/2017
8244	10^60959+57	60960	Patrick De Geest	12/2008
8243	6*10^60959-91	60960	Robert Price	11/2017
8246	10^60959-60959	60959	Henri Lifchitz	08/2002
8245	10^60959-29177	60959	Patrick De Geest	08/2008
8247	5^87206+4^(87206+1)	60955	Robert Price	07/2016
8248	2^202476-15909	60952	Enzo Doria	04/2013
8249	2^202472-17513	60951	Enzo Doria	05/2013
8250	14858^12651+12651^14858	60950	Hans Havermann	12/2016

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PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)