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 (> 30000)	Who ?	When ?
8251	(11*10^55254+1)/3	55255	Erik Branger	03/2014
8252	3^115802-26	55252	Lelio R Paula	10/2012
8253	2^183534-3645	55250	Lelio R Paula	01/2011
8254	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
8255	5^79032-13766	55241	Enzo Doria	02/2013
8256	8*3^115759-7	55232	Lelio R Paula	03/2014
8257	6^70974-137	55229	Lelio R Paula	10/2012
8258	2^183446-113073	55223	Enzo Doria	07/2014
8259	2^183441+577294575	55222	Lelio R Paula	03/2013
8260	5^79000-6	55219	Lelio R Paula	10/2012
8261	2^183413-901	55213	Yves Minet	01/2012
8262	19^43168-50	55202	Lelio R Paula	02/2013
8263	2^183340+19683	55191	Lelio R Paula	02/2012
8264	6^70923+35	55189	Lelio R Paula	10/2012
8265	2^183317-4035	55184	Lelio R Paula	01/2011
8266	2^183284-15	55174	Lelio R Paula	03/2011
8267	2^183255+149	55166	Lelio R Paula	02/2011
8268	4*10^55165+87	55166	Robert Price	05/2016
8270	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
8269	2^183165-112333	55139	Enzo Doria	06/2014
8271	2^183142+855	55132	Lelio R Paula	01/2011
8272	(49*10^55129+383)/9	55130	Robert Price	04/2017
8273	2^183019+255255	55095	Lelio R Paula	01/2011
8274	3*10^55077+7	55078	Erik Branger	11/2013
8275	(62*10^55075-71)/9	55076	Robert Price	09/2015
8276	27499!2-32	55070	Robert Price	10/2015
8277	15307^3958+3958^15307	55067	Hans Havermann	08/2016
8278	70^29836-69	55051	Norbert Schneider	10/2012
8279	18^43854-83	55049	Lelio R Paula	02/2013
8280	7^65126+58	55038	Lelio R Paula	10/2012
8281	2^182827-1615	55037	Lelio R Paula	11/2009
8282	7*10^55030-9	55031	Dmitry Domanov	11/2010
8283	6^70702+23	55017	Lelio R Paula	10/2012
8284	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
8285	2^182743-1615	55012	Lelio R Paula	11/2009
8286	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
8287	3^115280-9568	55003	Enzo Doria	02/2013
8288	2^182656-12849	54985	Enzo Doria	10/2012
8289	9*19^42995+16	54981	Curtis Bright	05/2015
8290	2^182627+28425	54977	Lelio R Paula	11/2009
8291	2^182597-113053	54968	Enzo Doria	07/2014
8292	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
8293	2^182581-1975	54963	Yves Minet	09/2012
8294	27449!!-16	54959	Robert Price	06/2015
8296	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
8295	2^182565+107	54958	Lelio R Paula	11/2009
8297	2^182560+2053	54957	Lelio R Paula	12/2010
8298	2^182451-182451	54924	Henri Lifchitz	10/2004
8299	2^182444+81	54922	Henri Lifchitz	10/2005
8300	2^182433+74105	54918	Enzo Doria	04/2016
8301	20^42206-5243	54912	Enzo Doria	03/2013
8302	2^182394+85	54907	Lelio R Paula	02/2011
8303	2^182374-112287	54901	Enzo Doria	06/2014
8304	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
8305	2^182363-113167	54897	Enzo Doria	07/2014
8306	2^182359-112221	54896	Enzo Doria	06/2014
8307	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
8308	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
8309	18^43698-5	54853	Lelio R Paula	02/2013
8310	2^182209-1893	54851	Yves Minet	09/2012
8311	2^182194-3443	54846	Yves Minet	12/2016
8312	15023^4468+4468^15023	54836	Hans Havermann	08/2016
8313	2^182135+90143	54829	Yves Minet	10/2010
8314	2^182119+74333	54824	Enzo Doria	04/2016
8315	14289^6860+6860^14289	54818	Hans Havermann	08/2016
8316	3^114892-114892^3	54818	Norbert Schneider	03/2017
8317	2^182070-47355	54809	Lelio R Paula	01/2011
8318	3^114869+76	54807	Lelio R Paula	10/2012
8319	8^60681-60681^8	54801	Norbert Schneider	12/2016
8320	1897^16710+16710^1897	54777	Serge Batalov	05/2014
8321	Phi(61868,59)	54776	Enzo Doria	04/2012
8322	113^26679+2	54775	Lelio R Paula	05/2013
8323	3^114789-74	54769	Lelio R Paula	10/2012
8324	15^46567+98	54768	Lelio R Paula	02/2013
8325	(2*10^54767-71)/3	54767	Robert Price	01/2017
8326	(298*10^54765-7)/3	54767	Robert Price	06/2017
8327	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
8329	2^181913+29	54762	Henri Lifchitz	06/2005
8328	(31*10^54761-121)/9	54762	Robert Price	06/2016
8330	2^181887+189	54754	Lelio R Paula	02/2011
8331	2^181874+181874^2-1	54750	Robert Price	04/2014
8332	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
8333	5^78314-92	54740	Lelio R Paula	10/2012
8334	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
8335	15^46531+74	54725	Lelio R Paula	02/2013
8336	277^22400-348	54712	Enzo Doria	07/2012
8337	6^70302+101	54706	Lelio R Paula	10/2012
8338	3^114622-10408	54689	Enzo Doria	02/2013
8340	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
8339	2^181669-1551	54688	Yves Minet	08/2012
8341	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
8342	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
8343	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
8344	13^49073+46	54665	Lelio R Paula	01/2013
8345	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
8347	20^42000+73	54644	Lelio R Paula	02/2013
8346	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
8348	33*10^54634+7	54636	Robert Price	07/2016
8349	20^41988+61	54628	Lelio R Paula	01/2013
8350	20^41988-8123	54628	Enzo Doria	03/2013
8351	2^181420+21181	54613	Yves Minet	03/2011
8352	(19*10^54608+161)/9	54609	Robert Price	07/2016
8353	19^42696-24	54598	Lelio R Paula	02/2013
8354	(74*10^54583+61)/9	54584	Robert Price	10/2015
8355	2^181316-94395	54582	Lelio R Paula	09/2011
8356	14751^5006+5006^14751	54572	Hans Havermann	08/2016
8357	14^47609+39	54567	Lelio R Paula	02/2013
8358	3^114327-74	54548	Lelio R Paula	10/2012
8359	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
8360	(17*10^54537-47)/3	54538	Robert Price	05/2017
8361	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
8362	Phi(61672,83)	54533	Enzo Doria	05/2012
8363	9*2^181128+7	54526	Lelio R Paula	03/2014
8364	89*10^54518-7	54520	Robert Price	03/2017
8365	2^181090-113247	54514	Enzo Doria	07/2014
8366	14031^7670+7670^14031	54508	Hans Havermann	08/2016
8367	14210^6849+6849^14210	54505	Hans Havermann	08/2016
8368	2^181043-199	54500	Lelio R Paula	02/2011
8369	12^50499+5	54498	Lelio R Paula	01/2013
8370	12^50491+5	54489	Lelio R Paula	01/2013
8371	6^70016-145	54484	Lelio R Paula	10/2012
8372	11^52313-9600	54479	Enzo Doria	02/2013
8373	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
8374	2^180946-111041	54471	Enzo Doria	05/2014
8375	(64*10^54467+287)/9	54468	Robert Price	04/2016
8376	5^77907-2*3^77907	54455	Mike Oakes	11/2009
8377	20^41853-5623	54453	Enzo Doria	03/2013
8378	14^47506-75	54448	Lelio R Paula	02/2013
8379	2^180839-113437	54438	Enzo Doria	08/2014
8380	3^114085+28	54433	Lelio R Paula	10/2012
8381	Phi(141230,10)	54432	Ray Chandler	08/2009
8382	6^69946-55	54429	Lelio R Paula	10/2012
8383	5*2^180796+3	54426	Lelio R Paula	03/2014
8384	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
8385	9*6^69928-7	54416	Lelio R Paula	09/2014
8386	92^27701-91^27701	54399	Robert Price	08/2015
8387	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
8388	(5*10^54388-11)/3	54389	Erik Branger	12/2013
8389	20^41799-3043	54382	Enzo Doria	03/2013
8390	13860^8387+8387^13860	54382	Hans Havermann	08/2016
8391	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
8392	7^64329-18	54365	Lelio R Paula	10/2012
8393	2^180551-967	54352	Yves Minet	01/2012
8394	15^46209-74	54347	Lelio R Paula	02/2013
8395	10^54345+29739	54346	Patrick De Geest	08/2013
8396	10^54345-141381	54345	Patrick De Geest	09/2013
8397	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
8398	2^180496+15	54335	Lelio R Paula	02/2011
8399	1845^16636+16636^1845	54334	Serge Batalov	05/2014
8400	11^52169-70	54329	Lelio R Paula	01/2013
8401	13693^9262+9262^13693	54317	Hans Havermann	06/2016
8402	2^180429-113101	54315	Enzo Doria	07/2014
8403	2^180423-112051	54313	Enzo Doria	05/2014
8404	16112^2349+2349^16112	54312	Hans Havermann	06/2016
8405	(13^48751+4^48751)/17	54305	Robert Price	05/2013
8406	2^180370+12915	54297	Lelio R Paula	09/2012
8407	(10^54290+41)/3	54290	Robert Price	01/2017
8408	15108^3917+3917^15108	54283	Hans Havermann	06/2016
8409	2^180317-3019	54281	Yves Minet	10/2014
8410	2^180314+855	54280	Lelio R Paula	10/2009
8411	19^42425+94	54252	Lelio R Paula	02/2013
8412	2^180180-1005449	54240	Paul Bourdelais	11/2012
8413	2^180173-2773	54238	Yves Minet	07/2014
8414	13367^11418+11418^13367	54238	Hans Havermann	06/2016
8415	427^20614+20614^427	54224	Norbert Schneider	06/2016
8416	2^180124-87959	54223	Gary Barnes	08/2009
8417	2^180111-113101	54219	Enzo Doria	07/2014
8418	2^180101-114871	54216	Enzo Doria	05/2015
8419	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
8421	2^180070+465	54207	Lelio R Paula	09/2012
8420	13683^9154+9154^13683	54207	Hans Havermann	06/2016
8422	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
8423	2^180014+613	54190	Jason Earls	04/2008
8424	2^180007+101	54188	Lelio R Paula	02/2011
8425	2^180001+41877	54186	Jim Fougeron	08/2002
8426	2^180000+130153	54186	Jim Fougeron	09/2002
8427	3^113565-74	54185	Lelio R Paula	10/2012
8428	50^31891-49	54182	Norbert Schneider	07/2014
8429	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
8430	3^113548+26	54177	Lelio R Paula	10/2012
8431	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
8432	4159^14969-138	54173	Enzo Doria	07/2012
8433	2^179955+5775	54172	Lelio R Paula	10/2009
8434	2^179953-231313	54172	Enzo Doria	05/2014
8435	5^77485+6	54160	Lelio R Paula	10/2012
8436	18^43141+85	54154	Lelio R Paula	02/2013
8437	10^54149+187647	54150	Patrick De Geest	07/2017
8440	3^113489-340	54149	Lelio R Paula	10/2012
8438	10^54149-800001	54149	Robert Price	06/2017
8439	10^54149-36501	54149	Patrick De Geest	07/2017
8441	7^64070+90	54146	Lelio R Paula	10/2012
8442	18^43131+71	54142	Lelio R Paula	02/2013
8443	2^179826-131	54134	Lelio R Paula	02/2011
8444	2^179815-112735	54130	Enzo Doria	06/2014
8445	2^179806+73849	54127	Enzo Doria	04/2016
8446	2^179790+33	54123	Donovan Johnson	02/2006
8447	14287^6138+6138^14287	54120	Hans Havermann	06/2016
8448	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
8449	2^179763-189	54115	Lelio R Paula	02/2011
8450	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
8451	1828^16589+16589^1828	54113	Serge Batalov	05/2014
8453	20^41588-5883	54108	Enzo Doria	03/2013
8452	50^31847-49	54108	Norbert Schneider	07/2014
8454	2^179733-6855	54106	Lelio R Paula	10/2009
8455	20^41584-5583	54103	Enzo Doria	03/2013
8456	10^54084+3*3^54084	54085	Mike Oakes	05/2010
8457	2^179613-1795	54069	Lelio R Paula	10/2009
8458	2^179589-1011523	54062	Paul Bourdelais	11/2012
8459	2^179574-2531	54058	Yves Minet	07/2014
8460	(41*10^54051-23)/9	54052	Robert Price	05/2015
8461	117^26131-116	54044	Norbert Schneider	10/2013
8462	(10^54038-31)/3	54038	Serge Batalov	12/2014
8463	11^51885-84	54033	Lelio R Paula	01/2013
8464	14990^4011+4011^14990	54013	Hans Havermann	07/2016
8465	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
8466	3^113182-10408	54002	Enzo Doria	02/2013
8467	35^34970-8786	53997	Enzo Doria	03/2013
8468	2^179371-1637587	53997	Enzo Doria	05/2015
8469	19^42225-92	53996	Lelio R Paula	01/2013
8470	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
8471	7*3^113162+8	53993	Lelio R Paula	03/2014
8472	(10^53991+179)/9	53991	Serge Batalov	12/2014
8473	2^179350-2145	53990	Lelio R Paula	10/2009
8474	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
8475	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
8476	3*7^63861+8	53970	Lelio R Paula	09/2014
8477	2^179274+71389	53967	Enzo Doria	04/2016
8478	2^179259-58695	53963	Lelio R Paula	10/2009
8479	6^69345+61	53961	Lelio R Paula	10/2012
8480	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
8481	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
8482	89*10^53951-9	53953	Robert Price	05/2017
8483	14^47067-3	53945	Lelio R Paula	01/2013
8484	p(11700)#/2-512	53937	Robert Price	07/2017
8485	(2^179168-5)/59	53934	Lelio R Paula	02/2012
8486	2^179128+8415	53923	Lelio R Paula	07/2012
8487	2^179120+2533	53921	Henri Lifchitz	09/2004
8488	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
8489	74^28842+73	53913	Norbert Schneider	11/2012
8490	1271^17368+17368^1271	53913	Serge Batalov	05/2014
8491	2^179079+53	53909	Lelio R Paula	02/2011
8492	17^43807+54	53903	Lelio R Paula	01/2013
8493	17^43807+30	53903	Lelio R Paula	01/2013
8494	3^112951-310	53892	Lelio R Paula	10/2012
8495	Phi(7,2957!)	53888	Robert Price	05/2015
8496	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
8497	2^178944-219209	53868	Enzo Doria	11/2012
8498	(10^53859+149)/3	53859	Serge Batalov	12/2014
8499	2^178910-191	53858	Lelio R Paula	02/2011
8500	16170^2141+2141^16170	53857	Hans Havermann	07/2016

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PRP Records

Probable Primes Top 10000

(180278 PRPs in the top)