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 ?
8751	20^42696-2043	55549	Enzo Doria	03/2013
8752	(35*10^55547-737)/9	55548	Robert Price	11/2017
8753	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
8754	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
8755	5003^15013-160	55537	Enzo Doria	07/2012
8756	39^34896-2	55522	Lelio R Paula	08/2013
8757	(6^71345-61)/5	55517	Lelio R Paula	05/2014
8758	2^184407-3019	55513	Yves Minet	10/2014
8759	(43*10^55512-61)/9	55513	Robert Price	06/2015
8760	20^42667-843	55512	Enzo Doria	03/2013
8761	133^26134-132	55505	Norbert Schneider	03/2015
8762	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
8763	9*7^65667-4	55497	Lelio R Paula	09/2014
8764	2^184342-173	55493	Lelio R Paula	03/2011
8765	15^47182+92	55491	Lelio R Paula	02/2013
8766	5^79378+6	55483	Lelio R Paula	10/2012
8767	581^20068+20068^581	55472	Norbert Schneider	06/2016
8768	(2^184232+1)/257	55457	Donovan Johnson	03/2005
8769	18^44177-1415	55455	Enzo Doria	03/2013
8770	2^184203-2797867	55451	Enzo Doria	04/2016
8771	2^184189+17	55447	Lelio R Paula	03/2011
8772	2^184183+26123	55445	Yves Minet	01/2010
8773	Phi(77077,10)	55441	Ray Chandler	05/2009
8774	2^184141-113251	55432	Enzo Doria	07/2014
8775	2^184093-504613	55418	Gary Barnes	09/2009
8776	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
8777	2^184044-111269	55403	Enzo Doria	05/2014
8778	14051^8766+8766^14051	55401	Hans Havermann	07/2016
8779	98^27819+27819^98	55394	Serge Batalov	05/2014
8780	(178*10^55390-7)/9	55392	Robert Price	08/2017
8781	58046^9+9^58046	55390	Andrey Kulsha	02/2004
8782	7^65536+2*59232-2	55385	Jiahao He	07/2017
8783	2^183980+75241	55384	Enzo Doria	04/2016
8784	10^55372+37	55373	Robert Price	01/2011
8785	10^55372-49967	55372	Patrick De Geest	12/2012
8786	(13*10^55367+17)/3	55368	Robert Price	06/2015
8787	2*6^71150+7	55366	Lelio R Paula	09/2014
8788	19^43296-62	55365	Lelio R Paula	02/2013
8789	19^43295+10	55364	Lelio R Paula	02/2013
8790	(29*10^55362-11)/9	55363	Robert Price	04/2015
8791	(37*10^55359+53)/9	55360	Robert Price	05/2015
8792	19^43283+72	55349	Lelio R Paula	02/2013
8793	2^183800-65	55330	Lelio R Paula	03/2011
8794	21001^12801-110	55329	Enzo Doria	07/2012
8795	33^36433-32^36433	55325	Robert Price	04/2012
8796	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
8798	9^57952+8^(57952-1)	55301	Robert Price	03/2016
8797	14872^5229+5229^14872	55301	Hans Havermann	08/2016
8799	61^30972-2	55296	Lelio R Paula	08/2013
8800	2^183671-112537	55291	Enzo Doria	06/2014
8801	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
8802	3^115873+56	55286	Lelio R Paula	10/2012
8803	13^49629-84	55284	Lelio R Paula	01/2013
8804	2^183632-5	55279	Henri Lifchitz	08/2005
8805	13981^8988+8988^13981	55277	Hans Havermann	07/2016
8806	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
8807	2^183576+171	55262	Lelio R Paula	03/2011
8808	13^49604+82	55257	Lelio R Paula	01/2013
8809	(11*10^55254+1)/3	55255	Erik Branger	03/2014
8810	3^115802-26	55252	Lelio R Paula	10/2012
8811	2^183534-3645	55250	Lelio R Paula	01/2011
8812	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
8813	5^79032-13766	55241	Enzo Doria	02/2013
8814	8*3^115759-7	55232	Lelio R Paula	03/2014
8815	6^70974-137	55229	Lelio R Paula	10/2012
8816	2^183446-113073	55223	Enzo Doria	07/2014
8817	2^183441+577294575	55222	Lelio R Paula	03/2013
8818	5^79000-6	55219	Lelio R Paula	10/2012
8819	2^183413-901	55213	Yves Minet	01/2012
8820	19^43168-50	55202	Lelio R Paula	02/2013
8821	2^183340+19683	55191	Lelio R Paula	02/2012
8822	6^70923+35	55189	Lelio R Paula	10/2012
8823	2^183317-4035	55184	Lelio R Paula	01/2011
8824	2^183284-15	55174	Lelio R Paula	03/2011
8825	2^183255+149	55166	Lelio R Paula	02/2011
8826	4*10^55165+87	55166	Robert Price	05/2016
8828	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
8827	2^183165-112333	55139	Enzo Doria	06/2014
8829	(109^27061-1)/108	55133	Richard Fischer	09/2017
8830	2^183142+855	55132	Lelio R Paula	01/2011
8831	(49*10^55129+383)/9	55130	Robert Price	04/2017
8832	2^183019+255255	55095	Lelio R Paula	01/2011
8833	(10^55084-19)/9	55084	Robert Price	10/2017
8834	3*10^55077+7	55078	Erik Branger	11/2013
8835	(62*10^55075-71)/9	55076	Robert Price	09/2015
8836	27499!2-32	55070	Robert Price	10/2015
8837	15307^3958+3958^15307	55067	Hans Havermann	08/2016
8838	70^29836-69	55051	Norbert Schneider	10/2012
8839	18^43854-83	55049	Lelio R Paula	02/2013
8840	7^65126+58	55038	Lelio R Paula	10/2012
8841	2^182827-1615	55037	Lelio R Paula	11/2009
8842	7*10^55030-9	55031	Dmitry Domanov	11/2010
8843	2^182768-4055	55019	Yves Minet	02/2018
8844	6^70702+23	55017	Lelio R Paula	10/2012
8845	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
8846	2^182743-1615	55012	Lelio R Paula	11/2009
8847	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
8848	3^115280-9568	55003	Enzo Doria	02/2013
8849	2^182656-12849	54985	Enzo Doria	10/2012
8850	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
8851	9*19^42995+16	54981	Curtis Bright	05/2015
8852	2^182627+28425	54977	Lelio R Paula	11/2009
8853	2^182597-113053	54968	Enzo Doria	07/2014
8854	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
8855	2^182581-1975	54963	Yves Minet	09/2012
8856	(2*10^54960-179)/3	54960	Robert Price	11/2017
8857	27449!!-16	54959	Robert Price	06/2015
8858	(22*10^54958-73)/3	54959	Robert Price	09/2017
8860	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
8859	2^182565+107	54958	Lelio R Paula	11/2009
8861	2^182560+2053	54957	Lelio R Paula	12/2010
8862	2^182451-182451	54924	Henri Lifchitz	10/2004
8863	2^182444+81	54922	Henri Lifchitz	10/2005
8864	2^182433+74105	54918	Enzo Doria	04/2016
8865	20^42206-5243	54912	Enzo Doria	03/2013
8866	2^182394+85	54907	Lelio R Paula	02/2011
8867	2^182374-112287	54901	Enzo Doria	06/2014
8868	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
8869	2^182363-113167	54897	Enzo Doria	07/2014
8870	2^182359-112221	54896	Enzo Doria	06/2014
8871	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
8872	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
8873	18^43698-5	54853	Lelio R Paula	02/2013
8874	2^182209-1893	54851	Yves Minet	09/2012
8875	2^182194-3443	54846	Yves Minet	12/2016
8876	15023^4468+4468^15023	54836	Hans Havermann	08/2016
8877	2^182135+90143	54829	Yves Minet	10/2010
8878	2^182119+74333	54824	Enzo Doria	04/2016
8879	14289^6860+6860^14289	54818	Hans Havermann	08/2016
8880	3^114892-114892^3	54818	Norbert Schneider	03/2017
8881	2^182070-47355	54809	Lelio R Paula	01/2011
8882	3^114869+76	54807	Lelio R Paula	10/2012
8883	8^60681-60681^8	54801	Norbert Schneider	12/2016
8884	1897^16710+16710^1897	54777	Serge Batalov	05/2014
8885	Phi(61868,59)	54776	Enzo Doria	04/2012
8886	113^26679+2	54775	Lelio R Paula	05/2013
8887	3^114789-74	54769	Lelio R Paula	10/2012
8888	15^46567+98	54768	Lelio R Paula	02/2013
8889	(2*10^54767-71)/3	54767	Robert Price	01/2017
8890	(298*10^54765-7)/3	54767	Robert Price	06/2017
8891	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
8893	2^181913+29	54762	Henri Lifchitz	06/2005
8892	(31*10^54761-121)/9	54762	Robert Price	06/2016
8894	2^181887+189	54754	Lelio R Paula	02/2011
8895	2^181874+181874^2-1	54750	Robert Price	04/2014
8896	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
8897	5^78314-92	54740	Lelio R Paula	10/2012
8898	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
8899	15^46531+74	54725	Lelio R Paula	02/2013
8900	277^22400-348	54712	Enzo Doria	07/2012
8901	6^70302+101	54706	Lelio R Paula	10/2012
8902	3^114622-10408	54689	Enzo Doria	02/2013
8904	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
8903	2^181669-1551	54688	Yves Minet	08/2012
8905	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
8906	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
8907	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
8908	13^49073+46	54665	Lelio R Paula	01/2013
8909	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
8911	20^42000+73	54644	Lelio R Paula	02/2013
8910	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
8912	33*10^54634+7	54636	Robert Price	07/2016
8913	20^41988+61	54628	Lelio R Paula	01/2013
8914	20^41988-8123	54628	Enzo Doria	03/2013
8915	2^181420+21181	54613	Yves Minet	03/2011
8916	(19*10^54608+161)/9	54609	Robert Price	07/2016
8917	19^42696-24	54598	Lelio R Paula	02/2013
8918	(44*10^54596-503)/9	54597	Robert Price	10/2017
8919	(74*10^54583+61)/9	54584	Robert Price	10/2015
8920	2^181316-94395	54582	Lelio R Paula	09/2011
8921	14751^5006+5006^14751	54572	Hans Havermann	08/2016
8922	14^47609+39	54567	Lelio R Paula	02/2013
8923	12696^13295-13295^12696	54559	Norbert Schneider	01/2018
8924	(2^124979+lucasV(2,-2,124979)+1)/3	54552	Paul Vanderveen	12/2017
8926	3^114327-74	54548	Lelio R Paula	10/2012
8925	(44*10^54547-161)/9	54548	Robert Price	11/2017
8927	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
8928	(17*10^54537-47)/3	54538	Robert Price	05/2017
8929	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
8930	Phi(61672,83)	54533	Enzo Doria	05/2012
8931	(2*10^54527-197)/3	54527	Robert Price	11/2017
8932	9*2^181128+7	54526	Lelio R Paula	03/2014
8933	89*10^54518-7	54520	Robert Price	03/2017
8934	2^181090-113247	54514	Enzo Doria	07/2014
8935	14031^7670+7670^14031	54508	Hans Havermann	08/2016
8936	14210^6849+6849^14210	54505	Hans Havermann	08/2016
8937	2^181043-199	54500	Lelio R Paula	02/2011
8938	12^50499+5	54498	Lelio R Paula	01/2013
8939	12^50491+5	54489	Lelio R Paula	01/2013
8940	6^70016-145	54484	Lelio R Paula	10/2012
8941	11^52313-9600	54479	Enzo Doria	02/2013
8942	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
8943	2^180946-111041	54471	Enzo Doria	05/2014
8944	(64*10^54467+287)/9	54468	Robert Price	04/2016
8945	(32*10^54458+319)/9	54459	Robert Price	10/2017
8946	5^77907-2*3^77907	54455	Mike Oakes	11/2009
8947	20^41853-5623	54453	Enzo Doria	03/2013
8948	14^47506-75	54448	Lelio R Paula	02/2013
8949	(25*10^54443-67)/3	54444	Robert Price	11/2017
8950	2^180839-113437	54438	Enzo Doria	08/2014
8951	3^114085+28	54433	Lelio R Paula	10/2012
8952	Phi(141230,10)	54432	Ray Chandler	08/2009
8953	6^69946-55	54429	Lelio R Paula	10/2012
8954	p(11796)#/2-1024	54427	Robert Price	09/2017
8955	5*2^180796+3	54426	Lelio R Paula	03/2014
8956	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
8957	9*6^69928-7	54416	Lelio R Paula	09/2014
8958	92^27701-91^27701	54399	Robert Price	08/2015
8959	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
8960	(5*10^54388-11)/3	54389	Erik Branger	12/2013
8962	20^41799-3043	54382	Enzo Doria	03/2013
8961	13860^8387+8387^13860	54382	Hans Havermann	08/2016
8963	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
8964	7^64329-18	54365	Lelio R Paula	10/2012
8965	2^180551-967	54352	Yves Minet	01/2012
8966	15^46209-74	54347	Lelio R Paula	02/2013
8967	10^54345+29739	54346	Patrick De Geest	08/2013
8968	10^54345-141381	54345	Patrick De Geest	09/2013
8969	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
8970	177^24171-2	54336	Lelio R Paula	10/2017
8971	2^180496+15	54335	Lelio R Paula	02/2011
8972	1845^16636+16636^1845	54334	Serge Batalov	05/2014
8973	11^52169-70	54329	Lelio R Paula	01/2013
8974	2^180446-4031	54320	Yves Minet	02/2018
8975	13693^9262+9262^13693	54317	Hans Havermann	06/2016
8976	2^180429-113101	54315	Enzo Doria	07/2014
8977	2^180423-112051	54313	Enzo Doria	05/2014
8978	16112^2349+2349^16112	54312	Hans Havermann	06/2016
8979	(79^28621-1)/78	54311	Paul Bourdelais	08/2017
8980	(13^48751+4^48751)/17	54305	Robert Price	05/2013
8981	2^180370+12915	54297	Lelio R Paula	09/2012
8982	(10^54290+41)/3	54290	Robert Price	01/2017
8983	15108^3917+3917^15108	54283	Hans Havermann	06/2016
8984	2^180317-3019	54281	Yves Minet	10/2014
8985	2^180314+855	54280	Lelio R Paula	10/2009
8986	19^42425+94	54252	Lelio R Paula	02/2013
8987	2^180180-1005449	54240	Paul Bourdelais	11/2012
8989	2^180173-2773	54238	Yves Minet	07/2014
8988	13367^11418+11418^13367	54238	Hans Havermann	06/2016
8990	427^20614+20614^427	54224	Norbert Schneider	06/2016
8991	2^180124-87959	54223	Gary Barnes	08/2009
8992	2^180111-113101	54219	Enzo Doria	07/2014
8993	2^180101-114871	54216	Enzo Doria	05/2015
8994	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
8995	2^180070+465	54207	Lelio R Paula	09/2012
8996	13683^9154+9154^13683	54207	Hans Havermann	06/2016
8997	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
8998	2^180014+613	54190	Jason Earls	04/2008
8999	2^180007+101	54188	Lelio R Paula	02/2011
9000	2^180001+41877	54186	Jim Fougeron	08/2002

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Probable Primes Top 10000

(205869 PRPs in the top)