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	15215^4762+4762^15215	55958	Hans Havermann	03/2016
8752	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
8753	13582^13165+13165^13582	55950	Hans Havermann	08/2016
8754	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
8755	15^47562-86	55938	Lelio R Paula	02/2013
8756	4*10^55932+91	55933	Robert Price	11/2017
8757	3^117222+4	55930	Lelio R Paula	03/2012
8758	24^40519-23^40519	55925	Robert Price	07/2012
8759	13636^12623+12623^13636	55924	Hans Havermann	07/2016
8760	2^185767-99	55922	Lelio R Paula	03/2011
8761	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
8763	15^47542-58	55914	Lelio R Paula	02/2013
8762	52211!4+2	55914	Robert Price	08/2017
8764	20^42973-5583	55910	Enzo Doria	03/2013
8765	4*10^55906+21	55907	Robert Price	08/2016
8766	2^185713-111	55906	Lelio R Paula	03/2011
8767	13^50174+88	55891	Lelio R Paula	01/2013
8768	14569^6846+6846^14569	55879	Hans Havermann	08/2016
8769	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
8770	3^117087-80	55865	Lelio R Paula	10/2012
8771	(7*10^55851-43)/9	55851	Robert Price	10/2014
8772	2^185519-169	55847	Lelio R Paula	03/2011
8773	7^66074+10	55840	Lelio R Paula	10/2012
8774	(19*10^55833-49)/3	55834	Robert Price	02/2017
8775	(2*10^55834-59)/3	55834	Robert Price	05/2017
8776	12^51732+5	55829	Lelio R Paula	01/2013
8777	3*2^185429+7	55821	Lelio R Paula	03/2014
8778	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
8779	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
8780	14427^7396+7396^14427	55819	Hans Havermann	08/2016
8781	10^55811+21	55812	Robert Price	01/2011
8782	10^55811-74103	55811	Patrick De Geest	12/2012
8783	11^53591-1530	55810	Enzo Doria	11/2012
8784	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
8785	2^185355-2145	55798	Lelio R Paula	03/2011
8786	14531^6912+6912^14531	55794	Hans Havermann	07/2016
8787	2^185327-1615	55789	Lelio R Paula	03/2011
8788	2^185280-12779	55775	Enzo Doria	10/2012
8789	15504^3955+3955^15504	55771	Hans Havermann	07/2016
8790	(2*10^55762-59)/3	55762	Robert Price	05/2017
8791	5^79770-44	55757	Lelio R Paula	10/2012
8792	18^44416-85	55755	Lelio R Paula	02/2013
8793	2^185208-459995	55754	Enzo Doria	06/2015
8794	2^185200+1185	55751	Lelio R Paula	03/2011
8795	(536*10^55748-23)/9	55750	Robert Price	11/2017
8796	7^65964+6^(65964-1)	55747	Robert Price	03/2016
8797	2^185151-237157	55737	Gary Barnes	09/2009
8798	110017^11055-102	55734	Enzo Doria	07/2012
8799	14754^5987+5987^14754	55729	Hans Havermann	07/2016
8800	40090!3-9	55711	Robert Price	09/2014
8801	9*10^55707+89	55708	Robert Price	11/2016
8802	2^185023-2257	55698	Yves Minet	06/2009
8803	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
8804	2^185006-93	55693	Lelio R Paula	03/2011
8805	2^185003-2515	55692	Yves Minet	07/2014
8806	2^184992-78557	55689	Jorge Menendez	02/2018
8807	3*10^55679+37	55680	Robert Price	10/2017
8808	6^71524-19	55657	Lelio R Paula	10/2012
8809	2^184872-2195	55653	Yves Minet	08/2013
8810	507^20572+20572^507	55648	Norbert Schneider	06/2016
8811	(86*10^55645-311)/9	55646	Robert Price	10/2017
8812	134^26151-133	55626	Norbert Schneider	03/2015
8813	15340^4221+4221^15340	55614	Hans Havermann	07/2016
8814	27743!2+2	55612	Robert Price	01/2013
8815	20^42744+81	55612	Lelio R Paula	02/2013
8816	14609^6406+6406^14609	55611	Hans Havermann	07/2016
8817	2^184724-112883	55608	Enzo Doria	06/2014
8818	13507^13074+13074^13507	55601	Hans Havermann	07/2016
8819	2^184689+129	55597	Lelio R Paula	03/2011
8820	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
8821	(22*10^55592-19)/3	55593	Robert Price	02/2017
8822	Phi(59984,89)	55582	Enzo Doria	05/2012
8823	11^53368+16	55578	Lelio R Paula	01/2013
8824	20^42717-1923	55577	Enzo Doria	03/2013
8825	117^26870+26870^117	55573	Serge Batalov	05/2014
8826	12^51488+55	55565	Lelio R Paula	01/2013
8827	(44*10^55558-17)/9	55559	Robert Price	06/2015
8828	(2*10^55559-23)/3	55559	Robert Price	09/2017
8829	10^55555+32857	55556	Patrick De Geest	06/2010
8830	10^55555-136721	55555	Patrick De Geest	06/2010
8831	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014
8832	20^42696-2043	55549	Enzo Doria	03/2013
8833	(35*10^55547-737)/9	55548	Robert Price	11/2017
8834	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
8835	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
8836	5003^15013-160	55537	Enzo Doria	07/2012
8837	39^34896-2	55522	Lelio R Paula	08/2013
8838	(6^71345-61)/5	55517	Lelio R Paula	05/2014
8839	2^184407-3019	55513	Yves Minet	10/2014
8840	(43*10^55512-61)/9	55513	Robert Price	06/2015
8841	20^42667-843	55512	Enzo Doria	03/2013
8842	133^26134-132	55505	Norbert Schneider	03/2015
8843	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
8844	9*7^65667-4	55497	Lelio R Paula	09/2014
8845	2^184342-173	55493	Lelio R Paula	03/2011
8846	15^47182+92	55491	Lelio R Paula	02/2013
8847	5^79378+6	55483	Lelio R Paula	10/2012
8848	581^20068+20068^581	55472	Norbert Schneider	06/2016
8849	(2^184232+1)/257	55457	Donovan Johnson	03/2005
8850	18^44177-1415	55455	Enzo Doria	03/2013
8851	2^184203-2797867	55451	Enzo Doria	04/2016
8852	2^184189+17	55447	Lelio R Paula	03/2011
8853	2^184183+26123	55445	Yves Minet	01/2010
8854	Phi(77077,10)	55441	Ray Chandler	05/2009
8855	2^184141-113251	55432	Enzo Doria	07/2014
8856	2^184093-504613	55418	Gary Barnes	09/2009
8857	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
8858	2^184044-111269	55403	Enzo Doria	05/2014
8859	14051^8766+8766^14051	55401	Hans Havermann	07/2016
8860	98^27819+27819^98	55394	Serge Batalov	05/2014
8861	(178*10^55390-7)/9	55392	Robert Price	08/2017
8862	58046^9+9^58046	55390	Andrey Kulsha	02/2004
8863	7^65536+2*59232-2	55385	Jiahao He	07/2017
8864	2^183980+75241	55384	Enzo Doria	04/2016
8865	10^55372+37	55373	Robert Price	01/2011
8866	10^55372-49967	55372	Patrick De Geest	12/2012
8867	(13*10^55367+17)/3	55368	Robert Price	06/2015
8868	2*6^71150+7	55366	Lelio R Paula	09/2014
8869	19^43296-62	55365	Lelio R Paula	02/2013
8870	19^43295+10	55364	Lelio R Paula	02/2013
8871	(29*10^55362-11)/9	55363	Robert Price	04/2015
8872	(37*10^55359+53)/9	55360	Robert Price	05/2015
8873	19^43283+72	55349	Lelio R Paula	02/2013
8874	2^183800-65	55330	Lelio R Paula	03/2011
8875	21001^12801-110	55329	Enzo Doria	07/2012
8876	33^36433-32^36433	55325	Robert Price	04/2012
8877	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
8879	9^57952+8^(57952-1)	55301	Robert Price	03/2016
8878	14872^5229+5229^14872	55301	Hans Havermann	08/2016
8880	61^30972-2	55296	Lelio R Paula	08/2013
8881	2^183671-112537	55291	Enzo Doria	06/2014
8882	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
8883	3^115873+56	55286	Lelio R Paula	10/2012
8884	13^49629-84	55284	Lelio R Paula	01/2013
8885	2^183632-5	55279	Henri Lifchitz	08/2005
8886	13981^8988+8988^13981	55277	Hans Havermann	07/2016
8887	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
8888	2^183576+171	55262	Lelio R Paula	03/2011
8889	13^49604+82	55257	Lelio R Paula	01/2013
8890	(11*10^55254+1)/3	55255	Erik Branger	03/2014
8891	12609^13474-13474^12609	55253	Norbert Schneider	05/2018
8892	3^115802-26	55252	Lelio R Paula	10/2012
8893	2^183534-3645	55250	Lelio R Paula	01/2011
8894	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
8895	5^79032-13766	55241	Enzo Doria	02/2013
8896	8*3^115759-7	55232	Lelio R Paula	03/2014
8897	6^70974-137	55229	Lelio R Paula	10/2012
8898	2^183446-113073	55223	Enzo Doria	07/2014
8899	2^183441+577294575	55222	Lelio R Paula	03/2013
8900	5^79000-6	55219	Lelio R Paula	10/2012
8901	2^183413-901	55213	Yves Minet	01/2012
8902	19^43168-50	55202	Lelio R Paula	02/2013
8903	2^183340+19683	55191	Lelio R Paula	02/2012
8904	6^70923+35	55189	Lelio R Paula	10/2012
8905	2^183317-4035	55184	Lelio R Paula	01/2011
8906	2^183284-15	55174	Lelio R Paula	03/2011
8907	2^183255+149	55166	Lelio R Paula	02/2011
8908	4*10^55165+87	55166	Robert Price	05/2016
8909	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
8910	2^183165-112333	55139	Enzo Doria	06/2014
8911	(109^27061-1)/108	55133	Richard Fischer	09/2017
8912	2^183142+855	55132	Lelio R Paula	01/2011
8913	(49*10^55129+383)/9	55130	Robert Price	04/2017
8914	2^183019+255255	55095	Lelio R Paula	01/2011
8915	(10^55084-19)/9	55084	Robert Price	10/2017
8916	3*10^55077+7	55078	Erik Branger	11/2013
8917	(62*10^55075-71)/9	55076	Robert Price	09/2015
8918	27499!2-32	55070	Robert Price	10/2015
8919	15307^3958+3958^15307	55067	Hans Havermann	08/2016
8920	70^29836-69	55051	Norbert Schneider	10/2012
8921	18^43854-83	55049	Lelio R Paula	02/2013
8922	7^65126+58	55038	Lelio R Paula	10/2012
8923	2^182827-1615	55037	Lelio R Paula	11/2009
8924	7*10^55030-9	55031	Dmitry Domanov	11/2010
8925	2^182768-4055	55019	Yves Minet	02/2018
8926	6^70702+23	55017	Lelio R Paula	10/2012
8927	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
8928	2^182743-1615	55012	Lelio R Paula	11/2009
8929	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
8930	3^115280-9568	55003	Enzo Doria	02/2013
8931	2^182656-12849	54985	Enzo Doria	10/2012
8932	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
8933	9*19^42995+16	54981	Curtis Bright	05/2015
8934	2^182627+28425	54977	Lelio R Paula	11/2009
8935	2^182597-113053	54968	Enzo Doria	07/2014
8936	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
8937	2^182581-1975	54963	Yves Minet	09/2012
8938	(2*10^54960-179)/3	54960	Robert Price	11/2017
8939	27449!!-16	54959	Robert Price	06/2015
8940	(22*10^54958-73)/3	54959	Robert Price	09/2017
8942	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
8941	2^182565+107	54958	Lelio R Paula	11/2009
8943	2^182560+2053	54957	Lelio R Paula	12/2010
8944	2^182451-182451	54924	Henri Lifchitz	10/2004
8945	2^182444+81	54922	Henri Lifchitz	10/2005
8946	2^182433+74105	54918	Enzo Doria	04/2016
8947	20^42206-5243	54912	Enzo Doria	03/2013
8948	2^182394+85	54907	Lelio R Paula	02/2011
8949	2^182374-112287	54901	Enzo Doria	06/2014
8950	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
8951	2^182363-113167	54897	Enzo Doria	07/2014
8952	2^182359-112221	54896	Enzo Doria	06/2014
8953	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
8954	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
8955	18^43698-5	54853	Lelio R Paula	02/2013
8956	2^182209-1893	54851	Yves Minet	09/2012
8957	2^182194-3443	54846	Yves Minet	12/2016
8958	15023^4468+4468^15023	54836	Hans Havermann	08/2016
8959	2^182135+90143	54829	Yves Minet	10/2010
8960	2^182119+74333	54824	Enzo Doria	04/2016
8961	14289^6860+6860^14289	54818	Hans Havermann	08/2016
8962	3^114892-114892^3	54818	Norbert Schneider	03/2017
8963	2^182070-47355	54809	Lelio R Paula	01/2011
8964	3^114869+76	54807	Lelio R Paula	10/2012
8965	8^60681-60681^8	54801	Norbert Schneider	12/2016
8966	1897^16710+16710^1897	54777	Serge Batalov	05/2014
8967	Phi(61868,59)	54776	Enzo Doria	04/2012
8968	113^26679+2	54775	Lelio R Paula	05/2013
8969	3^114789-74	54769	Lelio R Paula	10/2012
8970	15^46567+98	54768	Lelio R Paula	02/2013
8971	(2*10^54767-71)/3	54767	Robert Price	01/2017
8972	(298*10^54765-7)/3	54767	Robert Price	06/2017
8973	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
8974	2^181913+29	54762	Henri Lifchitz	06/2005
8975	(31*10^54761-121)/9	54762	Robert Price	06/2016
8976	2^181887+189	54754	Lelio R Paula	02/2011
8977	2^181874+181874^2-1	54750	Robert Price	04/2014
8978	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
8979	5^78314-92	54740	Lelio R Paula	10/2012
8980	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
8981	15^46531+74	54725	Lelio R Paula	02/2013
8982	277^22400-348	54712	Enzo Doria	07/2012
8983	6^70302+101	54706	Lelio R Paula	10/2012
8984	3^114622-10408	54689	Enzo Doria	02/2013
8986	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
8985	2^181669-1551	54688	Yves Minet	08/2012
8987	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
8988	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
8989	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
8990	13^49073+46	54665	Lelio R Paula	01/2013
8991	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
8993	20^42000+73	54644	Lelio R Paula	02/2013
8992	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
8994	33*10^54634+7	54636	Robert Price	07/2016
8995	20^41988+61	54628	Lelio R Paula	01/2013
8996	20^41988-8123	54628	Enzo Doria	03/2013
8997	2^181420+21181	54613	Yves Minet	03/2011
8998	(19*10^54608+161)/9	54609	Robert Price	07/2016
8999	19^42696-24	54598	Lelio R Paula	02/2013
9000	(44*10^54596-503)/9	54597	Robert Price	10/2017

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PRP Records

Probable Primes Top 10000

(211563 PRPs in the top)