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 ?
8751	(85*10^60026+23)/9	60027	Robert Price	11/2015
8752	65^33107+62	60021	Lelio R Paula	01/2016
8754	2^199362-1215	60014	Lelio R Paula	06/2011
8753	2^199362-111633	60014	Enzo Doria	05/2014
8755	1537^18832+18832^1537	60012	Serge Batalov	05/2014
8756	2^199324-17433	60003	Enzo Doria	05/2013
8758	10^60000+204331	60001	Milton L. Brown	04/2006
8759	10^60000+87129	60001	Milton L. Brown	04/2006
8757	143^27838-2	60001	Lelio R Paula	10/2017
8760	10^59999+65197	60000	Patrick De Geest	04/2005
8778	10^60000-32529	60000	Patrick De Geest	08/2009
8774	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
8775	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
8776	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
8777	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
8761	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
8762	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
8763	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
8764	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
8765	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
8766	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
8767	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
8768	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
8769	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
8770	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
8771	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
8772	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
8773	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
8779	2^199313-225675	60000	Stefano Morozzi	05/2019
8780	2^199313-326901	60000	Stefano Morozzi	05/2019
8781	2^199313-532171	60000	Stefano Morozzi	05/2019
8782	2^199313-632851	60000	Stefano Morozzi	05/2019
8783	2^199313-825289	60000	Stefano Morozzi	05/2019
8784	2^199313-857691	60000	Stefano Morozzi	05/2019
8785	2^199313+83705	60000	Stefano Morozzi	05/2019
8786	2^199313+175439	60000	Stefano Morozzi	05/2019
8787	2^199313+401715	60000	Stefano Morozzi	05/2019
8788	2^199313+418367	60000	Stefano Morozzi	05/2019
8789	2^199313+520517	60000	Stefano Morozzi	05/2019
8790	2^199313+582975	60000	Stefano Morozzi	05/2019
8791	2^199313+600329	60000	Stefano Morozzi	05/2019
8792	2^199313+601161	60000	Stefano Morozzi	05/2019
8793	2^199313+601467	60000	Stefano Morozzi	05/2019
8794	2^199313+929705	60000	Stefano Morozzi	05/2019
8803	10^59999-516267	59999	Patrick De Geest	06/2009
8801	20^46116-41	59999	Lelio R Paula	03/2013
8802	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
8804	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
8795	(2^199313+804446)/2	59999	Stefano Morozzi	06/2019
8796	(2^199313+885410)/2	59999	Stefano Morozzi	06/2019
8797	(2^199313+916374)/2	59999	Stefano Morozzi	06/2019
8798	(2^199313+501865)/3	59999	Stefano Morozzi	06/2019
8799	(2^199313+979327)/3	59999	Stefano Morozzi	06/2019
8800	(2^199313+870498)/10	59999	Stefano Morozzi	06/2019
8805	(2^199313+911951)/53	59998	Stefano Morozzi	06/2019
8806	(2^199313+622557)/59	59998	Stefano Morozzi	06/2019
8807	(2^199313+548359)/111	59998	Stefano Morozzi	06/2019
8808	(2^199313+881010)/142	59998	Stefano Morozzi	06/2019
8809	(2^199313+20613)/415	59997	Stefano Morozzi	06/2019
8810	(2^199313+846966)/158	59997	Stefano Morozzi	06/2019
8811	(2^199313+689239)/213	59997	Stefano Morozzi	06/2019
8812	(2^199313+792637)/303	59997	Stefano Morozzi	06/2019
8813	(2^199313+979299)/733	59997	Stefano Morozzi	06/2019
8814	(2^199313+760551)/1481	59997	Stefano Morozzi	06/2019
8817	6^77100-55	59996	Lelio R Paula	10/2012
8815	(2^199313+8825)/7733	59996	Stefano Morozzi	06/2019
8816	(2^199313+621926)/1598	59996	Stefano Morozzi	06/2019
8818	(2^199313+17227)/1467741879771	59988	Stefano Morozzi	06/2019
8821	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
8820	(23^44053+1)/24	59987	Robert Price	06/2013
8819	(2^199313+30419)/1952230291007	59987	Stefano Morozzi	06/2019
8822	(2^199313+4605)/7769355879406087	59984	Stefano Morozzi	06/2019
8823	(2^199313+47559)/7830445067929369	59984	Stefano Morozzi	06/2019
8824	(2^199313+16238)/709623753063172030	59982	Stefano Morozzi	06/2019
8825	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010
8826	11438^14775-14775^11438	59963	Norbert Schneider	05/2019
8827	15852^6061+6061^15852	59961	Hans Havermann	08/2016
8828	19^46880-20	59948	Lelio R Paula	03/2013
8829	2^199107-17737	59938	Enzo Doria	05/2013
8830	(13*10^59928+83)/3	59929	Robert Price	09/2016
8831	10^59913+108931431	59914	Marisa Kirisame	02/2015
8832	10^59913+48619	59914	Patrick De Geest	04/2016
8833	10^59913-74123	59913	Patrick De Geest	03/2016
8834	t(199528)	59890	Robert Price	01/2015
8835	2^198903-17901	59876	Enzo Doria	05/2013
8836	9*10^59862-19	59863	Robert Price	10/2017
8837	gcd(V(776555),5F(155311)(F(155311)+1)+1)	59858	Serge Batalov	04/2015
8838	(3^125447+7)/2	59854	Lelio R Paula	04/2012
8839	5^85630+4^(85630-1)	59853	Robert Price	03/2016
8840	2^198824-2135	59852	Yves Minet	06/2013
8841	(124^28591-1)/123	59851	Richard Fischer	10/2017
8842	2^198799-16117	59845	Enzo Doria	04/2013
8843	7^70811+6^(70811+1)	59843	Robert Price	07/2016
8844	2^198774-15945	59837	Enzo Doria	04/2013
8845	2^198753-15873	59831	Enzo Doria	04/2013
8846	(31*2^198748-1)/45	59829	Lelio R Paula	01/2014
8847	2^198725+69	59823	Lelio R Paula	04/2011
8848	(68*10^59821+31)/9	59822	Robert Price	10/2015
8849	(37*25^42785+1867)/8	59812	Curtis Bright	05/2015
8850	3^125354+2660	59810	Lelio R Paula	10/2012
8851	105^29591-104	59810	Norbert Schneider	08/2013
8852	4*5^85565-3	59808	Lelio R Paula	09/2014
8853	13963842222*Bern(19550)/55727275	59803	Thomas Ritschel	03/2014
8856	125330^3+3^125330	59798	Anatoly F. Selevich	06/2010
8854	2^198643-3189	59798	Yves Minet	10/2014
8855	(13*10^59797+191)/3	59798	Robert Price	08/2017
8857	(7*10^59796-1)/3	59797	Erik Branger	03/2014
8858	2^198595+153	59784	Lelio R Paula	04/2011
8859	(19*10^59766+161)/9	59767	Robert Price	07/2016
8860	2^198510-1965	59758	Lelio R Paula	06/2011
8861	2^198506-19077	59757	Enzo Doria	05/2013
8862	2^198484-16005	59750	Enzo Doria	04/2013
8863	2^198473-16821	59747	Enzo Doria	05/2013
8864	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
8865	2^198400-189	59725	Lelio R Paula	04/2011
8866	2^198384-12837	59720	Enzo Doria	10/2012
8867	42694!3-729	59719	Robert Price	09/2014
8868	2^198320-18717	59701	Enzo Doria	05/2013
8869	20^45881-1183	59693	Enzo Doria	03/2013
8870	2^198224-6855	59672	Lelio R Paula	05/2011
8871	2^198181-19101	59659	Enzo Doria	05/2013
8872	5*10^59650+41	59651	Robert Price	08/2017
8873	2^198149-112213	59649	Enzo Doria	06/2014
8874	2^198138+73699	59646	Enzo Doria	04/2016
8875	2^198129-55	59643	Lelio R Paula	04/2011
8876	16029^5258+5258^16029	59642	Hans Havermann	05/2019
8877	5^85318-14636	59635	Enzo Doria	02/2013
8878	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
8879	2^198090-16097	59632	Enzo Doria	04/2013
8880	9*10^59617+89	59618	Robert Price	11/2016
8881	42625!3+81	59612	Robert Price	09/2014
8882	5^85277-84	59607	Lelio R Paula	10/2012
8883	(871*10^59599-7)/9	59601	Robert Price	11/2017
8884	2^197984-18245	59600	Enzo Doria	05/2013
8885	12202^14583-14583^12202	59593	Norbert Schneider	01/2019
8886	2^197951-2137	59590	Yves Minet	06/2013
8887	(38*10^59589+187)/9	59590	Robert Price	11/2017
8888	66^32749-65^32749	59589	Robert Price	09/2013
8889	5*10^59586-3	59587	Dmitry Domanov	11/2010
8890	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
8891	2^197932-3959	59584	Yves Minet	04/2017
8892	2^197909-18961	59577	Enzo Doria	05/2013
8893	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
8894	2^197872+81	59566	Henri Lifchitz	10/2005
8895	2^197873-18469	59566	Enzo Doria	05/2013
8896	(22*10^59558-31)/9	59559	Robert Price	04/2015
8897	12003^14600-14600^12003	59558	Norbert Schneider	02/2019
8898	2^197840-465	59556	Lelio R Paula	05/2011
8899	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
8900	2^197808-17805	59547	Enzo Doria	05/2013
8901	2^197781-17905	59539	Enzo Doria	05/2013
8902	2^197777-17473	59537	Enzo Doria	05/2013
8903	6^76507-149	59535	Lelio R Paula	10/2012
8905	Phi(61456,109)	59526	Enzo Doria	05/2012
8904	18^47420+23	59526	Lelio R Paula	03/2013
8906	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8907	3^124747+94	59520	Lelio R Paula	10/2012
8908	17^48370+18	59517	Lelio R Paula	03/2013
8909	20^45740-1523	59510	Enzo Doria	03/2013
8910	(47*10^59509+493)/9	59510	Robert Price	11/2017
8911	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
8912	18^47390-1853	59488	Enzo Doria	03/2013
8914	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
8913	10621^14772-14772^10621	59475	Norbert Schneider	05/2019
8915	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
8916	2^197540-2459	59466	Yves Minet	07/2014
8917	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
8918	2^197494-17805	59452	Enzo Doria	05/2013
8919	2^197482-16821	59449	Enzo Doria	05/2013
8920	2^197485+75767	59449	Enzo Doria	04/2016
8921	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
8922	2^197466-1868351	59444	Enzo Doria	04/2016
8923	2^197411-17781	59427	Enzo Doria	05/2013
8924	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
8925	2^197392-114629	59421	Enzo Doria	05/2015
8926	15441^7046+7046^15441	59417	Hans Havermann	05/2019
8927	2^197355-157	59410	Lelio R Paula	04/2011
8928	5^84992-84	59407	Lelio R Paula	10/2012
8929	2*3^124504-5	59404	Lelio R Paula	04/2014
8930	2^197307-19165	59396	Enzo Doria	05/2013
8932	2^197303+32769	59395	Lelio R Paula	05/2011
8931	2*10^59394-69	59395	Robert Price	07/2017
8933	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
8934	6^76316-35	59386	Lelio R Paula	10/2012
8935	2^197259-2929	59381	Yves Minet	09/2014
8936	15036^8893+8893^15036	59378	Hans Havermann	05/2019
8937	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
8939	17^48253-6	59373	Lelio R Paula	03/2013
8938	14678^11091+11091^14678	59373	Hans Havermann	05/2019
8940	2^197156-15837	59350	Enzo Doria	04/2013
8941	2^197152-4295	59349	Yves Minet	08/2018
8942	2^197149-18481	59348	Enzo Doria	05/2013
8943	2^197142-17157	59346	Enzo Doria	05/2013
8945	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
8944	(8^65707-5^65707)/3	59339	Robert Price	12/2012
8946	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
8947	15267^7682+7682^15267	59320	Hans Havermann	05/2019
8948	2^197012-111719	59307	Enzo Doria	05/2014
8949	2^196975+513	59296	Lelio R Paula	05/2011
8950	(61*10^59294+119)/9	59295	Robert Price	09/2017
8951	4*10^59292+39	59293	Robert Price	11/2017
8952	2^196960+97	59291	Lelio R Paula	04/2011
8953	9^62116+8^(62116-1)	59274	Robert Price	03/2016
8954	2^196900-97305	59273	Lelio R Paula	09/2011
8955	13706^14327-14327^13706	59270	Norbert Schneider	05/2019
8956	5*6^76155+7	59261	Lelio R Paula	09/2014
8957	15^50385-14	59258	Wojciech Florek	06/2006
8958	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
8959	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
8960	14694^10717+10717^14694	59218	Hans Havermann	05/2019
8961	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
8962	2^196696-112967	59212	Enzo Doria	06/2014
8963	20^45508-4223	59208	Enzo Doria	03/2013
8964	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
8965	14^51651-81	59199	Lelio R Paula	03/2013
8966	2^196650-1451	59198	Yves Minet	08/2012
8967	2^196636-2797799	59194	Enzo Doria	04/2016
8968	1111*2^196610-555	59189	Henri Lifchitz	04/2005
8969	3^124041+658	59183	Lelio R Paula	10/2012
8970	2^196590-111797	59180	Enzo Doria	05/2014
8971	(10^59174-13)/3	59174	Robert Price	02/2017
8972	(2*10^59174-113)/3	59174	Robert Price	09/2017
8973	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
8974	11267^14600-14600^11267	59157	Norbert Schneider	02/2019
8975	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
8976	(404*10^59149-53)/9	59151	Robert Price	11/2017
8977	13^53095+40	59145	Lelio R Paula	03/2013
8978	2*F(282999)-1	59144	Henri Lifchitz	12/2009
8979	4*7^69984+3	59144	Lelio R Paula	09/2014
8980	(5*10^59142+1)/3	59143	Erik Branger	12/2013
8981	2^196463+5711	59142	Lelio R Paula	10/2011
8982	2^196453-97305	59139	Lelio R Paula	09/2011
8983	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
8984	(28*10^59133+113)/3	59134	Robert Price	03/2016
8985	2^196434+7	59133	Lelio R Paula	04/2011
8986	(8*10^59127-29)/3	59128	Robert Price	05/2016
8987	2^196414+255	59127	Lelio R Paula	05/2011
8988	5^84586-92	59124	Lelio R Paula	10/2012
8989	2^196388-17177	59119	Enzo Doria	05/2013
8990	79427!6-6	59119	Robert Price	08/2018
8991	3^123890+20	59111	Lelio R Paula	10/2012
8992	2^196355-1021777	59109	Paul Bourdelais	11/2012
8993	11^56754-1410	59104	Enzo Doria	11/2012
8994	10902^14635-14635^10902	59089	Norbert Schneider	02/2019
8995	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
8996	(16*10^59062-19)/3	59063	Robert Price	03/2016
8997	35^38249-1228	59060	Enzo Doria	03/2013
8998	5^84475-18	59046	Lelio R Paula	10/2012
8999	2^196123-17701	59039	Enzo Doria	05/2013
9000	12^54702-31	59034	Lelio R Paula	03/2013

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Probable Primes Top 10000

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