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	2^331746-11655	99866	Lelio R Paula	09/2016
8752	11^95891-28	99861	Lelio R Paula	08/2016
8753	(2^331694-5)/11	99849	Lelio R Paula	10/2013
8754	(3^209246+7)/64	99834	Lelio R Paula	09/2013
8755	25062^9617+9617^25062	99823	Hans Havermann	04/2018
8756	15^84866-52	99811	Lelio R Paula	08/2016
8757	13^89600+30	99810	Lelio R Paula	08/2016
8758	2^331527+100280245065	99800	Paul Bourdelais	10/2021
8759	22950^22309+22309^22950	99798	Hans Havermann	03/2018
8760	5^142772-38	99794	Lelio R Paula	08/2016
8761	(7482^25759-1)/7481	99787	Serge Batalov	06/2022
8762	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
8763	2^331416-331416+1	99767	Robert Price	10/2014
8764	2^331256-57	99718	Lelio R Paula	12/2012
8765	28192^3443+3443^28192	99714	Hans Havermann	03/2018
8766	2^331185+737	99697	Lelio R Paula	01/2013
8767	(4*10^99693+149)/9	99693	Robert Price	03/2017
8768	2^331154+1880527	99688	Enzo Doria	10/2016
8770	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
8769	24354^12385+12385^24354	99679	Hans Havermann	03/2018
8771	2^331110+1870459	99675	Enzo Doria	05/2016
8772	5*2^331075+7	99665	Lelio R Paula	08/2014
8773	25776^7351+7351^25776	99659	Hans Havermann	02/2018
8774	(16*10^99656-31)/3	99657	Robert Price	03/2016
8775	(6059^26347-1)/6058	99652	Serge Batalov	06/2022
8776	(15544^23773-1)/15543	99642	Serge Batalov	06/2022
8778	2^330968+345	99632	Lelio R Paula	09/2016
8777	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
8780	2*5^142528-7	99624	Lelio R Paula	11/2014
8779	2^330942+77329	99624	Enzo Doria	05/2016
8781	14^86914-99	99615	Lelio R Paula	08/2016
8782	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
8783	22971^21692+21692^22971	99610	Hans Havermann	03/2018
8784	2^330845+71687	99595	Enzo Doria	04/2016
8785	(26667^22501-1)/26666	99585	Serge Batalov	06/2022
8786	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
8787	24494^11613+11613^24494	99567	Hans Havermann	03/2018
8788	2^330735+8415	99562	Lelio R Paula	09/2016
8789	2^330720+74071	99557	Enzo Doria	04/2016
8790	(10405^24781-1)/10404	99548	Serge Batalov	06/2022
8792	31^66738-2	99531	Lelio R Paula	09/2013
8791	(9002^25171-1)/9001	99531	Serge Batalov	06/2022
8793	(5023^26893-1)/5022	99527	Serge Batalov	06/2022
8794	7*3^208567+4	99513	Lelio R Paula	08/2014
8795	(15881^23689-1)/15880	99511	Serge Batalov	06/2022
8796	(13*10^99508+47)/3	99509	Robert Price	01/2017
8797	2^330553+779	99507	Lelio R Paula	01/2013
8798	15^84606-94	99505	Lelio R Paula	08/2016
8799	(10^99497+173)/3	99497	Robert Price	05/2021
8800	9*10^99493-43	99494	Robert Price	09/2021
8801	6^127858+47	99493	Lelio R Paula	08/2016
8802	5^142337+48	99490	Lelio R Paula	08/2016
8803	7^117724-20	99489	Lelio R Paula	08/2016
8804	(559^36209-1)/558	99479	Serge Batalov	06/2022
8805	(13470^24091-1)/13469	99477	Serge Batalov	06/2022
8806	(29*10^99474-17)/3	99475	Erik Branger	09/2014
8807	(185*10^99466-11)/3	99468	Robert Price	10/2020
8808	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
8809	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
8810	(516*32^66077-175)/31	99458	Eric Chen	04/2023
8811	(2863^28771-1)/2862	99453	Serge Batalov	06/2022
8812	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
8813	(68*10^99441+7)/3	99443	Robert Price	03/2016
8814	10^99434+155571	99435	Patrick De Geest	04/2020
8815	10^99434-123456789	99434	Robert Price	02/2020
8816	10^99434-191237	99434	Patrick De Geest	04/2020
8817	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
8818	23839^14802+14802^23839	99417	Hans Havermann	02/2018
8819	(2*10^99408+529)/9	99408	Robert Price	01/2017
8820	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
8821	53^57646-2	99398	Lelio R Paula	09/2013
8822	2^330165+1870025	99390	Enzo Doria	05/2016
8823	7*10^99383+97	99384	Robert Price	09/2021
8824	2^330142-155	99383	Lelio R Paula	12/2012
8825	2^330088-115259	99367	Enzo Doria	06/2015
8826	24216^12671+12671^24216	99354	Hans Havermann	01/2018
8827	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
8828	(746*10^99303+1)/9	99305	Robert Price	02/2017
8829	3^208107+40	99293	Lelio R Paula	08/2016
8830	2^329843+211343	99293	Enzo Doria	08/2023
8831	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
8832	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
8833	8*3^208093+5	99287	Lelio R Paula	08/2014
8834	5^142043+56	99284	Lelio R Paula	08/2016
8835	(13*10^99282-157)/9	99283	Robert Price	05/2021
8836	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
8837	22*10^99275+7	99277	Robert Price	04/2016
8838	2^329778+1876189	99274	Enzo Doria	07/2016
8839	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
8840	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
8841	(10^99239-13)/3	99239	Robert Price	02/2017
8842	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
8844	3^207987+62	99236	Lelio R Paula	08/2016
8843	(62*10^99235+91)/9	99236	Robert Price	07/2021
8845	2^329638+49	99231	Lelio R Paula	12/2012
8846	7^117413-18	99226	Lelio R Paula	08/2016
8847	2^329586-458903	99216	Enzo Doria	04/2015
8848	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
8850	2^329553+101	99206	Lelio R Paula	12/2012
8849	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
8851	2^329551-112897	99205	Enzo Doria	06/2014
8852	(3^207925+7)/50	99204	Lelio R Paula	09/2013
8853	6^127458-17993	99182	Enzo Doria	03/2013
8854	27197^4428+4428^27197	99166	Hans Havermann	10/2017
8855	(46*10^99143-1)/9	99144	Robert Price	12/2014
8856	(64*10^99135+161)/9	99136	Robert Price	08/2022
8857	7*10^99133+69	99134	Robert Price	10/2017
8858	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
8859	18^78968-3065	99127	Enzo Doria	03/2013
8861	25927^6654+6654^25927	99122	Hans Havermann	10/2017
8860	87915!4+16	99122	Robert Price	09/2019
8862	2^329259+189	99117	Lelio R Paula	12/2012
8863	8*10^99113+39	99114	Robert Price	01/2017
8864	6^127364+77	99109	Lelio R Paula	08/2016
8865	(82*10^99103+143)/9	99104	Robert Price	06/2021
8866	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
8867	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
8868	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
8869	(59*10^99069+391)/9	99070	Robert Price	03/2021
8870	(797*10^99061-41)/9	99063	Robert Price	04/2022
8871	2^329058-287681	99057	Harrison Mesh	06/2022
8872	6^127285+13	99047	Lelio R Paula	08/2016
8873	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
8874	2^329007+73283	99041	Enzo Doria	04/2016
8875	5*3^207543-8	99024	Lelio R Paula	08/2014
8876	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
8877	2^328885+149	99005	Lelio R Paula	12/2012
8879	23392^17075+17075^23392	99004	Hans Havermann	09/2017
8878	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
8880	(2^328879-9)/119	99001	Lelio R Paula	10/2013
8881	5^141618+54	98987	Lelio R Paula	08/2016
8882	8*10^98982+51	98983	Robert Price	05/2017
8883	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
8884	2^328794-2797601	98977	Enzo Doria	04/2016
8885	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
8886	6^127176+5	98963	Lelio R Paula	11/2014
8887	2*10^98961-21	98962	Robert Price	09/2020
8888	24262^11989+11989^24262	98960	Hans Havermann	09/2017
8889	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
8890	2^328700-109709	98949	Enzo Doria	04/2014
8891	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
8892	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
8893	87771!4-128	98944	Robert Price	11/2019
8894	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
8895	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
8896	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
8897	46711!2-2^46711	98916	Robert Price	09/2015
8898	9*7^117037+4	98909	Lelio R Paula	11/2014
8899	127^47012+126	98905	Norbert Schneider	01/2019
8900	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
8901	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
8902	(10^98890+149)/3	98890	Serge Batalov	12/2014
8903	22775^21978+21978^22775	98889	Hans Havermann	08/2017
8904	2^328497-216933	98888	Enzo Doria	05/2014
8905	2^328487+32769	98885	Lelio R Paula	08/2016
8906	3^207250-112358	98884	Enzo Doria	06/2014
8907	13^88754-90	98867	Lelio R Paula	08/2016
8908	2^328406+709	98861	Lelio R Paula	02/2013
8909	2*10^98860-21	98861	Robert Price	09/2020
8910	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
8911	7^116976+76	98857	Lelio R Paula	08/2016
8912	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
8913	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
8914	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
8916	2^328335+1155	98839	Lelio R Paula	08/2016
8915	2^328333-349003	98839	Harrison Mesh	06/2022
8918	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
8917	287^40210+40210^287	98832	Norbert Schneider	11/2014
8919	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
8920	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
8921	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
8922	24746^9825+9825^24746	98795	Hans Havermann	07/2020
8923	26620^5143+5143^26620	98793	Hans Havermann	07/2020
8924	65^54491+48	98788	Lelio R Paula	04/2016
8925	3^207042+98	98785	Lelio R Paula	08/2016
8926	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
8927	10^98754+73383	98755	Patrick De Geest	02/2021
8930	3^206977-112756	98754	Enzo Doria	07/2014
8929	10^98754-40000000001	98754	Robert Price	09/2020
8928	10^98754-169343	98754	Patrick De Geest	02/2021
8931	7^116846-50	98747	Lelio R Paula	08/2016
8932	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
8933	23267^17512+17512^23267	98730	Hans Havermann	04/2020
8934	2^327967-28635	98728	Lelio R Paula	08/2016
8935	707^34642+34642^707	98710	Norbert Schneider	12/2017
8936	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
8937	6^126850-47	98709	Lelio R Paula	08/2016
8938	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
8939	(22*10^98697+47)/3	98698	Robert Price	06/2021
8940	8*6^126830-7	98694	Lelio R Paula	11/2014
8941	11^94770-270	98693	Enzo Doria	08/2012
8942	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
8943	2^327832+43	98688	Lelio R Paula	12/2012
8944	2^327795+761	98677	Lelio R Paula	02/2013
8945	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
8946	10^98669+147411	98670	Patrick De Geest	11/2016
8948	10^98669-9^(98669-1)	98669	Robert Price	05/2016
8947	10^98669-105249	98669	Patrick De Geest	11/2016
8949	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
8950	2^327671-109801	98639	Enzo Doria	04/2014
8951	24398^11037+11037^24398	98638	Hans Havermann	10/2019
8952	5^141090-14	98618	Lelio R Paula	08/2016
8953	20^75799+47	98617	Lelio R Paula	08/2016
8954	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
8955	28101^3226+3226^28101	98597	Hans Havermann	07/2020
8956	2^327515-1017	98592	Lelio R Paula	08/2016
8957	6^126692+97681	98586	Mike Oakes	04/2011
8958	2^327467-741	98578	Lelio R Paula	08/2016
8959	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
8960	22713^21800+21800^22713	98540	Hans Havermann	05/2020
8961	(2^327329+9)/19	98535	Lelio R Paula	10/2013
8962	7^116577-66	98519	Lelio R Paula	08/2016
8963	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
8964	23220^17479+17479^23220	98512	Hans Havermann	03/2020
8965	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
8966	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
8967	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
8968	2^327162-66945	98486	Lelio R Paula	08/2016
8969	30139^1852+1852^30139	98484	Hans Havermann	02/2020
8970	23182^17703+17703^23182	98479	Hans Havermann	01/2020
8971	4*10^98472-3	98473	Erik Branger	11/2013
8972	26167^5794+5794^26167	98466	Hans Havermann	01/2020
8973	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
8974	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
8975	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
8976	13^88363+94	98432	Lelio R Paula	08/2016
8977	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
8978	6^126481+41	98422	Lelio R Paula	08/2016
8979	78*10^98413-7	98415	Robert Price	05/2017
8980	22634^22263+22263^22634	98404	Hans Havermann	07/2020
8981	(47*10^98386+241)/9	98387	Robert Price	06/2022
8982	7^116416+46	98383	Lelio R Paula	08/2016
8983	7^116407-24	98376	Lelio R Paula	07/2016
8984	439^37228+37228^439	98374	Norbert Schneider	08/2018
8985	2^326782-1860671	98372	Enzo Doria	03/2016
8986	17^79948+58	98372	Lelio R Paula	08/2016
8987	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
8988	3^206143-98	98356	Lelio R Paula	08/2016
8989	8*5^140705+7	98350	Lelio R Paula	11/2014
8990	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
8991	(638^35053-1)/637	98315	Serge Batalov	06/2022
8992	2^326585+11	98312	Lelio R Paula	12/2012
8993	2^326582-459161	98311	Enzo Doria	05/2015
8994	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
8996	(2^326548+9)/5	98301	Lelio R Paula	10/2013
8995	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
8997	2^326538+71659	98298	Enzo Doria	04/2016
8998	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
8999	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
9000	15^83575-58	98292	Lelio R Paula	08/2016

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Probable Primes Top 10000

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