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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
9751	23*31^66974+2970	99884	Eric Chen	04/2024
9752	2^331746-11655	99866	Lelio R Paula	09/2016
9753	11^95891-28	99861	Lelio R Paula	08/2016
9754	(2^331694-5)/11	99849	Lelio R Paula	10/2013
9755	(3^209246+7)/64	99834	Lelio R Paula	09/2013
9756	25062^9617+9617^25062	99823	Hans Havermann	04/2018
9757	15^84866-52	99811	Lelio R Paula	08/2016
9758	13^89600+30	99810	Lelio R Paula	08/2016
9759	2^331527+100280245065	99800	Paul Bourdelais	10/2021
9760	22950^22309+22309^22950	99798	Hans Havermann	03/2018
9761	5^142772-38	99794	Lelio R Paula	08/2016
9762	(7482^25759-1)/7481	99787	Serge Batalov	06/2022
9763	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
9764	2^331416-331416+1	99767	Robert Price	10/2014
9765	2^331256-57	99718	Lelio R Paula	12/2012
9766	28192^3443+3443^28192	99714	Hans Havermann	03/2018
9767	2^331185+737	99697	Lelio R Paula	01/2013
9768	(4*10^99693+149)/9	99693	Robert Price	03/2017
9769	2^331154+1880527	99688	Enzo Doria	10/2016
9771	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
9770	24354^12385+12385^24354	99679	Hans Havermann	03/2018
9772	2^331110+1870459	99675	Enzo Doria	05/2016
9773	5*2^331075+7	99665	Lelio R Paula	08/2014
9774	25776^7351+7351^25776	99659	Hans Havermann	02/2018
9775	(16*10^99656-31)/3	99657	Robert Price	03/2016
9776	(6059^26347-1)/6058	99652	Serge Batalov	06/2022
9777	(15544^23773-1)/15543	99642	Serge Batalov	06/2022
9779	2^330968+345	99632	Lelio R Paula	09/2016
9778	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
9781	2*5^142528-7	99624	Lelio R Paula	11/2014
9780	2^330942+77329	99624	Enzo Doria	05/2016
9782	14^86914-99	99615	Lelio R Paula	08/2016
9783	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
9784	22971^21692+21692^22971	99610	Hans Havermann	03/2018
9785	2^330845+71687	99595	Enzo Doria	04/2016
9786	(26667^22501-1)/26666	99585	Serge Batalov	06/2022
9787	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
9788	24494^11613+11613^24494	99567	Hans Havermann	03/2018
9789	2^330735+8415	99562	Lelio R Paula	09/2016
9790	2^330720+74071	99557	Enzo Doria	04/2016
9791	(10405^24781-1)/10404	99548	Serge Batalov	06/2022
9793	31^66738-2	99531	Lelio R Paula	09/2013
9792	(9002^25171-1)/9001	99531	Serge Batalov	06/2022
9794	(5023^26893-1)/5022	99527	Serge Batalov	06/2022
9795	7*3^208567+4	99513	Lelio R Paula	08/2014
9796	(15881^23689-1)/15880	99511	Serge Batalov	06/2022
9797	(13*10^99508+47)/3	99509	Robert Price	01/2017
9798	2^330553+779	99507	Lelio R Paula	01/2013
9799	15^84606-94	99505	Lelio R Paula	08/2016
9800	(10^99497+173)/3	99497	Robert Price	05/2021
9801	9*10^99493-43	99494	Robert Price	09/2021
9802	6^127858+47	99493	Lelio R Paula	08/2016
9803	5^142337+48	99490	Lelio R Paula	08/2016
9804	7^117724-20	99489	Lelio R Paula	08/2016
9805	(559^36209-1)/558	99479	Serge Batalov	06/2022
9806	(13470^24091-1)/13469	99477	Serge Batalov	06/2022
9807	(29*10^99474-17)/3	99475	Erik Branger	09/2014
9808	(185*10^99466-11)/3	99468	Robert Price	10/2020
9809	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
9810	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
9811	(516*32^66077-175)/31	99458	Eric Chen	04/2023
9812	(2863^28771-1)/2862	99453	Serge Batalov	06/2022
9813	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
9814	179^44142-44142^179	99446	Norman Luhn	08/2024
9815	(68*10^99441+7)/3	99443	Robert Price	03/2016
9816	10^99434+155571	99435	Patrick De Geest	04/2020
9817	10^99434-123456789	99434	Robert Price	02/2020
9818	10^99434-191237	99434	Patrick De Geest	04/2020
9819	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
9820	23839^14802+14802^23839	99417	Hans Havermann	02/2018
9821	(2*10^99408+529)/9	99408	Robert Price	01/2017
9822	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
9823	53^57646-2	99398	Lelio R Paula	09/2013
9824	2^330165+1870025	99390	Enzo Doria	05/2016
9825	7*10^99383+97	99384	Robert Price	09/2021
9826	2^330142-155	99383	Lelio R Paula	12/2012
9827	2^330088-115259	99367	Enzo Doria	06/2015
9828	24216^12671+12671^24216	99354	Hans Havermann	01/2018
9829	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
9830	(746*10^99303+1)/9	99305	Robert Price	02/2017
9831	3^208107+40	99293	Lelio R Paula	08/2016
9832	2^329843+211343	99293	Enzo Doria	08/2023
9833	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
9834	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
9835	8*3^208093+5	99287	Lelio R Paula	08/2014
9836	5^142043+56	99284	Lelio R Paula	08/2016
9837	(13*10^99282-157)/9	99283	Robert Price	05/2021
9838	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
9839	22*10^99275+7	99277	Robert Price	04/2016
9840	2^329778+1876189	99274	Enzo Doria	07/2016
9841	(149557^19321-1)/(149557^139-1)	99264	Ryan Propper	11/2023
9842	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
9843	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
9844	(10^99239-13)/3	99239	Robert Price	02/2017
9845	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
9847	3^207987+62	99236	Lelio R Paula	08/2016
9846	(62*10^99235+91)/9	99236	Robert Price	07/2021
9848	2^329638+49	99231	Lelio R Paula	12/2012
9849	7^117413-18	99226	Lelio R Paula	08/2016
9850	2^329586-458903	99216	Enzo Doria	04/2015
9851	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
9853	2^329553+101	99206	Lelio R Paula	12/2012
9852	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
9854	2^329551-112897	99205	Enzo Doria	06/2014
9855	(3^207925+7)/50	99204	Lelio R Paula	09/2013
9856	U(477331)/57279721	99202	Serge Batalov	07/2024
9857	6^127458-17993	99182	Enzo Doria	03/2013
9858	27197^4428+4428^27197	99166	Hans Havermann	10/2017
9859	(46*10^99143-1)/9	99144	Robert Price	12/2014
9860	(64*10^99135+161)/9	99136	Robert Price	08/2022
9861	7*10^99133+69	99134	Robert Price	10/2017
9862	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
9863	18^78968-3065	99127	Enzo Doria	03/2013
9864	25927^6654+6654^25927	99122	Hans Havermann	10/2017
9865	87915!4+16	99122	Robert Price	09/2019
9866	2^329259+189	99117	Lelio R Paula	12/2012
9867	8*10^99113+39	99114	Robert Price	01/2017
9868	6^127364+77	99109	Lelio R Paula	08/2016
9869	(82*10^99103+143)/9	99104	Robert Price	06/2021
9870	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
9871	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
9872	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
9873	(59*10^99069+391)/9	99070	Robert Price	03/2021
9874	(797*10^99061-41)/9	99063	Robert Price	04/2022
9875	2^329058-287681	99057	Harrison Mesh	06/2022
9876	6^127285+13	99047	Lelio R Paula	08/2016
9877	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
9878	2^329007+73283	99041	Enzo Doria	04/2016
9879	(145413^19321-1)/(145413^139-1)	99030	Ryan Propper	11/2023
9880	5*3^207543-8	99024	Lelio R Paula	08/2014
9881	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
9882	2^328885+149	99005	Lelio R Paula	12/2012
9883	23392^17075+17075^23392	99004	Hans Havermann	09/2017
9884	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
9885	(2^328879-9)/119	99001	Lelio R Paula	10/2013
9886	140^46129-46129^140	98999	Norman Luhn	08/2024
9887	169^44432-44432^169	98990	Norman Luhn	08/2024
9888	5^141618+54	98987	Lelio R Paula	08/2016
9889	2^328824+24391	98986	Enzo Doria	10/2023
9890	8*10^98982+51	98983	Robert Price	05/2017
9891	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
9892	2^328794-2797601	98977	Enzo Doria	04/2016
9893	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
9894	6^127176+5	98963	Lelio R Paula	11/2014
9895	2*10^98961-21	98962	Robert Price	09/2020
9896	24262^11989+11989^24262	98960	Hans Havermann	09/2017
9897	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
9898	2^328700-109709	98949	Enzo Doria	04/2014
9899	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
9900	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
9901	87771!4-128	98944	Robert Price	11/2019
9902	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
9903	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
9904	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
9905	46711!2-2^46711	98916	Robert Price	09/2015
9906	9*7^117037+4	98909	Lelio R Paula	11/2014
9907	127^47012+126	98905	Norbert Schneider	01/2019
9908	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
9910	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
9909	2^328524+625	98896	Henri Lifchitz	09/2024
9911	(10^98890+149)/3	98890	Serge Batalov	12/2014
9912	22775^21978+21978^22775	98889	Hans Havermann	08/2017
9913	2^328497-216933	98888	Enzo Doria	05/2014
9914	2^328487+32769	98885	Lelio R Paula	08/2016
9915	3^207250-112358	98884	Enzo Doria	06/2014
9916	13^88754-90	98867	Lelio R Paula	08/2016
9917	2^328406+709	98861	Lelio R Paula	02/2013
9918	2*10^98860-21	98861	Robert Price	09/2020
9919	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
9920	7^116976+76	98857	Lelio R Paula	08/2016
9921	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
9922	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
9923	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
9925	2^328335+1155	98839	Lelio R Paula	08/2016
9924	2^328333-349003	98839	Harrison Mesh	06/2022
9927	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
9926	287^40210+40210^287	98832	Norbert Schneider	11/2014
9928	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
9929	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
9930	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
9931	24746^9825+9825^24746	98795	Hans Havermann	07/2020
9932	26620^5143+5143^26620	98793	Hans Havermann	07/2020
9933	65^54491+48	98788	Lelio R Paula	04/2016
9934	3^207042+98	98785	Lelio R Paula	08/2016
9935	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
9936	10^98754+73383	98755	Patrick De Geest	02/2021
9939	3^206977-112756	98754	Enzo Doria	07/2014
9938	10^98754-40000000001	98754	Robert Price	09/2020
9937	10^98754-169343	98754	Patrick De Geest	02/2021
9940	7^116846-50	98747	Lelio R Paula	08/2016
9941	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
9942	23267^17512+17512^23267	98730	Hans Havermann	04/2020
9943	2^327967-28635	98728	Lelio R Paula	08/2016
9944	707^34642+34642^707	98710	Norbert Schneider	12/2017
9945	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
9946	6^126850-47	98709	Lelio R Paula	08/2016
9947	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
9948	(22*10^98697+47)/3	98698	Robert Price	06/2021
9949	(139706^19321-1)/(139706^139-1)	98696	Ryan Propper	11/2023
9950	8*6^126830-7	98694	Lelio R Paula	11/2014
9951	11^94770-270	98693	Enzo Doria	08/2012
9952	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
9953	2^327832+43	98688	Lelio R Paula	12/2012
9954	2^327795+761	98677	Lelio R Paula	02/2013
9955	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
9956	10^98669+147411	98670	Patrick De Geest	11/2016
9958	10^98669-9^(98669-1)	98669	Robert Price	05/2016
9957	10^98669-105249	98669	Patrick De Geest	11/2016
9959	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
9960	2^327671-109801	98639	Enzo Doria	04/2014
9961	24398^11037+11037^24398	98638	Hans Havermann	10/2019
9962	5^141090-14	98618	Lelio R Paula	08/2016
9963	20^75799+47	98617	Lelio R Paula	08/2016
9964	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
9965	28101^3226+3226^28101	98597	Hans Havermann	07/2020
9966	2^327515-1017	98592	Lelio R Paula	08/2016
9967	6^126692+97681	98586	Mike Oakes	04/2011
9968	2^327467-741	98578	Lelio R Paula	08/2016
9969	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
9970	22713^21800+21800^22713	98540	Hans Havermann	05/2020
9971	(2^327329+9)/19	98535	Lelio R Paula	10/2013
9972	7^116577-66	98519	Lelio R Paula	08/2016
9973	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
9974	23220^17479+17479^23220	98512	Hans Havermann	03/2020
9975	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
9976	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
9977	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
9978	2^327162-66945	98486	Lelio R Paula	08/2016
9979	30139^1852+1852^30139	98484	Hans Havermann	02/2020
9980	23182^17703+17703^23182	98479	Hans Havermann	01/2020
9981	4*10^98472-3	98473	Erik Branger	11/2013
9982	26167^5794+5794^26167	98466	Hans Havermann	01/2020
9983	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
9984	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
9985	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
9986	13^88363+94	98432	Lelio R Paula	08/2016
9987	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
9988	6^126481+41	98422	Lelio R Paula	08/2016
9989	78*10^98413-7	98415	Robert Price	05/2017
9990	22634^22263+22263^22634	98404	Hans Havermann	07/2020
9991	(47*10^98386+241)/9	98387	Robert Price	06/2022
9992	7^116416+46	98383	Lelio R Paula	08/2016
9993	7^116407-24	98376	Lelio R Paula	07/2016
9994	439^37228+37228^439	98374	Norbert Schneider	08/2018
9995	2^326782-1860671	98372	Enzo Doria	03/2016
9996	17^79948+58	98372	Lelio R Paula	08/2016
9997	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
9998	3^206143-98	98356	Lelio R Paula	08/2016
9999	8*5^140705+7	98350	Lelio R Paula	11/2014
10000	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295829 PRPs in the top)