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 ?
3501	(19*10^168173+77)/3	168174	Robert Price	05/2019
3502	(74*10^168170+529)/9	168171	Robert Price	02/2022
3503	2^558640-114149	168168	Enzo Doria	12/2014
3504	2^558498-1849277	168125	Enzo Doria	08/2015
3505	2^558476-1850249	168119	Enzo Doria	08/2015
3506	(7*10^168067+71)/3	168068	Robert Price	05/2018
3507	2^558150-1852211	168020	Enzo Doria	08/2015
3508	2^558125-113661	168013	Enzo Doria	09/2014
3509	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
3510	(8*10^167965-11)/3	167966	Robert Price	07/2023
3511	2^557916+216151	167950	Enzo Doria	12/2023
3512	(13*10^167911+179)/3	167912	Robert Price	11/2018
3513	(26*10^167861-167)/3	167862	Robert Price	10/2019
3514	36^107827-107827	167812	Kellen Shenton	06/2023
3515	32027^37242-37242^32027	167795	Frank Doornink	01/2024
3516	39^105456+2	167788	Robert Price	04/2015
3517	2^557322+217519	167771	Enzo Doria	01/2024
3518	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
3519	6*10^167662-13	167663	Robert Price	07/2022
3520	10^167639+121911	167640	Patrick De Geest	07/2018
3521	10^167639-8001	167639	Robert Price	03/2018
3522	2^556504-462059	167525	Enzo Doria	07/2015
3523	(88*10^167522-637)/9	167523	Robert Price	11/2020
3524	5*10^167510+9	167511	Robert Price	08/2015
3525	7*10^167437-93	167438	Robert Price	08/2020
3526	(43^102451-1)/7138097213378082	167335	Paul Vanderveen	05/2025
3527	25455^37978-37978^25455	167323	Frank Doornink	01/2024
3528	11^160663+6	167314	Paul Bourdelais	02/2021
3529	(7*10^167308-493)/9	167308	Robert Price	04/2021
3530	2^555759+74333	167301	Enzo Doria	07/2023
3531	26084^37871-37871^26084	167253	Frank Doornink	03/2024
3532	2^555343+1874333	167175	Enzo Doria	06/2016
3533	2^555210-461261	167135	Enzo Doria	07/2015
3534	9*10^166996+59	166997	Robert Price	01/2020
3535	(68*10^166976-329)/9	166977	Robert Price	03/2021
3536	(64*10^166901+683)/9	166902	Robert Price	06/2022
3537	2^554372+1880527	166883	Enzo Doria	11/2016
3538	2^554299+72173	166861	Enzo Doria	04/2016
3539	(185*10^166837+7)/3	166839	Robert Price	03/2020
3540	(14*10^166813+139)/9	166814	Robert Price	11/2021
3541	26084^37767-37767^26084	166794	Frank Doornink	03/2024
3542	2^554037-2797063	166782	Enzo Doria	03/2016
3543	31861^37028-37028^31861	166747	Frank Doornink	01/2024
3544	(49*10^166721-139)/9	166722	Robert Price	03/2019
3545	2*10^166646+69	166647	Robert Price	06/2020
3546	2^553484-29819	166616	Enzo Doria	08/2015
3547	(188*10^166611+7)/3	166613	Robert Price	03/2020
3548	2^553383-2784217	166585	Enzo Doria	10/2015
3549	2^553069+76427	166491	Enzo Doria	05/2016
3550	25218^37819-37819^25218	166469	Frank Doornink	12/2023
3551	2*10^166458+51	166459	Robert Price	05/2018
3552	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
3553	25214^37799-37799^25214	166378	Frank Doornink	11/2023
3554	11^159756-2424	166369	Mike Oakes	06/2010
3555	2^552649-361275	166364	Enzo Doria	05/2014
3556	2^552628-113669	166358	Enzo Doria	09/2014
3557	(19*10^166325+137)/3	166326	Robert Price	03/2022
3558	10^166324+550603	166325	Patrick De Geest	07/2018
3559	10^166324-801	166324	Robert Price	02/2018
3560	(85*10^166297-1)/3	166299	Robert Price	02/2020
3561	(19*10^166280-7)/3	166281	Robert Price	12/2023
3562	25533^37726-37726^25533	166263	Frank Doornink	02/2024
3563	8*10^166227+87	166228	Robert Price	10/2019
3564	2^552137+1879397	166210	Enzo Doria	09/2016
3565	262273205671539190984629()252475512364409752762433	166141	Anonymous	01/2025
3566	490079063773165613318095()218182139934160868002603	166141	Anonymous	01/2025
3567	140717254840416411192803()712689271538459396766869	166140	Anonymous	01/2025
3568	122398296040696255481419()271117913237372866926417	166140	Anonymous	01/2025
3569	(103*10^166126+11)/3	166128	Robert Price	01/2021
3570	(22*10^166077+179)/3	166078	Robert Price	02/2022
3571	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
3572	2^551576+236221	166041	Enzo Doria	05/2025
3573	2^551542+19249	166031	Payam Samidoost	08/2002
3574	2^551535-23821	166029	Enzo Doria	08/2013
3575	2^551507-23557	166021	Enzo Doria	08/2013
3576	32030^36841-36841^32030	165990	Frank Doornink	01/2024
3577	10^165947-7000000001	165947	Robert Price	12/2021
3578	4*10^165938-47	165939	Robert Price	10/2021
3579	7*10^165916-3	165917	Robert Price	08/2015
3580	(29*10^165796+67)/3	165797	Robert Price	12/2019
3581	81^86837-80^86837	165728	Robert Price	01/2015
3582	(71*10^165716-17)/9	165717	Serge Batalov	01/2023
3583	fibonacci(792909)+3	165708	Jon Grantham	08/2023
3584	(71*10^165663-539)/9	165664	Robert Price	07/2019
3585	25682^37567-37567^25682	165657	Frank Doornink	02/2024
3586	2^550270-69551	165648	Enzo Doria	12/2015
3587	2^550250+29329	165642	Enzo Doria	03/2024
3588	(202*10^165569-13)/9	165571	Robert Price	01/2020
3589	2^550000-23625	165567	Enzo Doria	08/2013
3590	31688^36783-36783^31688	165557	Frank Doornink	01/2024
3591	2^549675-1852057	165469	Enzo Doria	08/2015
3592	2^549663+212543	165466	Enzo Doria	08/2023
3593	(3^549633)%(2^549633)	165456	Henri Lifchitz	06/2025
3594	(529*10^165394-7)/9	165396	Robert Price	08/2021
3595	26253^37424-37424^26253	165384	Frank Doornink	03/2024
3596	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
3597	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
3598	2^549278+1879669	165350	Enzo Doria	09/2016
3599	(7*10^165350-439)/9	165350	Robert Price	02/2018
3600	2^549252-351269	165342	Enzo Doria	06/2015
3601	2^549221+335931	165332	Enzo Doria	09/2024
3602	67*10^165327-9	165329	Robert Price	03/2021
3603	(14*10^165282+73)/3	165283	Robert Price	12/2018
3604	(8*10^165283-629)/9	165283	Robert Price	01/2022
3605	2^549049+2797607	165281	Enzo Doria	04/2016
3606	(218*10^165258+7)/9	165260	Robert Price	06/2022
3607	(7*10^165239+107)/3	165240	Robert Price	02/2018
3608	2^548880+23961	165230	Enzo Doria	10/2023
3609	5*2^548778+3	165200	Jon Grantham	07/2023
3610	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
3611	(7*10^165134+107)/3	165135	Robert Price	02/2018
3612	(301*10^165082+23)/9	165084	Robert Price	06/2021
3613	(23*10^165060-83)/3	165061	Robert Price	08/2019
3614	7*10^165023-27	165024	Robert Price	11/2022
3615	(76*10^164984+77)/9	164985	Robert Price	10/2019
3616	31058^36715-36715^31058	164931	Frank Doornink	01/2024
3617	(4*10^164929-211)/9	164929	Robert Price	03/2022
3618	10^164878-500001	164878	Robert Price	03/2022
3619	9*10^164791-89	164792	Robert Price	04/2020
3620	(2^788414)%F(788414)	164769	Henri Lifchitz	05/2025
3621	2^547178-1856501	164717	Enzo Doria	10/2015
3622	11^158160-60	164707	Enzo Doria	07/2012
3623	(26*10^164643-167)/3	164644	Robert Price	10/2019
3624	(10^164643+83)/3	164643	Robert Price	08/2021
3625	2^546398-59201	164483	Enzo Doria	10/2015
3626	2^546332-114893	164463	Enzo Doria	05/2015
3627	36087^36087-36080^36080	164462	Henri Lifchitz	08/2024
3628	32003^36504-36504^32003	164458	Frank Doornink	01/2024
3629	(65*10^164427+277)/9	164428	Robert Price	08/2021
3630	2^545958+1876189	164350	Enzo Doria	07/2016
3631	2^545878-49841	164326	Enzo Doria	10/2015
3632	(10^164284+77)/3	164284	Robert Price	01/2018
3633	2^545668-4019	164263	Yves Minet	04/2017
3634	10^164216+780639	164217	Patrick De Geest	08/2021
3636	10^164216-50000000001	164216	Robert Price	12/2020
3635	10^164216-891051	164216	Patrick De Geest	08/2021
3637	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
3638	(16*10^164122+197)/3	164123	Robert Price	04/2019
3639	2^545185+76757	164118	Enzo Doria	05/2016
3640	2^545076-114329	164085	Enzo Doria	01/2015
3641	(2*10^164043-143)/3	164043	Robert Price	03/2018
3642	(33085^36481-1)/(33085^191-1)	164018	Ryan Propper	11/2023
3643	(29^112153+1)/30	164011	Lelio R Paula	03/2017
3644	2^544757+1874777	163989	Enzo Doria	06/2016
3645	2^544723+211193	163978	Enzo Doria	08/2023
3646	2^544444-457199	163894	Enzo Doria	01/2015
3647	(32804^36481-1)/(32804^191-1)	163883	Ryan Propper	11/2023
3648	2^544264-343529	163840	Enzo Doria	07/2015
3649	7*10^163780+9	163781	Robert Price	09/2015
3650	(2^783598)%L(783598)	163761	Henri Lifchitz	05/2025
3651	2^543989+2793047	163758	Enzo Doria	02/2016
3652	(28*10^163709+113)/3	163710	Robert Price	03/2020
3653	(2^543398)/(543398^2)	163568	Henri Lifchitz	05/2025
3654	(2013^49729-1)/(2013^223-1)	163561	Ryan Propper	11/2023
3655	L(2*543272)%(2^543272)	163541	Henri Lifchitz	07/2025
3656	(23*10^163523+301)/9	163524	Robert Price	06/2021
3657	(68*10^163521-329)/9	163522	Robert Price	03/2021
3658	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
3659	2^542870-69551	163421	Enzo Doria	12/2015
3660	2^542502+24799	163310	Enzo Doria	10/2023
3661	2^542395+72533	163278	Enzo Doria	04/2016
3662	2^542258+216949	163236	Enzo Doria	12/2023
3663	2^542072-3683	163180	Yves Minet	03/2017
3664	fibonacci(780566)-4	163129	Jon Grantham	08/2023
3665	(682*10^163106-7)/9	163108	Robert Price	08/2021
3666	2^541779-1867357	163092	Enzo Doria	04/2016
3667	(29*10^163056+313)/9	163057	Robert Price	04/2021
3668	2^541476+214743	163001	Enzo Doria	11/2023
3669	13^142159+14^142159-2	162933	Harsh Aggarwal	05/2024
3670	8*10^162924+9	162925	Robert Price	12/2015
3671	2^540905+81557	162829	Enzo Doria	08/2016
3672	2^540628-2939	162746	Yves Minet	09/2014
3673	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
3674	(203*10^162689+1)/3	162691	Robert Price	03/2020
3675	3*10^162620-59	162621	Robert Price	09/2018
3676	2^540180+26791	162611	Enzo Doria	12/2023
3677	3^340694-112960	162553	Enzo Doria	07/2014
3678	2^539925+81	162534	Henri Lifchitz	11/2024
3679	2^539807-114081	162499	Enzo Doria	12/2014
3680	414^62093+62093^414	162498	Norbert Schneider	03/2022
3681	2^539654-114893	162453	Enzo Doria	05/2015
3682	9*10^162449-71	162450	Robert Price	11/2020
3683	2^539617-1851583	162441	Enzo Doria	08/2015
3684	(509*10^162422+31)/9	162424	Robert Price	08/2022
3685	(91*10^162410+11)/3	162412	Robert Price	02/2020
3686	2^539346+81049	162360	Enzo Doria	07/2016
3687	2^539220-115499	162322	Enzo Doria	07/2015
3688	2^539217-113713	162321	Enzo Doria	09/2014
3689	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
3690	4*10^162263-39	162264	Robert Price	09/2020
3691	31243^36098-36098^31243	162252	Frank Doornink	01/2024
3692	31987^36000-36000^31987	162180	Frank Doornink	01/2024
3693	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
3694	(10^162138+11)/3	162138	Serge Batalov	07/2015
3695	(61*10^162100-403)/9	162101	Robert Price	10/2021
3696	2^538473-112723	162097	Enzo Doria	06/2014
3697	2^538157+79337	162002	Enzo Doria	06/2016
3698	2^538136-114749	161996	Enzo Doria	05/2015
3699	2^538104+1531	161986	Lelio R Paula	01/2013
3700	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
3701	((2^179294-1)^3+2)/11	161918	Serge Batalov	03/2023
3702	31198^36027-36027^31198	161910	Frank Doornink	01/2024
3703	2^537815-22737	161899	Enzo Doria	07/2013
3704	2^537804-39839	161896	Enzo Doria	09/2015
3705	(754*10^161816-7)/9	161818	Robert Price	05/2020
3706	2^537461+29867	161792	Enzo Doria	03/2024
3707	2^537458-59201	161791	Enzo Doria	10/2015
3708	2*10^161766+51	161767	Robert Price	05/2018
3709	(7*10^161760+131)/3	161761	Robert Price	06/2020
3710	2^537209-49849	161717	Enzo Doria	10/2015
3711	(58*10^161691+329)/9	161692	Robert Price	05/2019
3712	23*10^161668-3	161670	Robert Price	10/2021
3713	2^536937+1879397	161635	Enzo Doria	09/2016
3714	3*2^536868-5	161614	Jon Grantham	07/2023
3715	34*10^161593-9	161595	Robert Price	06/2020
3716	(31*10^161582-1)/3	161584	Robert Price	02/2020
3717	24494^36813+36813^24494	161575	Norbert Schneider	11/2023
3718	2^536569-22881	161524	Enzo Doria	07/2013
3719	(46*10^161505+593)/9	161506	Robert Price	04/2022
3720	10^161253+573493	161254	Patrick De Geest	07/2018
3721	10^161253-8001	161253	Robert Price	03/2018
3722	97*10^161247-3	161249	Robert Price	05/2020
3723	7*10^161192-9	161193	Robert Price	10/2015
3724	2^535415-19	161176	Stefano Morozzi	07/2022
3725	2^535269-113803	161133	Enzo Doria	09/2014
3726	2^535205-23295	161113	Enzo Doria	08/2013
3727	(49*10^161105+437)/9	161106	Robert Price	09/2021
3728	2^534961+6561	161040	Henri Lifchitz	11/2024
3729	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
3730	35385^35385-17692^17692	160960	Henri Lifchitz	10/2024
3731	2^534429-19	160880	Stefano Morozzi	07/2022
3732	2^534359-23229	160859	Enzo Doria	08/2013
3733	10^160836-1001	160836	Robert Price	10/2022
3734	457^60454+60454^457	160803	Norbert Schneider	07/2021
3735	8*10^160782+53	160783	Robert Price	08/2020
3736	67^88037-66^88037	160763	Robert Price	10/2013
3737	(88*10^160761-637)/9	160762	Robert Price	11/2020
3738	2^533981+81	160745	Henri Lifchitz	11/2024
3739	2^533948-1852559	160735	Enzo Doria	08/2015
3740	(2^769082)%F(769082)	160728	Henri Lifchitz	05/2025
3741	2^533665-23335	160650	Enzo Doria	08/2013
3742	2^533600+217981	160630	Enzo Doria	01/2024
3743	(19*10^160619+77)/3	160620	Robert Price	05/2019
3744	2^533350-5	160555	Stefano Morozzi	07/2022
3745	(38*10^160508+151)/9	160509	Robert Price	03/2022
3746	3^336353-2^336353	160482	Mike Oakes	10/2007
3747	26134^36315-36315^26134	160411	Frank Doornink	03/2024
3748	25821^36358-36358^25821	160411	Frank Doornink	03/2024
3749	2*10^160339-63	160340	Robert Price	01/2022
3750	24419^36532+36532^24419	160293	Norbert Schneider	10/2023

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Probable Primes Top 10000

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