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 ?
3501	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3502	6^125418-5	97595	Lelio R Paula	11/2014
3503	2^324076+1155	97557	Lelio R Paula	07/2016
3504	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3505	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3506	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3507	2^323946+73939	97518	Enzo Doria	04/2016
3508	2^323937+1866947	97515	Enzo Doria	03/2016
3509	6^125290-18533	97495	Enzo Doria	03/2013
3510	2^323845+101	97488	Lelio R Paula	12/2012
3511	18^77662+65	97487	Lelio R Paula	07/2016
3512	2^323772+76771	97466	Enzo Doria	05/2016
3513	2^323765-112213	97463	Enzo Doria	06/2014
3514	2^323720-6555	97450	Lelio R Paula	07/2016
3515	2^323694-1860401	97442	Enzo Doria	03/2016
3516	20^74886+3	97429	Lelio R Paula	06/2016
3518	3*10^97399+73	97400	Robert Price	04/2016
3517	7^115252-50	97400	Lelio R Paula	07/2016
3519	224737#+393581	97389	Nicolas PALAU	12/2016
3520	(26*10^97353+31)/3	97354	Robert Price	07/2016
3521	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3522	(38*10^97329+187)/9	97330	Robert Price	11/2017
3523	p(19982)#/2-1024	97293	Robert Price	09/2017
3524	6^125021-85	97286	Lelio R Paula	08/2016
3525	2^323164-47355	97283	Lelio R Paula	07/2016
3526	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3527	2^323054-6555	97249	Lelio R Paula	07/2016
3528	9*10^97247-29	97248	Robert Price	05/2017
3529	(31*10^97242+41)/9	97243	Robert Price	04/2015
3530	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3531	12^90098-41	97233	Lelio R Paula	07/2016
3532	2^322928-216929	97212	Enzo Doria	05/2014
3533	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3534	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3535	2^322725+75761	97150	Enzo Doria	04/2016
3536	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3537	(41*10^97085+373)/9	97086	Robert Price	04/2017
3538	2^322413+77	97056	Lelio R Paula	12/2012
3539	2^322406+177	97054	Lelio R Paula	12/2012
3540	(14*10^97044+31)/9	97045	Robert Price	02/2015
3541	2^322302+255255	97023	Lelio R Paula	07/2016
3542	2^322196-113093	96991	Enzo Doria	07/2014
3543	2^322000-1861469	96932	Enzo Doria	03/2016
3544	2^321971-112747	96923	Enzo Doria	06/2014
3545	11^93062-92	96915	Lelio R Paula	06/2016
3546	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3547	3^203051+34	96880	Lelio R Paula	05/2016
3548	2*10^96867-51	96868	Robert Price	11/2017
3549	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3550	2^321716-2786939	96847	Enzo Doria	03/2016
3551	2^321701-113053	96842	Enzo Doria	07/2014
3552	2^321700-28635	96842	Lelio R Paula	06/2016
3553	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3554	6^124433-124433	96828	Robert Price	01/2014
3555	2^321631+69	96821	Lelio R Paula	12/2012
3556	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3557	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3558	(59*10^96798+31)/9	96799	Robert Price	09/2015
3559	223319#+231223	96790	Makoto Morimoto	02/2016
3560	2^321519-28635	96787	Lelio R Paula	06/2016
3561	2^321487-1867237	96778	Enzo Doria	03/2016
3562	2^321461-63	96770	Lelio R Paula	12/2012
3563	2^321439+123	96763	Lelio R Paula	12/2012
3564	2^321434+709	96762	Lelio R Paula	02/2013
3565	14^84413+89	96749	Lelio R Paula	07/2016
3566	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3567	13^86847+96	96743	Lelio R Paula	06/2016
3568	9*2^321336-7	96733	Lelio R Paula	08/2014
3569	(209*10^96722-17)/3	96724	Robert Price	05/2017
3570	2^321187-1159	96687	Yves Minet	11/2012
3571	2^321182-1850081	96686	Enzo Doria	08/2015
3572	2^321116-112829	96666	Enzo Doria	06/2014
3573	2^321108-109499	96664	Enzo Doria	04/2014
3574	2^321098+2793859	96661	Enzo Doria	03/2016
3575	2^321057+4097	96648	Lelio R Paula	06/2016
3576	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3577	p(19849)#/2-64	96581	Robert Price	04/2017
3578	2^320817+189	96576	Lelio R Paula	12/2012
3579	(361*10^96567-163)/9	96569	Robert Price	10/2017
3580	2^320788-110327	96567	Enzo Doria	05/2014
3581	2^320764+793	96560	Lelio R Paula	02/2013
3582	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3583	2^320616-78795	96516	Lelio R Paula	03/2016
3584	2^320612-461939	96514	Enzo Doria	07/2015
3585	5*2^320431+7	96461	Lelio R Paula	08/2014
3586	19^75431-90	96458	Lelio R Paula	06/2016
3587	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3588	2^320309+1871477	96423	Enzo Doria	05/2016
3589	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3590	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3591	2^320232-173	96400	Lelio R Paula	12/2012
3592	175^42975-2	96395	Lelio R Paula	10/2017
3593	10^96377+199911	96378	Patrick De Geest	12/2016
3594	10^96377-20001	96377	Robert Price	11/2016
3595	2^320124-2790449	96367	Enzo Doria	03/2016
3596	2^320043-108775	96343	Enzo Doria	04/2014
3597	10^96338+424939	96339	Patrick De Geest	03/2016
3598	10^96338-9281	96338	Robert Price	09/2015
3599	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3600	2^319838+4257	96281	Lelio R Paula	03/2016
3601	2^319830-16995	96279	Lelio R Paula	03/2016
3602	6^123713+143	96268	Lelio R Paula	05/2016
3603	(28*10^96265-97)/3	96266	Robert Price	07/2016
3604	103^47825-102	96264	Norbert Schneider	10/2016
3605	2^319713-81	96244	Lelio R Paula	11/2012
3606	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3607	12^89153-43	96213	Lelio R Paula	06/2016
3608	(2*10^96195-59)/3	96195	Robert Price	05/2017
3609	2^319545+147	96193	Lelio R Paula	11/2012
3610	(50^56597+1)/51	96155	Robert Price	03/2014
3611	(41*10^96137-59)/9	96138	Robert Price	10/2017
3612	2^319353-110343	96135	Enzo Doria	05/2014
3613	11^92309-42	96130	Lelio R Paula	05/2016
3614	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3615	(7*10^96112+143)/3	96113	Robert Price	04/2016
3616	2^319237+65835	96100	Lelio R Paula	03/2016
3617	2^319194-1841	96087	Yves Minet	03/2013
3618	20^73847-31	96078	Lelio R Paula	05/2016
3619	2^319107-109555	96061	Enzo Doria	04/2014
3620	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3621	2^319098-112157	96059	Enzo Doria	06/2014
3622	15^81673+94	96055	Lelio R Paula	07/2016
3623	2^319074+1871749	96051	Enzo Doria	05/2016
3624	2^319007-112111	96031	Enzo Doria	06/2014
3625	2^318946-1421	96013	Yves Minet	01/2013
3626	2^318834-110411	95979	Enzo Doria	05/2014
3627	2^318831-1965	95978	Lelio R Paula	03/2016
3628	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3629	5*3^201089-8	95945	Lelio R Paula	08/2014
3630	2^318711-139	95942	Lelio R Paula	11/2012
3631	2^318635-1167	95919	Lelio R Paula	03/2016
3632	15^81555+16	95917	Lelio R Paula	07/2016
3633	(37*10^95895+377)/9	95896	Robert Price	10/2017
3634	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
3635	2^318496-97305	95877	Lelio R Paula	03/2016
3636	2^318466+15015	95868	Lelio R Paula	03/2016
3637	6^123187-173129	95859	Mike Oakes	04/2011
3638	2^318423-487	95855	Yves Minet	03/2012
3639	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
3640	45369!2+1024	95787	Robert Price	02/2015
3641	3^200758-86	95786	Lelio R Paula	05/2016
3642	3*10^95776-59	95777	Robert Price	10/2017
3643	193^41901-2	95768	Lelio R Paula	10/2017
3644	4*10^95752-71	95753	Robert Price	11/2017
3645	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
3646	4*10^95672+91	95673	Robert Price	11/2017
3647	(11*10^95641-113)/3	95642	Robert Price	01/2017
3648	(13*10^95588+11)/3	95589	Robert Price	05/2015
3649	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
3650	3^200325+70	95580	Lelio R Paula	05/2016
3651	(25*10^95574-7)/9	95575	Robert Price	12/2014
3652	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
3653	2^317464+31	95567	Lelio R Paula	11/2012
3654	7^113073+82	95558	Lelio R Paula	04/2016
3655	2^317251+465	95503	Lelio R Paula	03/2016
3656	19^74684+58	95503	Lelio R Paula	06/2016
3657	(2^317250-7)/339	95500	Lelio R Paula	07/2013
3658	6^122718-79	95494	Lelio R Paula	05/2016
3659	2^317141-110491	95469	Enzo Doria	05/2014
3660	2^317094+76309	95455	Enzo Doria	05/2016
3661	2^317085+95	95453	Lelio R Paula	11/2012
3662	(17*10^95451-377)/9	95452	Robert Price	11/2017
3663	2^317057-109551	95444	Enzo Doria	04/2014
3664	3^200026+28	95437	Lelio R Paula	05/2016
3665	2^317024+93	95434	Donovan Johnson	06/2008
3666	2^316999+1605	95427	Lelio R Paula	03/2016
3667	2^316995-110427	95426	Enzo Doria	05/2014
3669	2^316937+177	95408	Lelio R Paula	11/2012
3668	4*10^95407+91	95408	Robert Price	11/2017
3670	2^316908+1915	95399	Lelio R Paula	03/2016
3671	2^316894+99	95395	Lelio R Paula	11/2012
3672	6^122547+11	95361	Lelio R Paula	05/2016
3673	2^316771+82875	95358	Lelio R Paula	03/2016
3675	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
3674	1*10^95326+57	95327	Robert Price	03/2011
3676	10^95326-393687	95326	Patrick De Geest	09/2013
3677	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
3678	2^316654-109481	95323	Enzo Doria	04/2014
3679	8*10^95316+51	95317	Robert Price	05/2017
3680	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
3681	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
3682	(71*10^95277-539)/9	95278	Robert Price	11/2017
3683	19^74503-56	95271	Lelio R Paula	06/2016
3684	11^91475-4380	95262	Enzo Doria	01/2013
3685	(62*10^95251-611)/9	95252	Robert Price	05/2017
3686	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
3687	(79*10^95214-43)/9	95215	Erik Branger	11/2013
3688	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
3689	5*2^316213+9	95191	Lelio R Paula	08/2014
3690	2^316205-1848163	95188	Enzo Doria	07/2015
3691	2^316185-2787913	95182	Enzo Doria	04/2016
3692	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
3693	2^316140-5	95168	Henri Lifchitz	02/2006
3694	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
3695	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
3696	2^316069+76817	95147	Enzo Doria	05/2016
3697	(199*10^95134-7)/3	95136	Robert Price	02/2017
3698	2^316027-97305	95134	Lelio R Paula	03/2016
3699	2^316006-2798051	95128	Enzo Doria	04/2016
3700	2^315921-2797603	95102	Enzo Doria	04/2016
3701	2*10^95095+63	95096	Robert Price	10/2017
3702	2^315857+1299	95083	Lelio R Paula	03/2016
3703	14^82955-43	95078	Lelio R Paula	06/2016
3704	(2*10^95072-17)/3	95072	Robert Price	08/2014
3705	2^315727+65	95044	Lelio R Paula	11/2012
3706	2^315725+1885757	95043	Enzo Doria	03/2017
3707	1*10^94983+21	94984	Robert Price	03/2011
3708	10^94983-717	94983	Patrick De Geest	08/2013
3709	17^77187-82	94975	Lelio R Paula	07/2016
3710	3*10^94964+37	94965	Robert Price	10/2017
3711	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
3712	2^315423-110329	94952	Enzo Doria	05/2014
3713	11^91169-7230	94943	Enzo Doria	02/2013
3714	7*10^94938+61	94939	Robert Price	02/2017
3715	2^315351+1025	94931	Lelio R Paula	03/2016
3716	2^315350-112253	94930	Enzo Doria	06/2014
3717	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
3718	2^315268+7	94906	Lelio R Paula	10/2012
3719	11^91133+62	94906	Lelio R Paula	05/2016
3720	30^64244+41	94897	Lelio R Paula	08/2012
3721	(151*10^94885-7)/9	94887	Robert Price	07/2017
3722	4^157583+22147	94875	Mike Oakes	01/2011
3723	2^315098+123	94854	Lelio R Paula	11/2012
3724	3^198791-34	94848	Robert Price	11/2013
3725	3*2^315067+7	94846	Lelio R Paula	08/2014
3726	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
3727	(16*10^94822+53)/3	94823	Robert Price	12/2016
3728	8*6^121849-7	94818	Lelio R Paula	10/2014
3729	(85*10^94802+473)/9	94803	Robert Price	03/2017
3730	2^314870-108761	94786	Enzo Doria	03/2014
3731	5*2^314841-3	94778	Lelio R Paula	08/2014
3732	6^121772+113	94758	Lelio R Paula	05/2016
3733	6^121756-16253	94745	Enzo Doria	02/2013
3734	2^314718-112793	94740	Enzo Doria	06/2014
3735	2^314697-1847293	94734	Enzo Doria	07/2015
3736	2^314548-249	94689	Yves Minet	02/2012
3737	5^135469+42	94689	Lelio R Paula	04/2016
3738	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
3739	(2*10^94604+547)/9	94604	Robert Price	10/2017
3740	3*2^314152+5	94570	Lelio R Paula	08/2014
3741	2*6^121530-5	94570	Lelio R Paula	10/2014
3742	7*10^94563+87	94564	Robert Price	11/2016
3743	2^314114-109677	94558	Enzo Doria	04/2014
3744	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
3745	2^314059+76583	94542	Enzo Doria	05/2016
3746	2^314041-4035	94536	Lelio R Paula	03/2016
3747	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
3748	11^90760-4710	94517	Enzo Doria	01/2013
3749	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
3750	94*10^94493-3	94495	Robert Price	11/2016

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)