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	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3502	13^88363+94	98432	Lelio R Paula	08/2016
3503	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3504	6^126481+41	98422	Lelio R Paula	08/2016
3505	78*10^98413-7	98415	Robert Price	05/2017
3506	7^116416+46	98383	Lelio R Paula	08/2016
3507	7^116407-24	98376	Lelio R Paula	07/2016
3509	2^326782-1860671	98372	Enzo Doria	03/2016
3508	17^79948+58	98372	Lelio R Paula	08/2016
3510	3^206143-98	98356	Lelio R Paula	08/2016
3511	8*5^140705+7	98350	Lelio R Paula	11/2014
3512	2^326585+11	98312	Lelio R Paula	12/2012
3513	2^326582-459161	98311	Enzo Doria	05/2015
3514	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3515	2^326538+71659	98298	Enzo Doria	04/2016
3516	15^83575-58	98292	Lelio R Paula	08/2016
3517	10^98288+3	98289	Robert Price	03/2011
3518	10^98288-117017	98288	Patrick De Geest	11/2011
3519	(44*10^98284-719)/9	98285	Robert Price	12/2017
3520	2^326421-2797573	98263	Enzo Doria	04/2016
3521	2^326401+16095	98257	Lelio R Paula	07/2016
3522	7^116240-116240^7	98235	Norbert Schneider	05/2017
3523	17^79826-78	98222	Lelio R Paula	08/2016
3524	2^326268-809	98217	Yves Minet	04/2011
3525	(418*10^98199+23)/9	98201	Robert Price	08/2017
3526	12*10^98198-7	98200	Robert Price	11/2017
3527	15^83496-76	98199	Lelio R Paula	08/2016
3528	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3529	9*5^140471-4	98186	Lelio R Paula	11/2014
3530	2^326069-2383	98157	Yves Minet	10/2013
3531	2^325973+1185	98128	Lelio R Paula	07/2016
3532	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3533	2^325945-1847269	98120	Enzo Doria	07/2015
3534	8*10^98111-67	98112	Robert Price	10/2017
3535	2^325866+15	98096	Lelio R Paula	12/2012
3536	2^325765+1974305	98066	Enzo Doria	06/2016
3537	2^325733-58695	98056	Lelio R Paula	07/2016
3538	2^325717-3645	98051	Lelio R Paula	07/2016
3539	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3540	(7*10^98007-13)/3	98008	Robert Price	06/2016
3541	2^325512-459959	97989	Enzo Doria	05/2015
3542	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3543	2^325433+76817	97966	Enzo Doria	05/2016
3544	5*10^97963+81	97964	Robert Price	08/2017
3545	2^325390-109061	97953	Enzo Doria	04/2014
3546	13^87921+24	97940	Lelio R Paula	08/2016
3547	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3548	2^325215+12909	97900	Lelio R Paula	07/2016
3549	7*10^97874-69	97875	Robert Price	01/2017
3551	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3550	15^83212+22	97865	Lelio R Paula	08/2016
3552	2^325087-109057	97861	Enzo Doria	04/2014
3553	2^325074+1870657	97858	Enzo Doria	05/2016
3555	2^325066-2111	97855	Yves Minet	08/2013
3554	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3556	18^77944-89	97841	Lelio R Paula	07/2016
3557	6^125720-17663	97830	Enzo Doria	02/2013
3558	2^324972-2069	97827	Yves Minet	05/2013
3559	2^324944-2788319	97818	Enzo Doria	03/2016
3561	4*10^97799-9	97800	Erik Branger	11/2013
3560	2^324882+577294575	97800	Lelio R Paula	09/2016
3562	2^324863-1867921	97794	Enzo Doria	04/2016
3563	6^125662-18473	97785	Enzo Doria	03/2013
3564	12^90604+11	97779	Lelio R Paula	07/2016
3565	5^139830+24	97737	Lelio R Paula	04/2016
3566	2^324612+1155	97718	Lelio R Paula	07/2016
3567	19^76404-44	97702	Lelio R Paula	07/2016
3568	2^324505-2983	97686	Yves Minet	04/2011
3569	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3570	6^125488-17843	97649	Enzo Doria	02/2013
3571	7^115515-2	97622	Lelio R Paula	09/2013
3572	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3573	6^125418-5	97595	Lelio R Paula	11/2014
3574	2^324076+1155	97557	Lelio R Paula	07/2016
3575	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3576	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3577	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3578	2^323946+73939	97518	Enzo Doria	04/2016
3579	2^323937+1866947	97515	Enzo Doria	03/2016
3580	6^125290-18533	97495	Enzo Doria	03/2013
3581	2^323845+101	97488	Lelio R Paula	12/2012
3582	18^77662+65	97487	Lelio R Paula	07/2016
3583	2^323772+76771	97466	Enzo Doria	05/2016
3584	2^323765-112213	97463	Enzo Doria	06/2014
3585	2^323720-6555	97450	Lelio R Paula	07/2016
3586	2^323694-1860401	97442	Enzo Doria	03/2016
3587	20^74886+3	97429	Lelio R Paula	06/2016
3589	3*10^97399+73	97400	Robert Price	04/2016
3588	7^115252-50	97400	Lelio R Paula	07/2016
3590	224737#+393581	97389	Nicolas PALAU	12/2016
3591	(26*10^97353+31)/3	97354	Robert Price	07/2016
3592	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3593	(38*10^97329+187)/9	97330	Robert Price	11/2017
3594	p(19982)#/2-1024	97293	Robert Price	09/2017
3595	6^125021-85	97286	Lelio R Paula	08/2016
3596	2^323164-47355	97283	Lelio R Paula	07/2016
3597	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3598	2^323054-6555	97249	Lelio R Paula	07/2016
3599	9*10^97247-29	97248	Robert Price	05/2017
3600	(31*10^97242+41)/9	97243	Robert Price	04/2015
3601	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3602	12^90098-41	97233	Lelio R Paula	07/2016
3603	2^322928-216929	97212	Enzo Doria	05/2014
3604	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3605	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3606	2^322725+75761	97150	Enzo Doria	04/2016
3607	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3608	(41*10^97085+373)/9	97086	Robert Price	04/2017
3609	2^322413+77	97056	Lelio R Paula	12/2012
3610	2^322406+177	97054	Lelio R Paula	12/2012
3611	(14*10^97044+31)/9	97045	Robert Price	02/2015
3612	2^322302+255255	97023	Lelio R Paula	07/2016
3613	2^322196-113093	96991	Enzo Doria	07/2014
3614	2^322000-1861469	96932	Enzo Doria	03/2016
3615	2^321971-112747	96923	Enzo Doria	06/2014
3616	11^93062-92	96915	Lelio R Paula	06/2016
3617	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3618	3^203051+34	96880	Lelio R Paula	05/2016
3619	2*10^96867-51	96868	Robert Price	11/2017
3620	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3621	2^321716-2786939	96847	Enzo Doria	03/2016
3623	2^321701-113053	96842	Enzo Doria	07/2014
3622	2^321700-28635	96842	Lelio R Paula	06/2016
3624	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3625	6^124433-124433	96828	Robert Price	01/2014
3626	2^321631+69	96821	Lelio R Paula	12/2012
3627	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3628	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3629	(59*10^96798+31)/9	96799	Robert Price	09/2015
3630	223319#+231223	96790	Makoto Morimoto	02/2016
3631	2^321519-28635	96787	Lelio R Paula	06/2016
3632	2^321487-1867237	96778	Enzo Doria	03/2016
3633	2^321461-63	96770	Lelio R Paula	12/2012
3634	2^321439+123	96763	Lelio R Paula	12/2012
3635	2^321434+709	96762	Lelio R Paula	02/2013
3636	14^84413+89	96749	Lelio R Paula	07/2016
3637	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3638	13^86847+96	96743	Lelio R Paula	06/2016
3639	9*2^321336-7	96733	Lelio R Paula	08/2014
3640	(209*10^96722-17)/3	96724	Robert Price	05/2017
3641	2^321187-1159	96687	Yves Minet	11/2012
3642	2^321182-1850081	96686	Enzo Doria	08/2015
3643	2^321116-112829	96666	Enzo Doria	06/2014
3644	2^321108-109499	96664	Enzo Doria	04/2014
3645	2^321098+2793859	96661	Enzo Doria	03/2016
3646	2^321057+4097	96648	Lelio R Paula	06/2016
3647	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3648	p(19849)#/2-64	96581	Robert Price	04/2017
3649	2^320817+189	96576	Lelio R Paula	12/2012
3650	(361*10^96567-163)/9	96569	Robert Price	10/2017
3651	2^320788-110327	96567	Enzo Doria	05/2014
3652	2^320764+793	96560	Lelio R Paula	02/2013
3653	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3654	2^320616-78795	96516	Lelio R Paula	03/2016
3655	2^320612-461939	96514	Enzo Doria	07/2015
3656	5*2^320431+7	96461	Lelio R Paula	08/2014
3657	19^75431-90	96458	Lelio R Paula	06/2016
3658	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3659	2^320309+1871477	96423	Enzo Doria	05/2016
3660	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3661	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3662	2^320232-173	96400	Lelio R Paula	12/2012
3663	175^42975-2	96395	Lelio R Paula	10/2017
3664	10^96377+199911	96378	Patrick De Geest	12/2016
3665	10^96377-20001	96377	Robert Price	11/2016
3666	2^320124-2790449	96367	Enzo Doria	03/2016
3667	2^320043-108775	96343	Enzo Doria	04/2014
3668	10^96338+424939	96339	Patrick De Geest	03/2016
3669	10^96338-9281	96338	Robert Price	09/2015
3670	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3671	2^319838+4257	96281	Lelio R Paula	03/2016
3672	2^319830-16995	96279	Lelio R Paula	03/2016
3673	6^123713+143	96268	Lelio R Paula	05/2016
3674	(28*10^96265-97)/3	96266	Robert Price	07/2016
3675	103^47825-102	96264	Norbert Schneider	10/2016
3676	2^319713-81	96244	Lelio R Paula	11/2012
3677	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3678	12^89153-43	96213	Lelio R Paula	06/2016
3679	(2*10^96195-59)/3	96195	Robert Price	05/2017
3680	2^319545+147	96193	Lelio R Paula	11/2012
3681	(50^56597+1)/51	96155	Robert Price	03/2014
3682	(41*10^96137-59)/9	96138	Robert Price	10/2017
3683	2^319353-110343	96135	Enzo Doria	05/2014
3684	11^92309-42	96130	Lelio R Paula	05/2016
3685	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3686	(7*10^96112+143)/3	96113	Robert Price	04/2016
3687	2^319237+65835	96100	Lelio R Paula	03/2016
3688	2^319194-1841	96087	Yves Minet	03/2013
3689	20^73847-31	96078	Lelio R Paula	05/2016
3690	2^319107-109555	96061	Enzo Doria	04/2014
3691	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3692	2^319098-112157	96059	Enzo Doria	06/2014
3693	15^81673+94	96055	Lelio R Paula	07/2016
3694	2^319074+1871749	96051	Enzo Doria	05/2016
3695	2^319007-112111	96031	Enzo Doria	06/2014
3696	2^318946-1421	96013	Yves Minet	01/2013
3697	2^318834-110411	95979	Enzo Doria	05/2014
3698	2^318831-1965	95978	Lelio R Paula	03/2016
3699	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3700	5*3^201089-8	95945	Lelio R Paula	08/2014
3701	2^318711-139	95942	Lelio R Paula	11/2012
3702	2^318635-1167	95919	Lelio R Paula	03/2016
3703	15^81555+16	95917	Lelio R Paula	07/2016
3704	(37*10^95895+377)/9	95896	Robert Price	10/2017
3705	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
3706	2^318496-97305	95877	Lelio R Paula	03/2016
3707	2^318466+15015	95868	Lelio R Paula	03/2016
3708	6^123187-173129	95859	Mike Oakes	04/2011
3709	2^318423-487	95855	Yves Minet	03/2012
3710	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
3711	45369!2+1024	95787	Robert Price	02/2015
3712	3^200758-86	95786	Lelio R Paula	05/2016
3713	3*10^95776-59	95777	Robert Price	10/2017
3714	193^41901-2	95768	Lelio R Paula	10/2017
3715	4*10^95752-71	95753	Robert Price	11/2017
3716	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
3717	4*10^95672+91	95673	Robert Price	11/2017
3718	(11*10^95641-113)/3	95642	Robert Price	01/2017
3719	(13*10^95588+11)/3	95589	Robert Price	05/2015
3720	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
3721	3^200325+70	95580	Lelio R Paula	05/2016
3722	(25*10^95574-7)/9	95575	Robert Price	12/2014
3723	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
3724	2^317464+31	95567	Lelio R Paula	11/2012
3725	7^113073+82	95558	Lelio R Paula	04/2016
3726	2^317251+465	95503	Lelio R Paula	03/2016
3727	19^74684+58	95503	Lelio R Paula	06/2016
3728	(2^317250-7)/339	95500	Lelio R Paula	07/2013
3729	6^122718-79	95494	Lelio R Paula	05/2016
3730	2^317141-110491	95469	Enzo Doria	05/2014
3731	2^317094+76309	95455	Enzo Doria	05/2016
3732	2^317085+95	95453	Lelio R Paula	11/2012
3733	(17*10^95451-377)/9	95452	Robert Price	11/2017
3734	2^317057-109551	95444	Enzo Doria	04/2014
3735	3^200026+28	95437	Lelio R Paula	05/2016
3736	2^317024+93	95434	Donovan Johnson	06/2008
3737	2^316999+1605	95427	Lelio R Paula	03/2016
3738	2^316995-110427	95426	Enzo Doria	05/2014
3740	2^316937+177	95408	Lelio R Paula	11/2012
3739	4*10^95407+91	95408	Robert Price	11/2017
3741	2^316908+1915	95399	Lelio R Paula	03/2016
3742	2^316894+99	95395	Lelio R Paula	11/2012
3743	6^122547+11	95361	Lelio R Paula	05/2016
3744	2^316771+82875	95358	Lelio R Paula	03/2016
3745	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
3746	1*10^95326+57	95327	Robert Price	03/2011
3747	10^95326-393687	95326	Patrick De Geest	09/2013
3748	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
3749	2^316654-109481	95323	Enzo Doria	04/2014
3750	8*10^95316+51	95317	Robert Price	05/2017

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PRP Records

Probable Primes Top 10000

(211563 PRPs in the top)