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	11^90376+76	94117	Lelio R Paula	05/2016
3502	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
3503	2^312562-112685	94091	Enzo Doria	06/2014
3504	2^312404-869688105	94043	Lelio R Paula	09/2016
3505	2^312387+2793533	94038	Enzo Doria	03/2016
3506	10^94016+91	94017	Robert Price	04/2011
3507	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
3509	10^94016-188963	94016	Patrick De Geest	08/2013
3508	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
3510	6^120802+7661	94003	Mike Oakes	04/2011
3511	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
3512	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
3513	2^312201+51	93982	Lelio R Paula	11/2012
3514	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
3515	3^196892+58	93942	Lelio R Paula	05/2016
3516	2^312060+18915	93940	Lelio R Paula	03/2016
3517	2^311992-16209	93919	Enzo Doria	04/2013
3518	2^311965-39	93911	Lelio R Paula	11/2012
3519	2^311920-111689	93898	Enzo Doria	05/2014
3520	7*10^93887-47	93888	Robert Price	02/2017
3521	12^86965-13	93851	Lelio R Paula	06/2016
3522	2^311705+16095	93833	Lelio R Paula	03/2016
3523	2^311665-81	93821	Lelio R Paula	11/2012
3524	11^90073+92	93802	Lelio R Paula	05/2016
3525	6*10^93792+41	93793	Robert Price	01/2017
3526	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
3527	12^86900-77	93781	Lelio R Paula	06/2016
3528	2^311508-109769	93774	Enzo Doria	04/2014
3529	2^311486-1859621	93767	Enzo Doria	03/2016
3530	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
3531	2^311471+311469	93763	Renaud Lifchitz	01/2003
3532	2^311426+79459	93749	Enzo Doria	06/2016
3533	2^311294+5775	93709	Lelio R Paula	03/2016
3534	2^311252-1017	93697	Lelio R Paula	03/2016
3535	2^311247-112041	93695	Enzo Doria	06/2014
3536	2^311205-109645	93683	Enzo Doria	04/2014
3537	5^134027-84	93681	Lelio R Paula	04/2016
3538	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
3539	(2^311027-2^155514+1)/5	93628		11/2006
3540	3^196192-28	93608	Robert Price	12/2013
3541	216091#+261433	93606	Makoto Morimoto	12/2015
3542	5^133917+68	93604	Lelio R Paula	04/2016
3543	2^310924-1709	93598	Yves Minet	03/2013
3544	(266*10^93577-11)/3	93579	Robert Price	09/2016
3545	(16*10^93577+161)/3	93578	Robert Price	05/2016
3546	3^196113-56	93570	Lelio R Paula	04/2016
3547	2^310806-110345	93562	Enzo Doria	05/2014
3548	3^196093+86	93561	Lelio R Paula	04/2016
3549	2^310780-2327	93555	Yves Minet	10/2013
3550	30^63332+41	93550	Lelio R Paula	08/2012
3551	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
3552	8*5^133807+7	93528	Lelio R Paula	10/2014
3553	2^310686+8193	93526	Lelio R Paula	03/2016
3554	2^310646+63	93514	Lelio R Paula	11/2012
3555	(77*10^93508+31)/9	93509	Robert Price	10/2015
3556	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
3557	(2*10^93497+7)/9	93497	Erik Branger	03/2011
3558	3^195958-112852	93496	Enzo Doria	07/2014
3559	2^310583+16385	93495	Lelio R Paula	03/2016
3560	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
3561	9*7^110614+2	93481	Lelio R Paula	11/2014
3562	2^310469-8295	93461	Lelio R Paula	03/2016
3563	2^310459-1159	93458	Yves Minet	11/2012
3564	6^120075-95	93437	Lelio R Paula	05/2016
3565	2^310289+98327	93407	Yves Minet	11/2010
3566	2^310217-113143	93385	Enzo Doria	07/2014
3567	7^110494-68	93379	Lelio R Paula	04/2016
3568	2^310184-113093	93375	Enzo Doria	07/2014
3569	2^310180-110417	93374	Enzo Doria	05/2014
3570	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
3571	3^195669+68	93358	Lelio R Paula	04/2016
3572	10^93356+91	93357	Robert Price	04/2011
3573	10^93356-28313	93356	Patrick De Geest	08/2013
3574	(85*10^93346+23)/9	93347	Robert Price	11/2015
3575	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
3576	3^195556+8680	93304	Lelio R Paula	04/2016
3577	2^309942-109991	93302	Enzo Doria	04/2014
3578	2^309926-1867301	93298	Enzo Doria	03/2016
3579	2^309924+85951	93297	Yves Minet	03/2011
3580	(86*10^93263-77)/9	93264	Robert Price	05/2016
3581	6^119836-125	93251	Lelio R Paula	05/2016
3582	3^195430-2	93244	Theodore Burton	02/2007
3583	(13*10^93236+47)/3	93237	Robert Price	01/2017
3584	(86*10^93217-221)/9	93218	Robert Price	06/2017
3585	2^309637-16329	93211	Enzo Doria	04/2013
3586	(41*10^93207+49)/9	93208	Robert Price	04/2016
3587	14^81312-57	93194	Lelio R Paula	06/2016
3588	41^57783-40	93192	Theodore Burton	02/2007
3589	3*10^93179-97	93180	Robert Price	08/2017
3590	5*7^110252-4	93175	Lelio R Paula	11/2014
3591	2^309380-27	93133	Lelio R Paula	11/2012
3592	23*10^93116-7	93118	Robert Price	03/2016
3593	(29*10^93082+1)/3	93083	Robert Price	11/2015
3594	(58*10^93062-13)/9	93063	Robert Price	09/2015
3595	2^309131+1869383	93058	Enzo Doria	05/2016
3596	2^309066-93	93039	Lelio R Paula	11/2012
3597	2^309063-113269	93038	Enzo Doria	07/2014
3598	3^194965+16	93022	Robert Price	10/2013
3599	2^308979+1869143	93012	Enzo Doria	05/2016
3600	5^133064+54	93008	Lelio R Paula	04/2016
3601	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
3602	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
3603	(2*10^92976-17)/3	92976	Robert Price	08/2014
3604	2^308809+37967	92961	Phil Moore	03/2008
3605	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
3606	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
3607	2^308650+513	92913	Lelio R Paula	02/2016
3608	5*7^109936+6	92908	Lelio R Paula	10/2014
3609	2*10^92897+89	92898	Robert Price	07/2016
3610	12^86073-29	92889	Lelio R Paula	06/2016
3611	2^308566-117	92888	Lelio R Paula	11/2012
3612	(17*10^92869-11)/3	92870	Robert Price	07/2015
3613	2^308459+75431	92856	Enzo Doria	04/2016
3614	2^308426-1866377	92846	Enzo Doria	03/2016
3615	2^308349-112111	92823	Enzo Doria	06/2014
3616	9*10^92821+19	92822	Robert Price	05/2016
3617	2^308337-75	92819	Lelio R Paula	11/2012
3618	4*3^194508+7	92805	Lelio R Paula	08/2014
3619	22*25^66379-113	92796	Curtis Bright	05/2015
3620	11^89101-1080	92790	Enzo Doria	12/2012
3621	2^308236-1867859	92789	Enzo Doria	04/2016
3622	12^85963+25	92770	Lelio R Paula	06/2016
3623	7^109750-66	92750	Lelio R Paula	04/2016
3624	9*10^92742+11	92743	Robert Kinser	01/2017
3625	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
3626	2^307997-110655	92717	Enzo Doria	05/2014
3627	L(443609)	92709	Renaud Lifchitz	11/2003
3628	10^92691+9	92692	Robert Price	03/2011
3629	10^92691-252291	92691	Patrick De Geest	08/2013
3630	2^307879-2521	92681	Yves Minet	07/2014
3631	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
3632	14^80831+47	92643	Lelio R Paula	06/2016
3633	15^78744+92	92611	Lelio R Paula	07/2016
3634	65^51083-64	92610	Norbert Schneider	11/2014
3635	6^118996-16943	92597	Enzo Doria	02/2013
3636	(3^194014-7)/2	92568	Lelio R Paula	04/2013
3637	(26*10^92546-77)/3	92547	Robert Price	02/2017
3638	3^193954+340	92540	Lelio R Paula	04/2016
3639	2^307407-307407^2	92539	Henri Lifchitz	05/2005
3640	(17*10^92513-11)/3	92514	Robert Price	07/2015
3641	2^307318-4211	92512	Yves Minet	06/2011
3642	2^307280+193	92501	Lelio R Paula	11/2012
3643	20^71075-33	92471	Lelio R Paula	05/2016
3644	2^307126-78795	92455	Lelio R Paula	02/2016
3645	2^307125-49789	92454	Henri Lifchitz	08/2005
3646	2^307099+23	92447	Lelio R Paula	11/2012
3647	7*10^92414-69	92415	Robert Price	01/2017
3648	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
3649	2^306915+1873373	92391	Enzo Doria	06/2016
3650	2^306908+12915	92389	Lelio R Paula	02/2016
3651	19^72244-80	92383	Lelio R Paula	06/2016
3652	2^306849+75	92371	Lelio R Paula	11/2012
3653	2^306813-869688105	92360	Lelio R Paula	08/2016
3654	2^306672-109059	92318	Enzo Doria	04/2014
3655	6^118604-17063	92292	Enzo Doria	02/2013
3656	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
3657	2^306467-1835611	92256	Enzo Doria	04/2015
3658	2^306433+76427	92246	Enzo Doria	05/2016
3659	2^306430-113313	92245	Enzo Doria	07/2014
3660	(23*10^92244-59)/9	92245	Robert Price	03/2017
3661	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
3662	(25*10^92186+59)/3	92187	Robert Price	05/2016
3663	2^306213-286183	92180	Enzo Doria	06/2015
3664	10^92178+61	92179	Robert Price	04/2011
3665	10^92178-175509	92178	Patrick De Geest	07/2013
3666	2^306200+1185	92176	Lelio R Paula	02/2016
3667	2^306153+11	92162	Lelio R Paula	11/2012
3668	(2^306141-7)/5	92157	Lelio R Paula	06/2013
3669	(26*10^92152-23)/3	92153	Robert Price	08/2016
3670	(2*10^92152+67)/3	92152	Robert Price	04/2017
3671	410^92099+37^92099	92100	Mike Oakes	12/2010
3672	(2^305867-2^152934+1)/5	92075		11/2006
3673	2^305851-109495	92071	Enzo Doria	04/2014
3674	12^85300+35	92055	Lelio R Paula	06/2016
3675	3^192911+92	92042	Lelio R Paula	04/2016
3676	2^305723-276271	92032	Enzo Doria	07/2015
3677	2^305676+93	92018	Donovan Johnson	06/2008
3678	3^192819+4	91999	Lelio R Paula	04/2013
3679	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
3680	2^305539+72911	91977	Enzo Doria	04/2016
3681	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
3682	85^47642+84	91922	Norbert Schneider	10/2015
3683	10^91920+187651	91921	Patrick De Geest	07/2013
3684	10^91920-39	91920	Robert Price	05/2011
3685	(22*10^91903+41)/9	91904	Robert Price	02/2015
3687	2^305275-27	91897	Lelio R Paula	11/2012
3686	3^192607-7726	91897	Enzo Doria	05/2014
3688	(7*10^91856-61)/9	91856	Erik Branger	12/2009
3689	(89*10^91839-53)/9	91840	Robert Price	11/2015
3690	8*5^131351+7	91812	Lelio R Paula	10/2014
3691	3^192426-68	91811	Lelio R Paula	04/2016
3692	2^304973+117	91807	Lelio R Paula	11/2012
3693	2^304939-1863727	91796	Enzo Doria	03/2016
3694	2^304902+8415	91785	Lelio R Paula	02/2016
3695	18^73119+61	91785	Lelio R Paula	06/2016
3696	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
3697	2^304747+71355	91738	Lelio R Paula	02/2016
3698	8*3^192251+5	91728	Lelio R Paula	08/2014
3699	2^304674-87	91717	Lelio R Paula	11/2012
3700	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
3701	(5*10^91707-119)/3	91708	Robert Price	04/2016
3702	2^304633-112771	91704	Enzo Doria	06/2014
3703	2^304578-16713	91688	Enzo Doria	05/2013
3704	6^117824-18713	91685	Enzo Doria	03/2013
3705	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
3706	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
3707	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
3708	2^304507-16645	91666	Enzo Doria	04/2013
3709	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
3710	2^304471-1836127	91655	Enzo Doria	04/2015
3711	2^304433+32769	91644	Lelio R Paula	02/2016
3712	2^304410-16625	91637	Enzo Doria	04/2013
3713	4*5^131052+7	91603	Lelio R Paula	10/2014
3714	2^304278-4001	91597	Yves Minet	04/2017
3715	2^304272-1866377	91595	Enzo Doria	03/2016
3716	2^304268+19683	91594	Lelio R Paula	02/2016
3717	2^304162-161	91562	Lelio R Paula	11/2012
3718	5*7^108331+6	91552	Lelio R Paula	10/2014
3719	2^304082-2787821	91538	Enzo Doria	03/2016
3720	2^304015+64133	91518	David Broadhurst	06/2002
3721	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
3722	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
3723	2^303930+1880527	91493	Enzo Doria	10/2016
3724	3^191684-68	91457	Lelio R Paula	04/2016
3725	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
3726	11^87797-120	91432	Enzo Doria	07/2012
3727	2^303698-1847231	91423	Enzo Doria	07/2015
3728	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
3729	2^303554+77299	91379	Enzo Doria	05/2016
3730	2^303542+12705	91376	Lelio R Paula	02/2016
3731	31^61269-2	91375	Lelio R Paula	09/2013
3732	2^303516-64875	91368	Lelio R Paula	02/2016
3733	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
3734	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
3735	2^303344-2786969	91316	Enzo Doria	03/2016
3736	6^117346+65	91313	Lelio R Paula	05/2016
3737	2^303321+855	91309	Lelio R Paula	02/2016
3738	12^84606+47	91306	Lelio R Paula	06/2016
3739	2^303288+1874311	91299	Enzo Doria	06/2016
3740	11^87663-1710	91292	Enzo Doria	12/2012
3741	2^303224+2533	91280	Henri Lifchitz	05/2005
3742	6^117302+143	91279	Lelio R Paula	05/2016
3743	3^191306-112880	91277	Enzo Doria	07/2014
3744	2^303207+12915	91275	Lelio R Paula	02/2016
3745	2^303191-111259	91270	Enzo Doria	05/2014
3747	10^91230+9^(91230+1)	91231	Robert Price	08/2016
3746	10^91230+7921	91231	Patrick De Geest	11/2016
3748	10^91230-911141	91230	Patrick De Geest	11/2016
3749	6^117232-17423	91225	Enzo Doria	02/2013
3750	7*10^91215+3	91216	Erik Branger	11/2009

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Probable Primes Top 10000

(180278 PRPs in the top)