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	2^311294+5775	93709	Lelio R Paula	03/2016
3502	2^311252-1017	93697	Lelio R Paula	03/2016
3503	2^311247-112041	93695	Enzo Doria	06/2014
3504	2^311205-109645	93683	Enzo Doria	04/2014
3505	5^134027-84	93681	Lelio R Paula	04/2016
3506	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
3507	(2^311027-2^155514+1)/5	93628		11/2006
3508	3^196192-28	93608	Robert Price	12/2013
3509	216091#+261433	93606	Makoto Morimoto	12/2015
3510	5^133917+68	93604	Lelio R Paula	04/2016
3511	2^310924-1709	93598	Yves Minet	03/2013
3512	(266*10^93577-11)/3	93579	Robert Price	09/2016
3513	(16*10^93577+161)/3	93578	Robert Price	05/2016
3514	3^196113-56	93570	Lelio R Paula	04/2016
3515	2^310806-110345	93562	Enzo Doria	05/2014
3516	3^196093+86	93561	Lelio R Paula	04/2016
3517	2^310780-2327	93555	Yves Minet	10/2013
3518	30^63332+41	93550	Lelio R Paula	08/2012
3519	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
3520	8*5^133807+7	93528	Lelio R Paula	10/2014
3521	2^310686+8193	93526	Lelio R Paula	03/2016
3522	2^310646+63	93514	Lelio R Paula	11/2012
3523	(77*10^93508+31)/9	93509	Robert Price	10/2015
3524	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
3525	(2*10^93497+7)/9	93497	Erik Branger	03/2011
3526	3^195958-112852	93496	Enzo Doria	07/2014
3527	2^310583+16385	93495	Lelio R Paula	03/2016
3528	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
3529	9*7^110614+2	93481	Lelio R Paula	11/2014
3530	2^310469-8295	93461	Lelio R Paula	03/2016
3531	2^310459-1159	93458	Yves Minet	11/2012
3532	6^120075-95	93437	Lelio R Paula	05/2016
3533	2^310289+98327	93407	Yves Minet	11/2010
3534	2^310217-113143	93385	Enzo Doria	07/2014
3535	7^110494-68	93379	Lelio R Paula	04/2016
3536	2^310184-113093	93375	Enzo Doria	07/2014
3537	2^310180-110417	93374	Enzo Doria	05/2014
3538	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
3539	3^195669+68	93358	Lelio R Paula	04/2016
3540	10^93356+91	93357	Robert Price	04/2011
3541	10^93356-28313	93356	Patrick De Geest	08/2013
3542	(85*10^93346+23)/9	93347	Robert Price	11/2015
3543	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
3544	3^195556+8680	93304	Lelio R Paula	04/2016
3545	2^309942-109991	93302	Enzo Doria	04/2014
3546	2^309926-1867301	93298	Enzo Doria	03/2016
3547	2^309924+85951	93297	Yves Minet	03/2011
3548	(86*10^93263-77)/9	93264	Robert Price	05/2016
3549	6^119836-125	93251	Lelio R Paula	05/2016
3550	3^195430-2	93244	Theodore Burton	02/2007
3551	(13*10^93236+47)/3	93237	Robert Price	01/2017
3552	(86*10^93217-221)/9	93218	Robert Price	06/2017
3553	2^309637-16329	93211	Enzo Doria	04/2013
3554	(41*10^93207+49)/9	93208	Robert Price	04/2016
3555	14^81312-57	93194	Lelio R Paula	06/2016
3556	41^57783-40	93192	Theodore Burton	02/2007
3557	5*7^110252-4	93175	Lelio R Paula	11/2014
3558	2^309380-27	93133	Lelio R Paula	11/2012
3559	23*10^93116-7	93118	Robert Price	03/2016
3560	(29*10^93082+1)/3	93083	Robert Price	11/2015
3561	(58*10^93062-13)/9	93063	Robert Price	09/2015
3562	2^309131+1869383	93058	Enzo Doria	05/2016
3563	2^309066-93	93039	Lelio R Paula	11/2012
3564	2^309063-113269	93038	Enzo Doria	07/2014
3565	3^194965+16	93022	Robert Price	10/2013
3566	2^308979+1869143	93012	Enzo Doria	05/2016
3567	5^133064+54	93008	Lelio R Paula	04/2016
3568	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
3569	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
3570	(2*10^92976-17)/3	92976	Robert Price	08/2014
3571	2^308809+37967	92961	Phil Moore	03/2008
3572	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
3573	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
3574	2^308650+513	92913	Lelio R Paula	02/2016
3575	5*7^109936+6	92908	Lelio R Paula	10/2014
3576	2*10^92897+89	92898	Robert Price	07/2016
3577	12^86073-29	92889	Lelio R Paula	06/2016
3578	2^308566-117	92888	Lelio R Paula	11/2012
3579	(17*10^92869-11)/3	92870	Robert Price	07/2015
3580	2^308459+75431	92856	Enzo Doria	04/2016
3581	2^308426-1866377	92846	Enzo Doria	03/2016
3582	2^308349-112111	92823	Enzo Doria	06/2014
3583	9*10^92821+19	92822	Robert Price	05/2016
3584	2^308337-75	92819	Lelio R Paula	11/2012
3585	4*3^194508+7	92805	Lelio R Paula	08/2014
3586	22*25^66379-113	92796	Curtis Bright	05/2015
3587	11^89101-1080	92790	Enzo Doria	12/2012
3588	2^308236-1867859	92789	Enzo Doria	04/2016
3589	12^85963+25	92770	Lelio R Paula	06/2016
3590	7^109750-66	92750	Lelio R Paula	04/2016
3591	9*10^92742+11	92743	Robert Kinser	01/2017
3592	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
3593	2^307997-110655	92717	Enzo Doria	05/2014
3594	L(443609)	92709	Renaud Lifchitz	11/2003
3595	10^92691+9	92692	Robert Price	03/2011
3596	10^92691-252291	92691	Patrick De Geest	08/2013
3597	2^307879-2521	92681	Yves Minet	07/2014
3598	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
3599	14^80831+47	92643	Lelio R Paula	06/2016
3600	15^78744+92	92611	Lelio R Paula	07/2016
3601	65^51083-64	92610	Norbert Schneider	11/2014
3602	6^118996-16943	92597	Enzo Doria	02/2013
3603	(3^194014-7)/2	92568	Lelio R Paula	04/2013
3604	(26*10^92546-77)/3	92547	Robert Price	02/2017
3605	3^193954+340	92540	Lelio R Paula	04/2016
3606	2^307407-307407^2	92539	Henri Lifchitz	05/2005
3607	(17*10^92513-11)/3	92514	Robert Price	07/2015
3608	2^307318-4211	92512	Yves Minet	06/2011
3609	2^307280+193	92501	Lelio R Paula	11/2012
3610	20^71075-33	92471	Lelio R Paula	05/2016
3611	2^307126-78795	92455	Lelio R Paula	02/2016
3612	2^307125-49789	92454	Henri Lifchitz	08/2005
3613	2^307099+23	92447	Lelio R Paula	11/2012
3614	7*10^92414-69	92415	Robert Price	01/2017
3615	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
3616	2^306915+1873373	92391	Enzo Doria	06/2016
3617	2^306908+12915	92389	Lelio R Paula	02/2016
3618	19^72244-80	92383	Lelio R Paula	06/2016
3619	2^306849+75	92371	Lelio R Paula	11/2012
3620	2^306813-869688105	92360	Lelio R Paula	08/2016
3621	2^306672-109059	92318	Enzo Doria	04/2014
3622	6^118604-17063	92292	Enzo Doria	02/2013
3623	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
3624	2^306467-1835611	92256	Enzo Doria	04/2015
3625	2^306433+76427	92246	Enzo Doria	05/2016
3626	2^306430-113313	92245	Enzo Doria	07/2014
3627	(23*10^92244-59)/9	92245	Robert Price	03/2017
3628	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
3629	(25*10^92186+59)/3	92187	Robert Price	05/2016
3630	2^306213-286183	92180	Enzo Doria	06/2015
3631	10^92178+61	92179	Robert Price	04/2011
3632	10^92178-175509	92178	Patrick De Geest	07/2013
3633	2^306200+1185	92176	Lelio R Paula	02/2016
3634	2^306153+11	92162	Lelio R Paula	11/2012
3635	(2^306141-7)/5	92157	Lelio R Paula	06/2013
3636	(26*10^92152-23)/3	92153	Robert Price	08/2016
3637	(2*10^92152+67)/3	92152	Robert Price	04/2017
3638	410^92099+37^92099	92100	Mike Oakes	12/2010
3639	(2^305867-2^152934+1)/5	92075		11/2006
3640	2^305851-109495	92071	Enzo Doria	04/2014
3641	12^85300+35	92055	Lelio R Paula	06/2016
3642	3^192911+92	92042	Lelio R Paula	04/2016
3643	2^305723-276271	92032	Enzo Doria	07/2015
3644	2^305676+93	92018	Donovan Johnson	06/2008
3645	3^192819+4	91999	Lelio R Paula	04/2013
3646	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
3647	2^305539+72911	91977	Enzo Doria	04/2016
3648	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
3649	85^47642+84	91922	Norbert Schneider	10/2015
3650	10^91920+187651	91921	Patrick De Geest	07/2013
3651	10^91920-39	91920	Robert Price	05/2011
3652	(22*10^91903+41)/9	91904	Robert Price	02/2015
3654	2^305275-27	91897	Lelio R Paula	11/2012
3653	3^192607-7726	91897	Enzo Doria	05/2014
3655	(7*10^91856-61)/9	91856	Erik Branger	12/2009
3656	(89*10^91839-53)/9	91840	Robert Price	11/2015
3657	8*5^131351+7	91812	Lelio R Paula	10/2014
3658	3^192426-68	91811	Lelio R Paula	04/2016
3659	2^304973+117	91807	Lelio R Paula	11/2012
3660	2^304939-1863727	91796	Enzo Doria	03/2016
3661	2^304902+8415	91785	Lelio R Paula	02/2016
3662	18^73119+61	91785	Lelio R Paula	06/2016
3663	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
3664	2^304747+71355	91738	Lelio R Paula	02/2016
3665	8*3^192251+5	91728	Lelio R Paula	08/2014
3666	2^304674-87	91717	Lelio R Paula	11/2012
3667	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
3668	(5*10^91707-119)/3	91708	Robert Price	04/2016
3669	2^304633-112771	91704	Enzo Doria	06/2014
3670	2^304578-16713	91688	Enzo Doria	05/2013
3671	6^117824-18713	91685	Enzo Doria	03/2013
3672	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
3673	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
3674	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
3675	2^304507-16645	91666	Enzo Doria	04/2013
3676	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
3677	2^304471-1836127	91655	Enzo Doria	04/2015
3678	2^304433+32769	91644	Lelio R Paula	02/2016
3679	2^304410-16625	91637	Enzo Doria	04/2013
3680	4*5^131052+7	91603	Lelio R Paula	10/2014
3681	2^304278-4001	91597	Yves Minet	04/2017
3682	2^304272-1866377	91595	Enzo Doria	03/2016
3683	2^304268+19683	91594	Lelio R Paula	02/2016
3684	2^304162-161	91562	Lelio R Paula	11/2012
3685	5*7^108331+6	91552	Lelio R Paula	10/2014
3686	2^304082-2787821	91538	Enzo Doria	03/2016
3687	2^304015+64133	91518	David Broadhurst	06/2002
3688	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
3689	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
3690	2^303930+1880527	91493	Enzo Doria	10/2016
3691	3^191684-68	91457	Lelio R Paula	04/2016
3692	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
3693	11^87797-120	91432	Enzo Doria	07/2012
3694	2^303698-1847231	91423	Enzo Doria	07/2015
3695	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
3696	2^303554+77299	91379	Enzo Doria	05/2016
3697	2^303542+12705	91376	Lelio R Paula	02/2016
3698	31^61269-2	91375	Lelio R Paula	09/2013
3699	2^303516-64875	91368	Lelio R Paula	02/2016
3700	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
3701	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
3702	2^303344-2786969	91316	Enzo Doria	03/2016
3703	6^117346+65	91313	Lelio R Paula	05/2016
3704	2^303321+855	91309	Lelio R Paula	02/2016
3705	12^84606+47	91306	Lelio R Paula	06/2016
3706	2^303288+1874311	91299	Enzo Doria	06/2016
3707	11^87663-1710	91292	Enzo Doria	12/2012
3708	2^303224+2533	91280	Henri Lifchitz	05/2005
3709	6^117302+143	91279	Lelio R Paula	05/2016
3710	3^191306-112880	91277	Enzo Doria	07/2014
3711	2^303207+12915	91275	Lelio R Paula	02/2016
3712	2^303191-111259	91270	Enzo Doria	05/2014
3713	10^91230+9^(91230+1)	91231	Robert Price	08/2016
3714	10^91230+7921	91231	Patrick De Geest	11/2016
3715	10^91230-911141	91230	Patrick De Geest	11/2016
3716	6^117232-17423	91225	Enzo Doria	02/2013
3717	7*10^91215+3	91216	Erik Branger	11/2009
3718	97*10^91205-3	91207	Robert Price	01/2017
3719	2^302979-161181	91206	Enzo Doria	04/2013
3720	2^302949+81	91197	Henri Lifchitz	02/2007
3721	4*6^117192-5	91194	Lelio R Paula	10/2014
3722	2^302918+99	91188	Lelio R Paula	11/2012
3723	2^302797+1869587	91151	Enzo Doria	05/2016
3724	265^37614+37614^265	91148	Norbert Schneider	01/2015
3725	7^107852+82	91146	Lelio R Paula	04/2016
3726	(38*10^91144-11)/9	91145	Robert Price	05/2015
3727	249^38030+38030^249	91128	Norbert Schneider	01/2015
3728	6^117094-211049	91117	Mike Oakes	05/2011
3729	2^302602-1867181	91093	Enzo Doria	03/2016
3730	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
3731	15^77445-16	91083	Lelio R Paula	07/2016
3732	2^302505+81	91064	Henri Lifchitz	02/2007
3733	2^302496-112349	91061	Enzo Doria	06/2014
3734	17^73999-72	91052	Lelio R Paula	07/2016
3735	2^302332+577294575	91012	Lelio R Paula	08/2016
3736	2^302274+74209	90994	Enzo Doria	04/2016
3737	(3^190668+2)/89	90970	Lelio R Paula	04/2013
3738	2^302188+90195	90968	Lelio R Paula	02/2016
3739	(53*10^90965-71)/9	90966	Robert Price	09/2015
3740	2^302113+74105	90946	Enzo Doria	04/2016
3741	2^302102-6555	90942	Lelio R Paula	02/2016
3742	156(10^(422731)-1)/101-1	90925	Robert Price	05/2014
3743	3^190568+38	90925	Lelio R Paula	04/2016
3744	2^302009-16449	90914	Enzo Doria	04/2013
3745	(17*2^301951-1)/165	90896	Lelio R Paula	02/2014
3746	3^190497+74	90891	Lelio R Paula	04/2016
3747	(24737*2^301896+1)/399	90882	Lelio R Paula	06/2014
3748	18^72397+89	90878	Lelio R Paula	06/2016
3749	6^116769-47	90864	Lelio R Paula	05/2016
3750	2^301712-465	90825	Lelio R Paula	02/2016

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)