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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	39^67918-67918^39	108062	Norbert Schneider	02/2017
3502	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
3503	2^358785-16933	108006	Enzo Doria	05/2013
3504	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
3505	6^138770-77	107985	Lelio R Paula	02/2017
3506	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
3507	10^107976+19	107977	Lelio R Paula	02/2017
3508	10^107976-202103	107976	Patrick De Geest	03/2017
3509	2^358684+75781	107975	Enzo Doria	04/2016
3510	99^54094+2	107952	Lelio R Paula	06/2013
3511	(2^358583-9)/391	107942	Lelio R Paula	12/2013
3512	2^358538+55	107931	Lelio R Paula	12/2011
3513	2^358517-109009	107925	Enzo Doria	03/2014
3514	3^226159+104	107906	Lelio R Paula	03/2017
3515	2^358310-11655	107863	Lelio R Paula	03/2017
3516	2^358275-112987	107852	Enzo Doria	07/2014
3517	2^358233-20005	107839	Enzo Doria	06/2013
3518	2^358194+175	107828	Lelio R Paula	12/2011
3519	107^53125-106	107812	Norbert Schneider	12/2016
3520	(25*10^107804+161)/3	107805	Robert Price	09/2019
3521	3^225922-2	107793	Lelio R Paula	10/2013
3522	12^99874-95	107783	Lelio R Paula	03/2017
3523	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
3524	2^358030-171	107778	Lelio R Paula	12/2011
3525	11^103488-4170	107772	Enzo Doria	12/2012
3526	2^357930-4547	107748	Yves Minet	03/2019
3527	2^357911-20089	107742	Enzo Doria	06/2013
3528	2^357885+12857	107735	Yves Minet	07/2010
3529	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
3530	7^127473+40	107728	Lelio R Paula	03/2017
3531	5*2^357850+9	107725	Lelio R Paula	09/2014
3532	2^357786-291191	107705	Enzo Doria	06/2015
3533	18^85798-23	107700	Lelio R Paula	04/2017
3534	3*10^107697+61	107698	Robert Price	09/2020
3535	(14*10^107694-83)/3	107695	Robert Price	12/2018
3536	2^357688-1854269	107675	Enzo Doria	09/2015
3537	2^357671-112225	107670	Enzo Doria	06/2014
3538	2^357618-21005	107654	Enzo Doria	06/2013
3539	2^357615-17505	107653	Enzo Doria	05/2013
3540	(30^72871-1)/29	107638	Robert Price	12/2011
3541	2^357521+1870217	107625	Enzo Doria	05/2016
3542	2^357477-1203	107612	Lelio R Paula	03/2017
3543	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
3544	5^153894-18	107568	Lelio R Paula	02/2017
3545	2^357324-69059	107566	Enzo Doria	11/2015
3546	467^40296+40296^467	107563	Norbert Schneider	03/2019
3547	2^357283-869688105	107553	Lelio R Paula	01/2017
3548	2^357280-16805	107552	Enzo Doria	05/2013
3549	10^107547+481719	107548	Patrick De Geest	03/2017
3550	10^107547-47	107547	Lelio R Paula	02/2017
3551	17^87396-32	107537	Lelio R Paula	04/2017
3552	(746*10^107505+1)/9	107507	Robert Price	03/2020
3553	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
3554	2^357081+107	107493	Lelio R Paula	12/2011
3555	2^357058-3911	107486	Yves Minet	04/2017
3556	3^225274+64	107484	Lelio R Paula	03/2017
3557	18^85619-95	107476	Lelio R Paula	04/2017
3558	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
3559	3^225248-130	107471	Lelio R Paula	03/2017
3560	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
3561	2^356935-18085	107449	Enzo Doria	05/2013
3562	10^107409+37	107410	Lelio R Paula	02/2017
3563	10^107409-329633	107409	Patrick De Geest	03/2017
3564	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
3565	2^356787-109027	107404	Enzo Doria	04/2014
3566	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
3567	3*10^107389+77	107390	Robert Price	09/2018
3568	5^153622-42	107378	Lelio R Paula	02/2017
3569	2^356699-97305	107378	Lelio R Paula	03/2017
3570	2^356654+85	107364	Lelio R Paula	11/2011
3571	2^356641-19921	107360	Enzo Doria	06/2013
3572	5*10^107355+11	107356	Robert Price	08/2019
3573	2^356623-465	107355	Lelio R Paula	03/2017
3574	19^83945-92	107345	Lelio R Paula	02/2017
3575	10^107334+28149	107335	Patrick De Geest	03/2017
3576	10^107334-83	107334	Lelio R Paula	02/2017
3577	2^356518+885	107323	Lelio R Paula	03/2017
3578	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
3579	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
3580	2^356442-114713	107300	Enzo Doria	04/2015
3581	2^356425+72257	107295	Enzo Doria	04/2016
3582	2^356351-112237	107273	Enzo Doria	06/2014
3584	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
3583	2^356322+74539	107264	Enzo Doria	04/2016
3585	2^356274+1874479	107250	Enzo Doria	06/2016
3586	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
3587	20^82422-93	107234	Lelio R Paula	02/2017
3588	2^356157-20365	107214	Enzo Doria	06/2013
3589	2^356129-18949	107206	Enzo Doria	05/2013
3590	2^356100-109587	107197	Enzo Doria	04/2014
3591	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
3592	2^355968-64875	107158	Lelio R Paula	01/2017
3593	2^355952+1870321	107153	Enzo Doria	05/2016
3594	2^355915-117	107142	Lelio R Paula	11/2011
3595	(16*10^107140+77)/3	107141	Robert Price	03/2019
3596	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
3597	3^224495-8	107112	Lelio R Paula	12/2013
3598	7^126691-44	107067	Lelio R Paula	03/2017
3599	4^177830-8243	107065	Mike Oakes	02/2011
3600	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
3601	2^355524-21237	107024	Enzo Doria	06/2013
3602	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
3603	2^355494-19901	107015	Enzo Doria	06/2013
3604	2^355454-869688105	107003	Lelio R Paula	01/2017
3605	2^355366+54615	106976	Lelio R Paula	01/2017
3606	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
3607	2^355275-19861	106949	Enzo Doria	06/2013
3608	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
3609	4*10^106914-93	106915	Robert Price	07/2020
3610	4*10^106892-3	106893	Robert Price	10/2015
3611	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
3612	2^354946-3	106850	M. Frind & P. Underwood	08/2002
3613	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
3614	2^354873-18693	106828	Enzo Doria	05/2013
3615	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
3616	2^354828+4257	106814	Lelio R Paula	01/2017
3617	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
3618	436^40459+40459^436	106791	Norbert Schneider	03/2019
3619	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
3620	(115*10^106772-7)/9	106774	Robert Price	02/2020
3621	2^354640-354640+1	106758	Robert Price	10/2014
3622	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
3623	2^354585+95	106741	Lelio R Paula	10/2011
3624	2^354553+189	106732	Lelio R Paula	10/2011
3625	2^354514-109031	106720	Enzo Doria	04/2014
3626	2^354509-109465	106718	Enzo Doria	04/2014
3627	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
3628	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
3629	15^90710+28	106684	Lelio R Paula	04/2017
3630	7^126237+34	106683	Lelio R Paula	03/2017
3631	2^354385-115315	106681	Enzo Doria	06/2015
3632	2^354327-19305	106664	Enzo Doria	06/2013
3633	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
3634	10^106636+97	106637	Lelio R Paula	02/2017
3635	10^106636-22923	106636	Patrick De Geest	03/2017
3636	2^354220-57	106631	Lelio R Paula	10/2011
3637	(29*10^106620-77)/3	106621	Robert Price	02/2020
3638	(746*10^106618+1)/9	106620	Robert Price	03/2020
3639	2^354157-17041	106612	Enzo Doria	05/2013
3640	12^98778+73	106600	Lelio R Paula	02/2017
3641	2^354064+1870651	106584	Enzo Doria	05/2016
3642	2^353992-57	106563	Lelio R Paula	10/2011
3643	9*10^106559+59	106560	Robert Price	01/2020
3644	NSW(139160)	106535	Robert Price	12/2018
3645	(7*10^106516+113)/3	106517	Robert Price	02/2018
3646	2^353832-1853849	106515	Enzo Doria	09/2015
3647	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
3648	2^353794-18453	106503	Enzo Doria	05/2013
3649	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
3650	2^353728+7695	106483	Lelio R Paula	01/2017
3651	2^353672-303	106466	Yves Minet	02/2012
3652	6^136811+101	106460	Lelio R Paula	02/2017
3653	2^353641+1871981	106457	Enzo Doria	05/2016
3654	(8*10^106454-29)/3	106455	Robert Price	07/2018
3655	2^353553+54615	106431	Lelio R Paula	01/2017
3656	2^353544-18897	106428	Enzo Doria	05/2013
3657	6^136729-133	106396	Lelio R Paula	02/2017
3658	2^353418+1605	106390	Lelio R Paula	01/2017
3659	2^353387+65	106381	Lelio R Paula	10/2011
3660	2^353372+74311	106376	Enzo Doria	04/2016
3661	2^353344-3693	106368	Yves Minet	03/2017
3663	2^353277-20089	106347	Enzo Doria	06/2013
3662	2^353275+72173	106347	Enzo Doria	04/2016
3664	2^353268-17705	106345	Enzo Doria	05/2013
3665	2^353267-19857	106344	Enzo Doria	06/2013
3666	(46*10^106343+143)/9	106344	Robert Price	01/2019
3667	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
3668	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
3669	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
3670	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
3671	2^353025+72257	106272	Enzo Doria	04/2016
3673	2^352932-20345	106244	Enzo Doria	06/2013
3672	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
3674	2^352883-187	106229	Lelio R Paula	10/2011
3675	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
3676	(55*10^106222+377)/9	106223	Robert Price	02/2019
3677	2^352814-131	106208	Lelio R Paula	10/2011
3678	2^352752+73951	106189	Enzo Doria	04/2016
3679	6^136434+5	106167	Lelio R Paula	11/2014
3680	25296^15737+15737^25296	106166	Hans Havermann	09/2020
3681	8*10^106157-13	106158	Robert Price	08/2019
3682	7*5^151872-8	106155	Lelio R Paula	11/2014
3683	105^52520-2	106153	Lelio R Paula	10/2017
3684	2^352601-1604809	106144	Enzo Doria	05/2015
3685	12^98353-43	106141	Lelio R Paula	02/2017
3686	2^352585-18901	106139	Enzo Doria	05/2013
3687	26363^10614+10614^26363	106135	Hans Havermann	09/2020
3688	(2^352554-3)/193	106128	Lelio R Paula	12/2013
3689	2^352540+15015	106126	Lelio R Paula	01/2017
3690	25068^17119+17119^25068	106125	Hans Havermann	09/2020
3691	2^352524-3149	106121	Yves Minet	10/2014
3692	2^352486-1858781	106109	Enzo Doria	04/2016
3693	2^352444+12705	106097	Lelio R Paula	01/2017
3694	(182*10^106083+43)/9	106085	Robert Price	02/2020
3695	(266*10^106066+1)/3	106068	Robert Price	04/2020
3696	2^352228-18953	106032	Enzo Doria	05/2013
3697	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
3698	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
3699	2^352107+1872533	105995	Enzo Doria	05/2016
3700	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
3701	2^352066-2591	105983	Yves Minet	07/2014
3702	2^352030+715	105972	Lelio R Paula	10/2011
3703	9*6^136176-5	105967	Lelio R Paula	11/2014
3704	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3705	28582^5097+5097^28582	105963	Hans Havermann	09/2020
3706	155^48377+2	105962	Lelio R Paula	08/2013
3707	2^351865+1869707	105922	Enzo Doria	05/2016
3708	24974^17427+17427^24974	105921	Hans Havermann	09/2020
3709	25163^16194+16194^25163	105920	Hans Havermann	09/2020
3710	2^351831+23	105912	Lelio R Paula	10/2011
3711	9*2^351784-5	105899	Lelio R Paula	09/2014
3712	(85*10^105881+203)/9	105882	Robert Price	09/2020
3713	2^351671-112387	105864	Enzo Doria	06/2014
3714	2^351669-109501	105863	Enzo Doria	04/2014
3715	2^351644+74731	105856	Enzo Doria	04/2016
3716	13^95025-42	105853	Lelio R Paula	12/2016
3717	2^351599+15015	105842	Lelio R Paula	01/2017
3718	19^82763+90	105834	Lelio R Paula	01/2017
3719	26050^11551+11551^26050	105832	Hans Havermann	09/2020
3720	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3721	20^81329-51	105812	Lelio R Paula	01/2017
3722	(5*10^105811+211)/9	105811	Robert Price	02/2018
3723	2^351483+28425	105807	Lelio R Paula	01/2017
3724	25231^15610+15610^25231	105804	Hans Havermann	09/2020
3725	15^89960+86	105802	Lelio R Paula	02/2017
3726	2^351460-17289	105801	Enzo Doria	05/2013
3727	19^82735+22	105798	Lelio R Paula	01/2017
3728	2^351435-109077	105793	Enzo Doria	04/2014
3729	2^351393+1089	105780	Lelio R Paula	01/2017
3730	2^351364+72631	105772	Enzo Doria	04/2016
3731	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
3732	26818^8783+8783^26818	105761	Hans Havermann	09/2020
3734	2^351305+1872467	105754	Enzo Doria	05/2016
3735	3^221649+16	105754	Lelio R Paula	11/2016
3733	32511^1790+1790^32511	105754	Hans Havermann	09/2020
3736	8*3^221637-5	105749	Lelio R Paula	09/2014
3737	2^351279-2780449	105746	Enzo Doria	03/2016
3738	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
3739	15^89903-26	105735	Lelio R Paula	02/2017
3741	2^351213-73	105726	Lelio R Paula	10/2011
3740	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
3742	2^351192-4589	105720	Yves Minet	07/2011
3743	20^81250-33	105709	Lelio R Paula	12/2016
3744	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
3745	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
3746	2^351076-113159	105685	Enzo Doria	07/2014
3747	93^53688-2	105684	Lelio R Paula	09/2013
3748	2^351060-4559	105680	Yves Minet	07/2011
3749	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
3750	11^101473-750	105674	Enzo Doria	11/2012

Find by discoverer :

PRP Records

Probable Primes Top 10000

(271000 PRPs in the top)