205833 · 2^2976222 - 411665

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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:	205833 · 2^2976222 - 411665
Verification status (*):	Proven
Official Comment (*):	[none]
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	L4667 : Morelli, LLR
Decimal Digits:	895938 (log₁₀ is 895937.40927005)
Rank (*):	3392 (digit rank is 1)
Entrance Rank (*):	349
Currently on list? (*):	yes
Submitted:	8/20/2017 10:23:00 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	123859
Status Flags:	none
Score (*):	46.2958 (normalized score 3.2076)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Luigi Morelli writes (1 Sep 2017): (report abuse)

This number can also be written as 411666*(2^2976221-1)+1. Use Mersenne#36 (2^2976221-1) as a helper prime for the N-1 proof.

With a very low probability, a similar prime (i.e. of the form 2*k*Mp+1) could be a divisor for the double-Mersenne number 2^Mp-1, but this one isn't.

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value

prime_id 123859

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -hhelper -q"205833*2^2976222-411665" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 205833*2^2976222-411665 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 205833*2^2976222-411665 is prime! (35295.7567s+0.0011s) [Elapsed time: 9.80 hours] Helper File: 2^2976221-1

modified 2020-07-07 22:30:15

created 2017-08-26 17:13:44

id 169527

field	value
prime_id	123859
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -hhelper -q"2058332^2976222-411665" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2058332^2976222-411665 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 205833*2^2976222-411665 is prime! (35295.7567s+0.0011s) [Elapsed time: 9.80 hours] Helper File: 2^2976221-1
modified	2020-07-07 22:30:15
created	2017-08-26 17:13:44
id	169527

Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.

205833 · 22976222 - 411665

This prime's information:

User comments about this prime (disclaimer):

Verification data:

205833 · 2^2976222 - 411665