2 · 3^5570081 + 1

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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:	2 · 3^5570081 + 1
Verification status (*):	Proven
Official Comment (*):	Divides Phi(3^5570081,2) [g427]
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	L4965 : Propper, LLR
Decimal Digits:	2657605 (log₁₀ is 2657604.3366401)
Rank (*):	189 (digit rank is 1)
Entrance Rank (*):	51
Currently on list? (*):	yes
Submitted:	2/14/2020 08:29:25 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	130502
Status Flags:	none
Score (*):	49.6299 (normalized score 90.1971)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.

Divides Phi (archivable *)
Prime on list: yes, rank 1
Subcategory: "Divides Phi"
(archival tag id 224019, tag last modified 2023-03-11 15:53:59)

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.
Serge Batalov writes (19 May 2020): (report abuse)
This number extends OEIS A003306, and a subset of such primes (all with odd n) may divide a large cyclotomic evaluated at 2. The latter is submitted as OEIS A334993. Here is their complete list:
2*3^1+1 Divides Phi(3^1,2)
2*3^5+1 Divides Phi(3^5,2)
2*3^9+1 Divides Phi(3^7,2)
2*3^17+1 Divides Phi(3^15,2)
2*3^57+1 Divides Phi(3^56,2)
2*3^65+1 Divides Phi(3^65,2)
2*3^897+1 Divides Phi(3^896,2)
2*3^4217+1 Divides Phi(3^4217,2)
2*3^6225+1 Divides Phi(3^6223,2)
2*3^152529+1 Divides Phi(3^152528,2)
2*3^3648969+1 Divides Phi(3^3648964,2)
2*3^5570081+1 Divides Phi(3^5570081,2)

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 130502

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"2*3^5570081+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 2*3^5570081+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^5570081+1 is prime! (27063.3090s+0.1068s) [Elapsed time: 7.52 hours]

modified 2020-07-07 22:30:10

created 2020-02-14 08:31:02

id 176188

field	value
prime_id	130502
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/client/pfgw/pfgw64 -t -q"23^5570081+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 23^5570081+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^5570081+1 is prime! (27063.3090s+0.1068s) [Elapsed time: 7.52 hours]
modified	2020-07-07 22:30:10
created	2020-02-14 08:31:02
id	176188

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.

2 · 35570081 + 1

This prime's information:

Archival tags:

User comments about this prime (disclaimer):

Verification data:

2 · 3^5570081 + 1