# 2 · 35570081 + 1

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 · 35570081 + 1 Proven Divides Phi(3^5570081,2) [g427] This prime has 1 user comment below. L4965 : Propper, LLR 2657605   (log10 is 2657604.3366401) 125 (digit rank is 1) 51 short 2/14/2020 02:29:25 CDT 5/22/2020 18:20:03 CDT 130502 TrialDiv 49.6299 (normalized score 139.4806)

#### 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"

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.
fieldvalue
prime_id130502
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /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]
modified2020-07-07 17:30:10
created2020-02-14 02:31:02
id176188

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.