# 2 · 35570081 + 1

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Description: 2 · 35570081 + 1 Proven Divides Phi(3^5570081,2) [g427] This prime has 1 user comment below. L4965 : Propper, LLR 2657605   (log10 is 2657604.33664015) 77 (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 193.3322)

#### 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 2020-05-22 18:20:06)

#### User comments about this prime (disclaimer):

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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:

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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: 0.0018 seconds to select prime, 0.0007 seconds to seek comments.