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Metadata 
bibkey: sloane2014a000040
authors: N. J. A. Sloane; Gary Detlefs
year: 2014
title: "OEIS A000040, The prime numbers"
doi: null
url: https://oeis.org/A000040
claim: "A000040 %N: The prime numbers. A000040 %F: Conjecture: Sequence = {5 and n <> 5| ( Fibonacci(n) mod n = 1 or Fibonacci(n) mod n = n - 1) and 2^(n-1) mod n = 1}. - _Gary Detlefs_, May 25 2014 A000040 %F disclosed but not claimed: Conjecture: Sequence = {5 and n <> 5| ( Fibonacci(n) mod n = 1 or Fibonacci(n) mod n = n - 1) and 2^(3*n) mod 3*n = 8}. - _Gary Detlefs_, May 28 2014"
strata_touched:
  - D5/S0/Certificates/DetlefsFibonacciFermatPrimeCharacterizationRefutation
license: citation-only
triage: anchor

OEIS A000040

The NAME of A000040 states:

The prime numbers.

Gary Detlefs’s FORMULA of May 25, 2014 states:

Conjecture: Sequence = {5 and n <> 5| ( Fibonacci(n) mod n = 1 or Fibonacci(n) mod n = n - 1) and 2^(n-1) mod n = 1}. - Gary Detlefs, May 25 2014

His FORMULA of May 28, 2014 states:

Conjecture: Sequence = {5 and n <> 5| ( Fibonacci(n) mod n = 1 or Fibonacci(n) mod n = n - 1) and 2^(3n) mod 3n = 8}. - Gary Detlefs, May 28 2014

The AUTHOR line names:

N. J. A. Sloane

The AUTHOR line is undated; 2014 is the datable year of Detlefs’s conjectures.

Verified locator

  • URL: https://oeis.org/A000040
  • NAME (verbatim): The prime numbers.
  • FORMULA, May 25 2014 (verbatim): Conjecture: Sequence = {5 and n <> 5| ( Fibonacci(n) mod n = 1 or Fibonacci(n) mod n = n - 1) and 2^(n-1) mod n = 1}. - Gary Detlefs, May 25 2014
  • FORMULA, May 28 2014 (verbatim, disclosed but not claimed): Conjecture: Sequence = {5 and n <> 5| ( Fibonacci(n) mod n = 1 or Fibonacci(n) mod n = n - 1) and 2^(3n) mod 3n = 8}. - Gary Detlefs, May 28 2014
  • AUTHOR (verbatim): N. J. A. Sloane

Only the May 25 line is refuted: the composite 219781 = 271*811 passes both stated tests, while the literal statement also excludes the prime 2 at the degenerate boundary; the May 28 line is disclosed but not claimed. The Fibonacci-type pseudoprime status of 219781 is prior art recorded by OEIS A094401, A093372, and A212424.