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Metadata 
bibkey: hilliard2006a115039
authors: Cino Hilliard; Robert Israel
year: 2006
title: "OEIS A115039 and A115038, prime square perfect-power representation"
doi: null
url: https://oeis.org/A115039
claim: "Conjecture: There will always be an x,y,n such that x^2 + p = y^n for all primes p."
strata_touched:
  - D5/S3/Arith/PrimeSquarePerfectPowerRepresentation
license: citation-only
triage: anchor

Prime square perfect-power representation

Both OEIS entries state the same conjecture:

Conjecture: There will always be an x,y,n such that x^2 + p = y^n for all primes p.

The exponent is read as at least two, which is the standard perfect-power condition. Allowing exponent one would make the sentence immediate by taking the power base to be the square plus the prime.

Verified locator

  • https://oeis.org/A115039
  • https://oeis.org/A115038
  • Contributors recorded by the entries: Cino Hilliard and Robert Israel.