bibkey: price2013a228558 authors: Robert Price year: 2013 title: “OEIS A228558, Numbers k such that (17^k + 4^k)/21 is prime” doi: null url: https://oeis.org/A228558 claim: “A228558 %N: Numbers k such that (17^k + 4^k)/21 is prime. %C: Conjecture: All terms are prime. A231329 %N: Numbers n such that (19^n + 4^n)/23 is prime. %C: Conjecture: All terms are prime.” strata_touched:

• D5/S3/Arith/Congruence/PricePrimeQuotientExponent license: citation-only triage: anchor

OEIS A228558 and A231329

Robert Price authored both entries, and neither target COMMENT has a separate signature. The two conjectures are therefore attributed to the entry author.

One general prime-quotient exponent lemma settles both comments. The classical odd-power factorization behind the lemma is cited as background, not claimed as a new result.

Verified locator

• URL: https://oeis.org/A228558
• A228558 NAME (%N, verbatim): Numbers k such that (17^k + 4^k)/21 is prime.
• A228558 COMMENT (%C, verbatim): Conjecture: All terms are prime.
• A231329 URL: https://oeis.org/A231329
• A231329 NAME (%N, verbatim): Numbers n such that (19^n + 4^n)/23 is prime.
• A231329 COMMENT (%C, verbatim): Conjecture: All terms are prime.

The formal results settle only the two quoted conjectures. The search-bound comments, infinitude, and primality of particular terms are not claimed.