OEIS A000068: Numbers k for which k^4 + 1 is prime

We explore A000068—the integers k such that k^4 + 1 is prime—and its rich connection to Fermat numbers and the prime mysteries that surround them. From Fermat’s original conjecture and Euler’s disproof to modern primality tests and generalized Fermat numbers, we trace how this narrow sequence sits inside a vast landscape of primes, patterns, and open questions—like whether there are infinitely many such k and how computational advances are pushing the boundaries of what we know.

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