simply plugging $0,1,2,3$, and $4$ into $F_n=2^{2^n}+1$ and then observing that the results are prime. I can't think of any other way to 'prove' it, but the method I have proposed is a verification and not a proof.
2026-02-23 04:56:27.1771822587
To prove that the nth fermat number for $n \lt 4$ is prime, does the proof involve
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Listing all possibilities and showing them to all be prime is a perfectly valid proof, provided you prove all those numbers are prime. But it may not be what the asker is looking for.