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  "body": "\n## Definition\n\nFor a natural number $n$, the $n$-th Fermat number is $F_n = 2^{2^n} + 1$.\n\n## Remarks\n\nThe first values are $F_0 = 3$, $F_1 = 5$, $F_2 = 17$, $F_3 = 257$ and $F_4 = 65537$.\nThe Fermat numbers satisfy $F_0 F_1 \\cdots F_{n-1} = F_n - 2$ for $n \\ge 1$.\nA Fermat number that is prime is a [[Fermat prime|0N9E4G2P97]].\n\n## Explanations\n\n### L1 human\n\nThe Fermat numbers grow very fast, because the exponent itself is a power of $2$.\nFor example, $F_5 = 2^{32} + 1 = 4294967297$.\n",
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