Prime Decomposition of 2^58+1

Theorem
The number $2^{58} + 1$ has the prime decomposition:
 * $2^{58} + 1 = 5 \times 107 \, 367 \, 629 \times 536 \, 903 \, 681$

Proof
From Aurifeuillian Factorization of 2 Mod 4th Power of Two plus 1, we have:
 * $2^{4 n + 2} + 1 = \paren {2^{2 n + 1} - 2^{n + 1} + 1} \paren {2^{2 n + 1} + 2^{n + 1} + 1}$

Setting $n = 14$: