Just a Conjecture

\[ \begin{eqnarray} 2^{2^0} +1&= & 3 \\ 2^{2^1} +1&= & 5 \\ 2^{2^2} +1&= & 17 \\ 2^{2^3} +1&= & 257 \\ 2^{2^4} +1&= & 65537 \\ \end{eqnarray} \]

Fact: The numbers above: \( 3,5,17,257,65537\) are all primes.

True or false?

"\(2^{2^{5}} + 1 \) is a prime."

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