Just a Conjecture

220+1=3221+1=5222+1=17223+1=257224+1=65537 \begin{aligned} 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{aligned}

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

True or false?

"225+12^{2^{5}} + 1 is a prime."

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