It Must Be A Prime Number!

In mathematics, a Fermat Number is a positive integer of the form Fn=2(2n)+1 F_n = 2^{\left (2^n \right)} + 1

Given that F7=340282366920938463463374607431768211457,F_7 = 340282366920938463463374607431768211457,
what are the last three digits of the smallest prime factor of F7F_7 ?

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