Discrete Math Quiz
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NUMBER THEORY AND CRYPTOGRAPHY
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A factorization algorithm tests whether integers of the form 22n+12^{2^n} + 1 (Fermat numbers) are prime. For F4=216+1=65537F_4 = 2^{16} + 1 = 65537, the algorithm needs to check divisibility by primes up to F4\sqrt{F_4}. If the algorithm uses a sieve to pre-compute primes, what is the largest prime it needs to include in its sieve?
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