Another unproven conjecture is that there are an infinitude of primes that are 1 less than a power of 2, such as 3 = 22 − 1.
(a) Find four more of these primes.
(b) If p = 2k − 1 is prime, show that k is an odd integer, except when k = 2.
[Hint: 3|4n − 1 for all n ≥ 1.]
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