Element of number theory
(a) Give all primes p, if any, for which p
2 + 2 is also prime.
(b) Find 5 consecutive composite integers. [For example, 8, 9, 10 is a sequence of 3 consecutive
composite integers, but the integers before and after are both primes.]
(c) Prove that for each k ≥ 1, there exists a sequence of k consecutive composite integers.
2 + 2 is also prime.
(b) Find 5 consecutive composite integers. [For example, 8, 9, 10 is a sequence of 3 consecutive
composite integers, but the integers before and after are both primes.]
(c) Prove that for each k ≥ 1, there exists a sequence of k consecutive composite integers.
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