Abstract
It has been shown by different methods that there is an infinity of positive odd integers not representable as the sum of a prime and a (positive) power of 2, thus disproving a conjecture to the contrary which had been made in the nineteenth century. The question then arises as to whether or not all sufficiently large positive odd integers can be represented as the sum of a prime and of two positive powers of 2; that is, as p + 2α -f 2 6, where α, b > 0 and p is prime. (The corresponding question has been discussed for bases other than 2 but is really quite trivial.) Theorem I gives a negative answer to this question. THEOREM I. There is an infinity of distinct, positive odd integers not representable as the sum of a prime and of two positive powers of 2.
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