**dhc@exodus.UUCP (David H. Copp)** (05/01/84)

The author of the previous note requests a proof for the conjecture "Every positive odd integer >= 3 is the sum of a prime and a power of 2." The conjecture is false. The first six counterexamples are 127, 149, 251, 331, 337, 373. -- David H. Copp

**gmf@uvacs.UUCP** (05/02/84)

Concerning x odd & >= 3 --> x = 2^k + p for some k and prime p . This may be relevant: "It can be proved that for every natural number k there are infinitely many k-powers of natural numbers which are not of the form a^k + p, where a is an integer and p a prime. (cf. Clement [2])." W. Sierpinski * Elementary Theory of Numbers * (Warsaw, 1964), p. 113 "Clement, P. A. ... [2] Representation of integers in the form: a k-th power plus a prime, Amer. Math. Monthly 56 (1949), p. 561." Ibid., p. 450 Gordon Fisher

**djc1@ihu1g.UUCP (Dave)** (05/07/84)

Can anyone provide me with a proof for the following: "Every positive odd integer >= 3 is the sum of a prime and a power of 2." Please mail me whatever thoughts you may have on solving this. Thanks.... -- Dave Christensen AT&T Bell Labs - Indian Hill ..ihnp4!ihu1g!djc1