Another pair is 16,73. The hard question is: Are there infinitely many such pairs? Since we know little about prime numbers, we cannot answer this question. Look at this set:
S={n-2^i|n is odd, i=1,2,3...}
what we need for S is that S contains a unique prime which has i>1. S may have many primes (e.g. n=11) or may not have any prime (can you find an example?).
If we can find such S, then, the prime number in S, let call it n-2^m and 2^m is a solution.
S={n-2^i|n is odd, i=1,2,3...}
what we need for S is that S contains a unique prime which has i>1. S may have many primes (e.g. n=11) or may not have any prime (can you find an example?).
If we can find such S, then, the prime number in S, let call it n-2^m and 2^m is a solution.
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