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I thought this would be a hard problem but I found a link that seems to ask the answer to this question as a homework problem? Can somone help me out here, are there an infinite number of prime powers that differ by 1? or are there a finite number of them? If so which are they?

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    You mean like $\,|2^5-31^1|=1\,,\,|2^4-17^1|=1\,,...$ , or ...what happens with prime powers of *odd* primes?2012-11-14
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    If we count a prime itself as a prime power, then the answer is not known, since it is not known whether there are infinitely many Fermat primes. If we are looking at powers $\ge 2$, everything is known.2012-11-14

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