Problems & Puzzles: Puzzles

Puzzle 805. Prime gaps containing... Vic Bold sent the following nice puzzle: For 2^a * 3^b with a, b>=0 one finds two such numbers in these three prime gaps: 7, 8,9, 11; 23  24,27  29;  31, 32,36  37.  Is there a fourth example?  Q. Send all the examples you can find.

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Contributions came from Vicente Felipe Izquierdo, Tony D. Noe

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Vicente wrote:

For 200>a>=0 and 200>b>=0 I don't find any more example.

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Tony wrote:

I think {3,4} is the only other solution, which has primes 2 and 5 on
either side... [But 2 and 5 are not consecutive primes] ...That is true, but another way of looking at the problem is that {3,4} have no primes between them (just as the other pairs have no primes between
them).

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Later, Tony added:

See http://integersequences.org/s000742.html for a sequence derived from
this puzzle.

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