23

This number is a prime.

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Let c = 2^a * 3^b with a,b>0 and prime p with p^n, n>1, c-p^k=prime. Is prime=23 the most common? E.g., 48-25=23, 72-49=23, 144-121=23, 192-169=23, 648-625=23, etc. [Bergot]

Square 23 to get 529, square 529 to get 279841. Notice that the last three digits (841) equals 29^2, providing 29 as the next prime after 23. [Bergot]

To get to the next prime after 23, add 2+2+2 to get 29. Change 2+2+2 to 2*2*2 = 8, then 23*8 mod(23+8) = 29. [Bergot]