Among the first 10 primes, {2,3,...,23,29}, the largest difference is 29-23=6. Therefore 6 is the largest prime gap in the first ten primes.
MATHEMATICA
a = 1; b = 1; d = 0; k = 1; Do[ While[k <= 10^n, a = b; b = Prime[k]; If[b - a > d; d = b - a]; k++ ]; Print[d], {n, 12}] (* Robert G. Wilson v, Sep 24 2004 *)