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In this article we present the following new fact for prime p=11. For knots6_2 and 7_2, mincol_{11} 6_2 = 5 = mincol_{11} 7_2, along with the followingfeature. There is a pair of diagrams, one for 6_2 and the other one for 7_2,each of them admitting only non-trivial 11-colorings using 5 colors, butneither of them admitting being colored with the sets of 5 colors that colorthe other one. This is in full contrast with the behavior exhibited by linksadmitting non-trivial p-colorings over the smaller primes, p=2, 3, 5 or 7.  We also prove results concerning obstructions to the minimization of colorsover generic odd moduli. We apply these to find the right colors to eliminatefrom non-trivial colorings. We thus prove that 5 is the minimum number ofcolors for each knot of prime determinant 11 or 13 from Rolfsen's table.

The Minimization of the Number of Colors is Different at p=11