ilist = dlist = {};
Do[dlist = Append[dlist, Prime[n + 1] - Prime[n]], {n, 1000}];
Do[ilist = Append[ilist, dlist[[n + 1]] - dlist[[n]]], {n, 999} ];
dlist
{1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, 10, 14, 4, 2, 4, 14, 6, 10, 2, 4, 6, 8, 6, 6, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6, 4, 6, 8, 4, 2, 4, 12, 8, 4, 8, 4, 6, 12, 2, 18, 6, 10, 6, 6, 2, 6, 10, 6, 6, 2, 6, 6, 4, 2, 12, 10, 2, 4, 6, 6, 2, 12, 4, 6, 8, 10, 8, 10, 8, 6, 6, 4, 8, 6, 4, 8, 4, 14, 10, 12, 2, 10, 2, 4, 2, 10, 14, 4, 2, 4, 14, 4, 2, 4, 20, 4, 8, 10, 8, 4, 6, 6, 14, 4, 6, 6, 8, 6, 12, 4, 6, 2, 10, 2, 6, 10, 2, 10, 2, 6, 18, 4, 2, 4, 6, 6, 8, 6, 6, 22, 2, 10, 8, 10, 6, 6, 8, 12, 4, 6, 6, 2, 6, 12, 10, 18, 2, 4, 6, 2, 6, 4, 2, 4, 12, 2, 6, 34, 6, 6, 8, 18, 10, 14, 4, 2, 4, 6, 8, 4, 2, 6, 12, 10, 2, 4, 2, 4, 6, 12, 12, 8, 12, 6, 4, 6, 8, 4, 8, 4, 14, 4, 6, 2, 4, 6, 2, 6, 10, 20, 6, 4, 2, 24, 4, 2, 10, 12, 2, 10, 8, 6, 6, 6, 18, 6, 4, 2, 12, 10, 12, 8, 16, 14, 6, 4, 2, 4, 2, 10, 12, 6, 6, 18, 2, 16, 2, 22, 6, 8, 6, 4, 2, 4, 8, 6, 10, 2, 10, 14, 10, 6, 12, 2, 4, 2, 10, 12, 2, 16, 2, 6, 4, 2, 10, 8, 18, 24, 4, 6, 8, 16, 2, 4, 8, 16, 2, 4, 8, 6, 6, 4, 12, 2, 22, 6, 2, 6, 4, 6, 14, 6, 4, 2, 6, 4, 6, 12, 6, 6, 14, 4, 6, 12, 8, 6, 4, 26, 18, 10, 8, 4, 6, 2, 6, 22, 12, 2, 16, 8, 4, 12, 14, 10, 2, 4, 8, 6, 6, 4, 2, 4, 6, 8, 4, 2, 6, 10, 2, 10, 8, 4, 14, 10, 12, 2, 6, 4, 2, 16, 14, 4, 6, 8, 6, 4, 18, 8, 10, 6, 6, 8, 10, 12, 14, 4, 6, 6, 2, 28, 2, 10, 8, 4, 14, 4, 8, 12, 6, 12, 4, 6, 20, 10, 2, 16, 26, 4, 2, 12, 6, 4, 12, 6, 8, 4, 8, 22, 2, 4, 2, 12, 28, 2, 6, 6, 6, 4, 6, 2, 12, 4, 12, 2, 10, 2, 16, 2, 16, 6, 20, 16, 8, 4, 2, 4, 2, 22, 8, 12, 6, 10, 2, 4, 6, 2, 6, 10, 2, 12, 10, 2, 10, 14, 6, 4, 6, 8, 6, 6, 16, 12, 2, 4, 14, 6, 4, 8, 10, 8, 6, 6, 22, 6, 2, 10, 14, 4, 6, 18, 2, 10, 14, 4, 2, 10, 14, 4, 8, 18, 4, 6, 2, 4, 6, 2, 12, 4, 20, 22, 12, 2, 4, 6, 6, 2, 6, 22, 2, 6, 16, 6, 12, 2, 6, 12, 16, 2, 4, 6, 14, 4, 2, 18, 24, 10, 6, 2, 10, 2, 10, 2, 10, 6, 2, 10, 2, 10, 6, 8, 30, 10, 2, 10, 8, 6, 10, 18, 6, 12, 12, 2, 18, 6, 4, 6, 6, 18, 2, 10, 14, 6, 4, 2, 4, 24, 2, 12, 6, 16, 8, 6, 6, 18, 16, 2, 4, 6, 2, 6, 6, 10, 6, 12, 12, 18, 2, 6, 4, 18, 8, 24, 4, 2, 4, 6, 2, 12, 4, 14, 30, 10, 6, 12, 14, 6, 10, 12, 2, 4, 6, 8, 6, 10, 2, 4, 14, 6, 6, 4, 6, 2, 10, 2, 16, 12, 8, 18, 4, 6, 12, 2, 6, 6, 6, 28, 6, 14, 4, 8, 10, 8, 12, 18, 4, 2, 4, 24, 12, 6, 2, 16, 6, 6, 14, 10, 14, 4, 30, 6, 6, 6, 8, 6, 4, 2, 12, 6, 4, 2, 6, 22, 6, 2, 4, 18, 2, 4, 12, 2, 6, 4, 26, 6, 6, 4, 8, 10, 32, 16, 2, 6, 4, 2, 4, 2, 10, 14, 6, 4, 8, 10, 6, 20, 4, 2, 6, 30, 4, 8, 10, 6, 6, 8, 6, 12, 4, 6, 2, 6, 4, 6, 2, 10, 2, 16, 6, 20, 4, 12, 14, 28, 6, 20, 4, 18, 8, 6, 4, 6, 14, 6, 6, 10, 2, 10, 12, 8, 10, 2, 10, 8, 12, 10, 24, 2, 4, 8, 6, 4, 8, 18, 10, 6, 6, 2, 6, 10, 12, 2, 10, 6, 6, 6, 8, 6, 10, 6, 2, 6, 6, 6, 10, 8, 24, 6, 22, 2, 18, 4, 8, 10, 30, 8, 18, 4, 2, 10, 6, 2, 6, 4, 18, 8, 12, 18, 16, 6, 2, 12, 6, 10, 2, 10, 2, 6, 10, 14, 4, 24, 2, 16, 2, 10, 2, 10, 20, 4, 2, 4, 8, 16, 6, 6, 2, 12, 16, 8, 4, 6, 30, 2, 10, 2, 6, 4, 6, 6, 8, 6, 4, 12, 6, 8, 12, 4, 14, 12, 10, 24, 6, 12, 6, 2, 22, 8, 18, 10, 6, 14, 4, 2, 6, 10, 8, 6, 4, 6, 30, 14, 10, 2, 12, 10, 2, 16, 2, 18, 24, 18, 6, 16, 18, 6, 2, 18, 4, 6, 2, 10, 8, 10, 6, 6, 8, 4, 6, 2, 10, 2, 12, 4, 6, 6, 2, 12, 4, 14, 18, 4, 6, 20, 4, 8, 6, 4, 8, 4, 14, 6, 4, 14, 12, 4, 2, 30, 4, 24, 6, 6, 12, 12, 14, 6, 4, 2, 4, 18, 6, 12, 8}
ilist
{1, 0, 2, -2, 2, -2, 2, 2, -4, 4, -2, -2, 2, 2, 0, -4, 4, -2, -2, 4, -2, 2, 2, -4, -2, 2, -2, 2, 10, -10, 2, -4, 8, -8, 4, 0, -2, 2, 0, -4, 8, -8, 2, -2, 10, 0, -8, -2, 2, 2, -4, 8, -4, 0, 0, -4, 4, -2, -2, 8, 4, -10, -2, 2, 10, -8, 4, -8, 2, 2, 2, -2, 0, -2, 2, 2, -4, 4, 2, -8, 8, -8, 4, -2, 2, 2, -4, -2, 2, 8, -4, -4, 4, -4, 2, 6, -10, 16, -12, 4, -4, 0, -4, 4, 4, -4, 0, -4, 4, 0, -2, -2, 10, -2, -8, 2, 2, 0, -4, 10, -8, 2, 2, 2, -2, 2, -2, -2, 0, -2, 4, -2, -2, 4, -4, 10, -4, 2, -10, 8, -8, 2, -2, 8, 4, -10, -2, 2, 10, -10, -2, 2, 16, -16, 4, 2, -2, -4, 2, 0, 8, -10, 2, 0, 2, -2, 6, -8, 2, -4, 8, -8, 4, 4, -8, 8, -8, 4, 12, -14, -2, 2, 2, 0, 2, -2, 0, 16, -20, 8, -2, 2, -4, 0, 2, 4, -8, 2, 0, -4, 4, 6, -2, 8, -16, 2, 2, -4, 4, -2, -2, 2, 8, -10, 4, 28, -28, 0, 2, 10, -8, 4, -10, -2, 2, 2, 2, -4, -2, 4, 6, -2, -8, 2, -2, 2, 2, 6, 0, -4, 4, -6, -2, 2, 2, -4, 4, -4, 10, -10, 2, -4, 2, 2, -4, 4, 4, 10, -14, -2, -2, 22, -20, -2, 8, 2, -10, 8, -2, -2, 0, 0, 12, -12, -2, -2, 10, -2, 2, -4, 8, -2, -8, -2, -2, 2, -2, 8, 2, -6, 0, 12, -16, 14, -14, 20, -16, 2, -2, -2, -2, 2, 4, -2, 4, -8, 8, 4, -4, -4, 6, -10, 2, -2, 8, 2, -10, 14, -14, 4, -2, -2, 8, -2, 10, 6, -20, 2, 2, 8, -14, 2, 4, 8, -14, 2, 4, -2, 0, -2, 8, -10, 20, -16, -4, 4, -2, 2, 8, -8, -2, -2, 4, -2, 2, 6, -6, 0, 8, -10, 2, 6, -4, -2, -2, 22, -8, -8, -2, -4, 2, -4, 4, 16, -10, -10, 14, -8, -4, 8, 2, -4, -8, 2, 4, -2, 0, -2, -2, 2, 2, 2, -4, -2, 4, 4, -8, 8, -2, -4, 10, -4, 2, -10, 4, -2, -2, 14, -2, -10, 2, 2, -2, -2, 14, -10, 2, -4, 0, 2, 2, 2, 2, -10, 2, 0, -4, 26, -26, 8, -2, -4, 10, -10, 4, 4, -6, 6, -8, 2, 14, -10, -8, 14, 10, -22, -2, 10, -6, -2, 8, -6, 2, -4, 4, 14, -20, 2, -2, 10, 16, -26, 4, 0, 0, -2, 2, -4, 10, -8, 8, -10, 8, -8, 14, -14, 14, -10, 14, -4, -8, -4, -2, 2, -2, 20, -14, 4, -6, 4, -8, 2, 2, -4, 4, 4, -8, 10, -2, -8, 8, 4, -8, -2, 2, 2, -2, 0, 10, -4, -10, 2, 10, -8, -2, 4, 2, -2, -2, 0, 16, -16, -4, 8, 4, -10, 2, 12, -16, 8, 4, -10, -2, 8, 4, -10, 4, 10, -14, 2, -4, 2, 2, -4, 10, -8, 16, 2, -10, -10, 2, 2, 0, -4, 4, 16, -20, 4, 10, -10, 6, -10, 4, 6, 4, -14, 2, 2, 8, -10, -2, 16, 6, -14, -4, -4, 8, -8, 8, -8, 8, -4, -4, 8, -8, 8, -4, 2, 22, -20, -8, 8, -2, -2, 4, 8, -12, 6, 0, -10, 16, -12, -2, 2, 0, 12, -16, 8, 4, -8, -2, -2, 2, 20, -22, 10, -6, 10, -8, -2, 0, 12, -2, -14, 2, 2, -4, 4, 0, 4, -4, 6, 0, 6, -16, 4, -2, 14, -10, 16, -20, -2, 2, 2, -4, 10, -8, 10, 16, -20, -4, 6, 2, -8, 4, 2, -10, 2, 2, 2, -2, 4, -8, 2, 10, -8, 0, -2, 2, -4, 8, -8, 14, -4, -4, 10, -14, 2, 6, -10, 4, 0, 0, 22, -22, 8, -10, 4, 2, -2, 4, 6, -14, -2, 2, 20, -12, -6, -4, 14, -10, 0, 8, -4, 4, -10, 26, -24, 0, 0, 2, -2, -2, -2, 10, -6, -2, -2, 4, 16, -16, -4, 2, 14, -16, 2, 8, -10, 4, -2, 22, -20, 0, -2, 4, 2, 22, -16, -14, 4, -2, -2, 2, -2, 8, 4, -8, -2, 4, 2, -4, 14, -16, -2, 4, 24, -26, 4, 2, -4, 0, 2, -2, 6, -8, 2, -4, 4, -2, 2, -4, 8, -8, 14, -10, 14, -16, 8, 2, 14, -22, 14, -16, 14, -10, -2, -2, 2, 8, -8, 0, 4, -8, 8, 2, -4, 2, -8, 8, -2, 4, -2, 14, -22, 2, 4, -2, -2, 4, 10, -8, -4, 0, -4, 4, 4, 2, -10, 8, -4, 0, 0, 2, -2, 4, -4, -4, 4, 0, 0, 4, -2, 16, -18, 16, -20, 16, -14, 4, 2, 20, -22, 10, -14, -2, 8, -4, -4, 4, -2, 14, -10, 4, 6, -2, -10, -4, 10, -6, 4, -8, 8, -8, 4, 4, 4, -10, 20, -22, 14, -14, 8, -8, 8, 10, -16, -2, 2, 4, 8, -10, 0, -4, 10, 4, -8, -4, 2, 24, -28, 8, -8, 4, -2, 2, 0, 2, -2, -2, 8, -6, 2, 4, -8, 10, -2, -2, 14, -18, 6, -6, -4, 20, -14, 10, -8, -4, 8, -10, -2, 4, 4, -2, -2, -2, 2, 24, -16, -4, -8, 10, -2, -8, 14, -14, 16, 6, -6, -12, 10, 2, -12, -4, 16, -14, 2, -4, 8, -2, 2, -4, 0, 2, -4, 2, -4, 8, -8, 10, -8, 2, 0, -4, 10, -8, 10, 4, -14, 2, 14, -16, 4, -2, -2, 4, -4, 10, -8, -2, 10, -2, -8, -2, 28, -26, 20, -18, 0, 6, 0, 2, -8, -2, -2, 2, 14, -12, 6, -4}
In seeking the unattainable, simplicity only gets in the way. -- Epigrams in Programming, ACM SIGPLAN Sept. 1982