Gilbreath's Conjecture
Mathematica, 66 bytes

(For[z=1,Last@Nest[Abs@*Differences,Array[Prime,z+#],#]&lt;3,z++];z)&amp;


Pure function taking a positive integer as argument and returning a 1-indexed integer. Nest[Abs@*Differences,Array[Prime,z+#],#] computes the #th iterated absolute difference list of the list of the first z+# primes. For[z=1,Last@...&lt;3,z++] loops this computation until the last element of the resulting list is at least 3, and then z is output. (Note that the correctness of the algorithm assumes Gilbreath's conjecture!)