Recall that a sequence of integers
(a0, a1, ... ak-1)is an admissible k-tuple as long as it does not include a complete set of residues for any prime less than or equal to k. When the tuple is admissible, then it is conjectured that its translates be simultaneously prime infinitely often. In other words, there will be infinitely many integers n such that all k of the values
(n + a0, n + a1, ... n + ak-1)will be prime. Applying this conjecture to (0, 2) yields the twin prime conjecture.
Type the terms of the k-tuple into the boxes, then click "Check!" to see if it admissible. (The result will appear in the "result" box.) If the result is not admissible, the "Fix" button will try to make it admissible. Another option is to extend the k-tuple to a longer admissible tuple (this uses a greedy algorithm so may not yield the "shortest" possible k-tuples).
Note - this form uses a cookie in order to remember how many boxes you want. Without cookies it will default to 7.
(An insult to real coding by FatPhil, in the public domain with no restrictions on propagation or use.)