Claims

../

2020_07_03_ziller: Ziller's arXiv preprint shows that each of 2, 4, ..., 2k is a difference of consecutive integers coprime to the k-th primorial, so the least even non-gap is at least 2k+2; with computations through k = 44.

2026_07_27_white: A working report by Patrick White with Claude proves that the least even non-gap among totatives of the k-th primorial is at least (e^gamma - o(1)) k log log k, and computes it exactly through k = 13.

2026_08_20_dottedcalculator: DottedCalculator's partial claim, a write-up signed by GPT 5.6 Sol: for large k every even number up to a constant times p_k is a gap between consecutive totatives of the primorial; the least even non-gap is >> p_k.

---