Imran Ghory has used data on the largest prime gaps to confirm the conjecture for up to 1.3002 × 1016. Using a table of maximal gaps and the above gap inequality, the confirmation value can be extended exhaustively to 4 × 1018.
The discrete function is plotted in the figures opposite. The high-water marks for occur for n = 1, 2, and 4, with A4 ≈ 0.670873..., with no larger value among the first 105 primes. Since the Andrica function decreases asymptotically as n increases, a prime gap of ever increasing size is needed to make the difference large as n becomes large. It therefore seems highly likely the conjecture is true, although this has not yet been proven.