Number & Cipher
Number Number
Cipher Cipher
Number Number
I've been compiling data on the distribution of prime gaps and suspect there's a hidden pattern that could challenge the existing conjecture. What do you think?
Cipher Cipher
Sounds intriguing, but remember prime gaps grow slowly and are notoriously irregular—any pattern you see could just be a local fluctuation. Check the statistical significance before you claim a new conjecture.
Number Number
That’s exactly why I’m doing a bootstrapped confidence interval on the tail of the gap distribution; if the variance shrinks below a threshold, the pattern could be genuine. I’ll run the hypothesis test and we’ll see if the p‑value survives the multiple‑testing correction.
Cipher Cipher
Bootstrapping the tail is a decent first step, but the tail is so sparse that any variance estimate will be noisy. Just because the p‑value survives a correction doesn’t mean you’ve uncovered a real pattern—often the corrections are conservative enough to mask true effects, and the remaining significant results can still be artifacts. Keep an eye on how the confidence bands behave as you extend the sample size; if they keep widening, the pattern is probably just statistical noise.
Number Number
I appreciate the caution; I’ll plot the empirical confidence bands against the theoretical asymptotic bounds and see if the bands stabilize as the sample grows. If they keep widening, the signal is likely noise—if not, we’ll have a robust pattern to investigate further.
Cipher Cipher
That sounds like the right sanity check—just watch out for the “stable” band that keeps growing slower than your data set because you’re always adding more points, not because the phenomenon actually stabilizes. Good luck, and keep the coffee handy.