12 stories tagged number-theory, newest first.
![Screenshot of jdb19937.github.io: The logarithms of rational numbers have irrationality exponent 2 [pdf]](https://hn.urlbox.com/shots/renders/2026/10/10/3771ae7f-7658-4460-b339-470c583bc18c.jpg)
16 points by jdb1729 | 3 comments
A math paper by Dan Brown claiming the irrationality measure of log of any rational number other than 1 is 2, with the proof formalized in Lean 4 over Mathlib.
![Screenshot of jdb19937.github.io: The reciprocal sum of the prime-prefix-free numbers converges [pdf]](https://hn.urlbox.com/shots/renders/2026/10/9/782dd723-5a0f-4ad2-9aa4-d11ae9b968a4.jpg)
15 points by jdb1729 | 14 comments
A math paper proving, assuming the Riemann Hypothesis, that the reciprocal sum of prime-prefix-free integers (OEIS A287117) converges, with bounds verified in Lean 4.
733 points by pr337h4m | 508 comments
Scientific American article about an amateur who used ChatGPT to prove a 60-year-old Erdős conjecture with a novel method.
613 points by ColinWright | 100 comments
John D. Cook blog post examining why 987654321/123456789 is nearly 8 and whether analogous digit ratios in other bases are close to integers.
338 points by LorenDB | 144 comments
Eli Bendersky's blog post on the puzzle of generating any natural number using exactly four 2s and arbitrary mathematical operations.
782 points by philiplu | 399 comments
Quanta Magazine profile of Srinivasa Ramanujan, the self-taught Indian mathematician whose ideas continue to shape mathematics today.
375 points by igitur | 140 comments
Science magazine news article on a breakthrough in number theory toward understanding the hidden structure of prime numbers; capture shows a Cloudflare check.
516 points by pera | 144 comments
A Mastodon post by Terence Tao describing Guth and Maynard's improvement to Ingham's 1940 zero density bound for the Riemann zeta function.
443 points by gone35 | 90 comments
Wikipedia article on 6174, Kaprekar's constant, the fixed point reached by repeatedly subtracting ascending from descending digit arrangements of four-digit numbers.
416 points by sacrosanct | 185 comments
Blog post by Chris Grossack exploring the fact that 37 is the median value of the second smallest prime factor of an integer, verified with Sage.
331 points by nivethan | 88 comments
A 3Blue1Brown lesson page with an embedded video explaining why plotting prime numbers in polar coordinates produces spiral patterns.
486 points by keithmcnulty | 138 comments
A Medium article by Keith McNulty explaining why 2 and 4 are the only distinct positive integers satisfying m^n = n^m.