{"id":"hexagon/2611.00049","pdf":"https://hexagonmath.org/pdf/2611.00049v1","url":"https://hexagonmath.org/abs/2611.00049v1","tags":["math.NA","msc:11P32","msc:51M15","msc:11A25","Cram\\'er's conjecture","Goldbach Conjecture","additive energy","computational evidence","differences of primes","explicit sieve bounds"],"score":0,"title":"Nested Squares and Distinct-Prime Goldbach Partitions","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Frank Vega"],"reviews":0,"subject":"math.NT","summary":"The distinct-prime Goldbach conjecture asserts that for every $N\\geq 4$ there is $M\\in A_N=[1,N-3]$ with $N-M$ and $N+M$ both prime; geometrically, nested squares of side lengths $N$ and $M$ have an L-shaped difference of semiprime area $(N-M)(N+M)$. With $C_N$ and $D_N$ the sets of $M\\in A_N$ for which $N-M$, respectively $N+M$, is prime, the conjecture for $2N$ is $C_N\\cap D_N\\neq\\varnothing$. We embed this centered condition in a straddling one: $C_N\\cap D_N$ lies in the set $E_N$ of half-differences $(Q-P)/2\\in A_N$ of primes $2 0$, and with explicit constants we prove $|E_N|>N/760$ for…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}