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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

-4 votes
1 answer
302 views

Does Goldbach's Conjecture imply a stronger statement about prime pair distributions?

The discussion on F. Brunault's question and extensive calculations suggest: $$ \qquad f_{n+1} < 4p_n \quad\text{for}\quad n > 0$$ where $f_n$ is the Frobenius number of the numerical semigroup gener …
4 votes
0 answers
195 views

Effective bound for odd numbers expressed as sums of three primes

I am interested in the representation of odd numbers greater than five as sums of three primes, inspired by Harald Helfgott's seminal proof of the ternary Goldbach conjecture and the nuanced findings …