Primes in Half-Intervals of Consecutive Squares

Joseph Musonda’s research, Primes in Half-Intervals of Consecutive Squares, proposes a new conjecture in number theory asserting that every interval [n^2/4, (n+1)^2/4] for every integer greater than or equal to 2, contains at least one prime number. Motivated by observed patterns linking primes to multiples of four within intervals between consecutive squares, the study presents computational evidence verified for [2, 200 000] with no counterexample reported. It also uses the Prime Number Theorem and Cramér’s probabilistic model to provide heuristic support for the conjecture, which aims to establish the existence of primes in substantially shorter intervals than those considered in classical conjectures such as Legendre’s and Oppermann’s.