A Geometric Construction for Prime Numbers via Triangular Lattices

I present a conjecture relating to the representation of prime numbersas sums of three preceding primes, supported by a novel geometricconstruction using triangular lattices. This work introduces avisualization method that demonstrates empirical patterns in primenumber generation and proposes a recursive relationship. I verify thisconjecture computationally for primes up to the 10,000th prime number(104,729) and discuss its relationship to existing results in additivenumber theory, particularly the weak Goldbach conjecture.