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.
Yurii Sherehii (Sat,) studied this question.