The PKD Conjecture-Vô Conjecture 5 series 1(VC5S1)

Let $p, d$ be positive integers with (p, d) = 1, and define N = max(p, d). Consider the function: f(N) = e(ln N)² We propose the PKD Conjecture, which asserts that for every such pair $(p, d)$ there exists an integer k satisfying $0 < k < f(N)$ such that the linear form $q = pk + d$ is prime. This conjecture provides an explicit logarithmic-square bound for the occurrence of primes in arithmetic progressions. If true, it would represent a substantial strengthening of existing bounds for the least prime in a given progression.