Predicting Prime Distribution by Leading 1-Run Length in Binary Representation

We show that the number of primes with leading 1-run length exactly g in the L-bit range [2^(L-1), 2^L) is given by count(g, L) = integral from a to b of dt/ln(t), where [a, b) = [2^L - 2^(L-g), 2^L - 2^(L-g-1)). A closed-form approximation requiring only one division and one logarithm is also derived: count(g, L) = 2^(L-g-1) / ln(2^L - 3 * 2^(L-g-2)). Verified by exhaustive sieve for L = 10 to 32 (primes up to 4.3 billion), accuracy reaches 99.99%. For higher precision, Riemann's R function can be applied to each sub-interval. The practical application of this result is, at this point, unknown to the author. Includes LaTeX source and a self-contained Python verification script.