Three dominant singularities for compositions into parts of the form p-2.

Let S(z) be the sum of z to the power p-2 over the odd primes p, and let B(z) = 1/(1-S(z)) = sum b_n z^n near the origin. The coefficient b_n counts the ordered compositions of n into parts of the form p-2. The function F = 1-S has exactly three zeros, all simple, in the disk of radius 93/100: a real zero r in an explicit rational interval of length 2/10^14, and a complex conjugate pair in disks of radius 10^{-7}. For every n at least 0, b_n equals A r to the power -n, plus twice the real part of C u to the power -n, plus a remainder E_n bounded by 20 times (100/93) to the power n. The count is a finite integer-arithmetic certificate, by a winding number and Rouche's theorem. The same certificate gives the thresholds 62, 53, 52 and 42 for three classes of tail perturbations. The behaviour as z tends to 1 through the exponential sum over primes follows from the prime number theorem and, if the Riemann hypothesis is assumed, from von Koch's estimate. None of these statements is an assertion about the zeros of the Riemann zeta function. The record contains the English version (main file), a faithful Portuguese version, and the supplementary archive (Python scripts, figures, and the LaTeX sources). The decisive integer comparisons are checked by the script certificado.py. They were not formalised in a proof assistant.Paper 1 of 2 on generating functions built from the odd primes, with exponents of the form p-2.