Nonvanishing of Least-Witness Prime Floor Quotients for Decimal Powers

OEIS A090518 records the prime quotient associated with A090517, with the fallback wording “or 0 if A090517(n) = 0,” and conjectures that no term is zero. We prove this conjecture by a direct elementary construction. For every integer n ≥ 1, the positive integer k = 5 · 10^(n−1) gives the prime quotient 2. Hence an admissible witness exists. Since one already occurs at a finite index k0, there is a first admissible integer among 1, . . . , k0, and this is the least admissible witness overall. The quotient associated with that least witness is prime by definition and therefore nonzero. Thus every term of A090518 is nonzero. No theorem on the distribution of primes is required. Separately, all 19 values currently displayed by OEIS are recomputed from the least-witness definition as a finite consistency check; the first ten are also checked with an independent elementary trial-division primality routine.