Then the theorem states that given any real number N there exists a positive constant CN depending only on N such that
whenever (a, q) = 1 and
The constant CN is not effectively computable because Siegel's theorem is ineffective.
From the theorem we can deduce the following form of the prime number theorem for arithmetic progressions: If, for (a,q)=1, by we denote the number of primes less than or equal to x which are congruent to a mod q, then
where N, a, q, CN and φ are as in the theorem, and Li denotes the offset logarithmic integral.