# A theorem of Bombieri-Vinogradov type with few exceptional moduli

## TL;DR

This paper extends the Bombieri-Vinogradov theorem to a specific set of moduli, showing primes in arithmetic progressions behave as expected with few exceptions, under certain size constraints.

## Contribution

It establishes a Bombieri-Vinogradov type result for sets of pairwise coprime moduli with size less than x^(9/40), with a bound on exceptional moduli.

## Key findings

- Expected prime distribution in arithmetic progressions for specified moduli
- Bound on the number of exceptional moduli by a power of log x
- Extension of Bombieri-Vinogradov theorem to new set of moduli

## Abstract

If a set S of pairwise coprime moduli q, less than x^(9/40), is considered, one obtains the expected behavior for primes up to x in arithmetic progressions mod q, except for a subset of S whose cardinality is bounded by a power of log x.