Big biases amongst products of two primes

Abstract

We show that substantially more than a quarter of the odd integers of the form $pq$ up to $x$, with $p,q$ both prime, satisfy $p\equiv q\equiv 3(\mathrm{mod}4)$.

Cited by in corpus (7)

• Unexpected biases in the distribution of consecutive primes
• Chebyshev's bias for products of irreducible polynomials
• The $2$-Selmer group of a number field and heuristics for narrow class groups and signature ranks of units
• Distribution of Frobenius elements in families of Galois extensions
• An annotated bibliography for comparative prime number theory
• Large bias for integers with prime factors in arithmetic progressions
• Sums of two squares are strongly biased towards quadratic residues