Primes from sums of two squares and missing digits

Abstract

Let A ′ be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for counting primes of the form p = m 2 + ℓ 2 , with ℓ ∈ A ′ . The proof draws on ideas from the work of Friedlander–Iwaniec on primes of the form p = x 2 + y 4 , as well as ideas from the work of Maynard on primes with restricted digits.