Primes from sums of two squares and missing digits

© 2019 London Mathematical Society Let Aʹ 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 = m2 + l2, with l ϵ Aʹ. The proof draws on ideas from the work of Friedlander–Iwaniec on primes of the form p = x2 + y4, as well as ideas from the work of Maynard on primes with restricted digits.