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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.

Primes from sums of two squares and missing digits