Primes with restricted digits

@article{Maynard2016PrimesWR,
  title={Primes with restricted digits},
  author={James Maynard},
  journal={Inventiones mathematicae},
  year={2016},
  volume={217},
  pages={127-218}
}
  • James Maynard
  • Published 2016
  • Mathematics
  • Inventiones mathematicae
  • Let $$a_0\in \{0,\ldots ,9\}$$a0∈{0,…,9}. We show there are infinitely many prime numbers which do not have the digit $$a_0$$a0 in their decimal expansion. The proof is an application of the Hardy–Littlewood circle method to a binary problem, and rests on obtaining suitable ‘Type I’ and ‘Type II’ arithmetic information for use in Harman’s sieve to control the minor arcs. This is obtained by decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 19 REFERENCES
    Prescribing the binary digits of primes, II
    15
    Weyl sums over integers with affine digit restrictions
    12
    Arithmetic properties of numbers with restricted digits
    19
    Opera De Cribro
    226
    On arithmetic properties of integers with missing digits II: Prime factors
    23
    On the uniform distribution modulo one of some subsequences of polynomial sequences
    11
    The distribution of α p modulo one
    52
    Nombres presque premiers dont l'écriture en base r ne comporte pas certains chiffres
    23
    Ensembles de densité nulle contenant des entiers possédant au plus deux facteurs premiers
    14