Prime values of a^2+p^4

Many remarkably difficult conjectures in prime number theory take the form that there are infinitely many primes in some set of natural numbers S . In many interesting examples, we even have conjectured asymptotic formulas for the number of primes in S . Thus, we think that there are infinitely many...

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Detalhes bibliográficos
Principais autores: Heath-Brown, D, Li, X
Formato: Journal article
Publicado em: Springer 2016
Descrição
Resumo:Many remarkably difficult conjectures in prime number theory take the form that there are infinitely many primes in some set of natural numbers S . In many interesting examples, we even have conjectured asymptotic formulas for the number of primes in S . Thus, we think that there are infinitely many primes of the form p + 2, a^2 + 1, a^2 + b^6, and so on.