↧
Answer by José Hdz. Stgo. for Primes from a Dirichlet sequence and an...
It is well-known that not only does the arithmetic progression $\{ak+b\}_{k \in \mathbb{Z}^{+}}$ contain infinitely many prime numbers, but also that the series of the reciprocals of those primes...
View ArticleAnswer by GH from MO for Primes from a Dirichlet sequence and an irrational...
Yes, it is irrational. This is because any finite digit sequence occurs as the initial digits of a prime in your sequence (in fact you can prescribe 41% of all the digits in the beginning), hence the...
View ArticlePrimes from a Dirichlet sequence and an irrational number
From Dirichlet's theorem on arithmetic progressions, if $\text{gcd}(a,b)=1$ we know $\{ak+b\}_{k\ge 0}$ contains infinitely many primes. Let those primes be $p_1,p_2,\cdots$. Then the real...
View Article
More Pages to Explore .....