# Tag Info

Accepted

### Sum of reciprocals of Sophie Germain primes

Here is a general result. For a sequence of nonnegative numbers $\{a_n\}$, let $A(x) = \sum_{n \leq x} a_n$. For example, if $S \subset \mathbf Z^+$ and we set $a_n = 1$ when $n\in S$ and $a_n = 0$ ...
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### Sum of reciprocals of Sophie Germain primes

Googling "sum of reciprocals of Sophie Germain primes" brings up the very recent paper: Wagstaff, Samuel S. jun., Sum of reciprocals of germain primes, J. Integer Seq. 24, No. 9, Article 21....
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Accepted

### A question regarding Cramér's proof on prime gaps under the Riemann Hypothesis

On the Riemann hypothesis and the difference between primes by Adrian W. Dudek states the result (Theorem 3, at least in the arXiv version) that any $C>1$ works (for $n$ sufficiently large).
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### Reference request: Numbers composed of given primes

As Mikhail Tikhomirov commented, the denominator should have $\log$ of $p_j$ instead of $p_j$ itself. For a reference see Theorem 5.3, and more generally, section 2 (`The geometric method') of Chapter ...
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### Primality test for $\frac{(10 \cdot 2^n)^m-1}{10 \cdot 2^n-1} - 2$ and $\frac{(10 \cdot 2^n)^m+1}{10 \cdot 2^n+1} - 2$

It's often the case with such tests that the "only if" part is more or less easy to prove, while the "if" part is inaccessible for proving or disproving. Below I prove the "...
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