Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramanujan - Fourier Series and the Density of Sophie Germain Primes   A prime p is called Sophie Germain prime if 2p+1 is also prime. A formula for
the density of such primes is given in a more general setting using a new
approach. This method uses the Ramanujan-Fourier series for a modified von
Mangoldt function. The proof remains heuristic as interchange of certain limits
has not been justified. Experimental evidence using computer calculations is
provided for the plausibility of the result.

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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas