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. 
H. Gopalkrishna Gadiyar and R. Padma