Sophie Germain prime
If "p" is a Sophie Germain prime greater than 3, then "p" must be congruent to 2 mod 3. For, if not, it would be congruent to 1 mod 3 and 2"p" + 1 would be congruent to 3 mod 3, impossible for a prime number. Similar restrictions hold for larger prime moduli, and are the basis for the choice of the "correction factor" 2"C" in the Hardy–Littlewood estimate on the density of the Sophie Germain primes.