What is Sophie Germain prime?
A '''Sophie Germain prime''' is a type of [[prime number]]. If a prime number is still prime after being multiplied by 2 and adding 1 to the answer, then the original prime is a Sophie Germain prime. A mathematical definition is: a prime number, denoted by ''p'', is a Sophie Germain prime if ''2p+1'' is also a prime number. ''2p+1'' is called a [[safe prime]] if it is a prime number. Sophie Germain primes are named after the French mathematician [[Sophie Germain]]. Many mathematicians believe that there are an infinite amount of Sophie Germain primes, but this has not been proven. ==Examples== 11 is a Sophie Germain prime because 23 ((2 &times; 11) + 1 = 23) is also a prime number. 13 is a prime number but not a Sophie Germain prime because 27 ((2 &times; 13) + 1 = 27) is not a prime number. [[Category:Classes of prime numbers]]