Sophie Germain prime
Five is the third smallest prime number. Since it can be written as , five is classified as a Fermat prime; therefore, a regular polygon with 5 sides (a regular pentagon) is constructible with compass and an unmarked straightedge. Five is the third Sophie Germain prime, the first safe prime, the third Catalan number, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime. It is an Eisenstein prime with no imaginary part and real part of the form . It is also the only number that is part of more than one pair of twin primes. Five is also a super-prime, and a congruent number.