It has been shown that an n-sided regular polygon can be constructed with a compass and straightedge if and only if n is a power of two or the product of a power of two and two distinct prime members of this sequence.  
Goldbach proved that no two of them share a common factor.  It has been shown that an n-sided regular polygon can be constructed with a compass and straightedge if and only if n is a power of two or the product of a power of two and two distinct prime members of this sequence.  As such, there are only five known prime ones, despite their namesake's assertion that all of them are prime.  However, only the first twelve have been completely factored, and it is not known whether there are infinitely many composite ones.  FTP, name this sequence of integers of the form 2 to the quantity (2 to the n) + 1, which bears the name of an amateur mathematician with well-known last and little theorems.
Goldbach proved that no two of them share a common factor.  
Fermat numbers