180 (number) two square numbers: 12 + 6. It can be expressed as either the sum of six consecutive prime numbers: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive prime numbers: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. 180 is an Ulam number, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3. 180 is a 61-gonal number. Half a circle has 180 degrees. Summing Euler's totient function φ("x") over the first + 24 integers gives
Prime number are distinct Fermat primes. Likewise, a regular formula_1-gon may be constructed using straightedge, compass, and an angle trisector if and only if the prime factors of formula_1 are any number of copies of 2 or 3 together with a (possibly empty) set of distinct Pierpont primes, primes of the form formula_241. It is possible to partition any convex polygon into formula_1 smaller convex polygons of equal area and equal perimeter, when formula_1 is a power of a prime number, but this is not known for other values of formula_1. Beginning with the work of Hugh Montgomery and Freeman Dyson in