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 theorem column, , is the average prime gap below . The value for was originally computed assuming the Riemann hypothesis; it has since been verified unconditionally. There is an analogue of the prime number theorem that describes the "distribution" of irreducible polynomials over a finite field; the form it takes is strikingly similar to the case of the classical prime number theorem. To state it precisely, let be the finite field with elements, for some fixed , and let be the number of monic "irreducible" polynomials over whose degree is equal to . That is, we are looking at polynomials with