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 factorizations are based on Euclid's lemma: If formula_20 is a prime number and formula_20 divides a product formula_33 of integers formula_34 and formula_35, then formula_20 divides formula_34 or formula_20 divides formula_35 (or both). Conversely, if a number formula_20 has the property that when it divides a product it always divides at least one factor of the product, then formula_20 must be prime. There are infinitely many prime numbers. Another way of saying this is that the sequence of prime numbers never ends. This statement is referred to as "Euclid's theorem" in honor of the ancient Greek mathematician Euclid, since the