400 (number) sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59) 413 = 7 × 59, Mertens function returns 0, self number 414 = 2 × 3 × 23, Mertens function returns 0, nontotient, Harshad number 415 = 5 × 83, 416 = 2 × 13 417 = 3 × 139 418 = 2 × 11 × 19, sphenic number, A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0 A prime
Prime number values, and places on the rational numbers. The local-global principle allows certain problems over the rational numbers to be solved by piecing together solutions from each of their places, again underlining the importance of primes to number theory. A commutative ring is an algebraic structure where addition, subtraction and multiplication are defined. The integers are a ring, and the prime numbers in the integers have been generalized to rings in two different ways, "prime elements" and "irreducible elements". An element formula_20 of a ring formula_172 is called prime if it is nonzero, has no multiplicative inverse (that is, it is