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 so is every element in the sequence. Therefore, this progression contains only one prime number, 3 itself. In general, the infinite progression can have more than one prime only when its remainder formula_34 and modulus formula_107 are relatively prime. If they are relatively prime, Dirichlet's theorem on arithmetic progressions asserts that the progression contains infinitely many primes. The Green–Tao theorem shows that there are arbitrarily long finite arithmetic progressions consisting only of primes. Euler noted that the function yields prime numbers for formula_109, although composite numbers appear among its later values. The search for an explanation for this phenomenon led