400 (number) + 61 + 67), strictly non-palindromic number 440 = 2 × 5 × 11, the sum of the first seventeen prime numbers, Harshad number, 441 = 3 × 7 = 21 442 = 2 × 13 × 17, sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71) A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659. 444 = 2 × 3 × 37, refactorable number, Harshad number. 445 = 5 ×
Prime number of arithmetic, and shows the close connection between the zeta function and the prime numbers. It leads to another proof that there are infinitely many primes: if there were only finitely many, then the sum-product equality would also be valid at formula_113, but the sum would diverge (it is the harmonic series formula_114) while the product would be finite, a contradiction. The Riemann hypothesis states that the zeros of the zeta-function are all either negative even numbers, or complex numbers with real part equal to 1/2. The original proof of the prime number theorem was based on a weak form