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 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