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 prime and composite numbers. However, the earliest surviving records of the explicit study of prime numbers come from Ancient Greek mathematics. Euclid's "Elements" (circa 300 BC) proves the infinitude of primes and the fundamental theorem of arithmetic, and shows how to construct a perfect number from a Mersenne prime. Another Greek invention, the Sieve of Eratosthenes, is still used to construct lists of primes. Around 1000 AD, the Islamic mathematician Alhazen found Wilson's theorem, characterizing the prime numbers as the numbers formula_1 that evenly divide formula_17. Alhazen also conjectured that all even perfect numbers come from Euclid's construction using Mersenne