6
6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.[1]
Six is the smallest positive integer which is neither a square number nor a prime number. It is the second smallest composite number after four, equal to the sum and the product of its three proper divisors (1, 2 and 3).[1] As such, six is the only number that is both the sum and product of three consecutive positive numbers. 6 is the smallest perfect number, which are numbers that are equal to their aliquot sum, or sum of their proper divisors.[1][2] It is the largest of the four all-Harshad numbers (1, 2, 4, and 6),[3] where it represents the sum between the first prime and composite, 2 and 4.
6 is a pronic number and the only semiprime to be.[4] It is the first discrete biprime (2 × 3)[5] which makes it the first member of the (2 × q) discrete biprime family, where q is a higher prime. All primes above 3 are of the form 6n ± 1 for n ≥ 1.
Six is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including itself. Only five such numbers are known to exist; sixty (10 × 6) and ninety (15 × 6) are the next two.[8]
It is the first primitive pseudoperfect number,[9] and all integers that are multiples of 6 are pseudoperfect (all multiples of a perfect number are pseudoperfect); six is also the smallest Granville number, or -perfect number.[10]
Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler".[11] Six is a congruent number.[12]