• 6 can be written using four 4's:
• 6 + 1, 6 ⋅ 66 + 1, 6 ⋅ 66 ⋅ 666 + 1, 6 ⋅ 66 ⋅ 666 ⋅ 6666 ⋅ 66666 ⋅ 666666 + 1 and 6 ⋅ 66 ⋅ 666 ⋅ 6666 ⋅ 66666 ⋅ 666666 ⋅ 6666666 + 1 are prime numbers.
• 6 is the kissing number in R2:
6 has 4 divisors (see below), whose sum is σ = 12. Its totient is φ = 2.
The previous prime is 5. The next prime is 7.
It is a primorial, being the product of the first 2 primes.
It is a factorial (6 = 3 ! = 1 ⋅ 2 ⋅ 3 ), and thus also a Jordan-Polya number.
6 is nontrivially palindromic in base 5.
6 is an esthetic number in base 4 and base 6, because in such bases its adjacent digits differ by 1.
6 is a nontrivial binomial coefficient, being equal to C(4, 2).
It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length.
It is an interprime number because it is at equal distance from previous prime (5) and next prime (7).
It is a harmonic number, since the harmonic mean of its divisors is an integer.
6 is an anti-perfect number.
It is a tcefrep number.
It is an automorphic number since its square, 36, ends in 6.
It is a trimorphic number since its cube, 216, ends in 6.
It is a Harshad number since it is a multiple of its sum of digits (6).
It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.
It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.
6 is an idoneal number.
It is an Ulam number.
It is (trivially) a d-powerful number and an alternating number.
It is one of the 548 Lynch-Bell numbers.
It is a Curzon number.
6 is a nontrivial repdigit in base 5.
It is a plaindrome in base 4 and base 5.
It is a nialpdrome in base 2, base 3, base 5 and base 6.
It is a zygodrome in base 5.
It is a congruent number.
It is a panconsummate number.
It is a pernicious number, because its binary representation contains a prime number (2) of ones.
A polygon with 6 sides can be constructed with ruler and compass.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 1 + 2 + 3.
It is an arithmetic number, because the mean of its divisors is an integer number (3).
It is a (trivial) narcissistic number.
6 is a highly composite number, because it has more divisors than any smaller number.
6 is a superabundant number, because it has a larger abundancy index than any smaller number.
It is a pronic number, being equal to 2×3.
6 is the 3-rd triangular number and also the 2-nd hexagonal number.
6 is the 2-nd centered pentagonal number.
It is a practical number, because each smaller number is the sum of distinct divisors of 6, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6).
6 is a perfect number, since it is equal to the sum of its proper divisors.
6 is a wasteful number, since it uses less digits than its factorization.
With its predecessor (5) it forms a Ruth-Aaron pair, since the sum of their distinct prime factors is the same (5).
6 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 5.
The product of its digits is 6, while the sum is 6.
The square root of 6 is about 2.4494897428. The cubic root of 6 is about 1.8171205928.
The spelling of 6 in words is "six", and thus it is an aban number, an eban number, an oban number, and an uban number.
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