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3 is a prime number

• 3 can be written using four 4's:

See also 113.

• 3 ways are known to express 3 as a sum of 3 integer cubes: 3 = 13 + 13 + 13, 3 = 43 + 43 + (-5)3, and
3 = 5699368212219623807203 + (-569936821113563493509)3 + (-472715493453327032)3.
The last expression has been found by Booker & Sutherland in 2019.

• Gauss proved that every positive integer is the sum of at most 3 triangular numbers;

• Cilleruelo & Luca have proved in 2016 that every number can be written as the sum of 3 palindromes.

3 has 2 divisors, whose sum is σ = 4. Its totient is φ = 2.

The previous prime is 2. The next prime is 5.

It is the 4-th Fibonacci number F4.

It is a double factorial (3 = 3 !! = 1 ⋅ 3 ).

3 is nontrivially palindromic in base 2.

It is a Cunningham number, because it is equal to 22-1.

3 is an esthetic number in base 3, because in such base its adjacent digits differ by 1.

It is a weak prime.

Together with 1006003 it forms a Wieferich pair.

It is a cyclic number.

It is a Cullen number, since it is equal to 1×21+1.

It is a de Polignac number, because none of the positive numbers 2k-3 is a prime.

It is a Sophie Germain prime.

Together with 5, it forms a pair of twin primes.

It is a Chen prime.

It is a Harshad number since it is a multiple of its sum of digits (3).

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.

It is an iccanobiF number.

3 is an idoneal number.

It is a Lucas number.

It is the 3-rd Jacobsthal number.

It is an Ulam number.

It is (trivially) a d-powerful number and an alternating number.

It is the 2-nd Hogben number.

It is one of the 548 Lynch-Bell numbers.

It is the 3-rd Perrin number.

It is a partition number, being equal to the number of ways a set of 3 identical objects can be partitioned into subset.

3 is a lucky number.

3 is a nontrivial repdigit in base 2.

It is a plaindrome in base 2.

It is a nialpdrome in base 2 and base 3.

It is a zygodrome in base 2.

It is a self number, because there is not a number n which added to its sum of digits gives 3.

It is a panconsummate number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a Pierpont prime, being equal to 21 ⋅ 30 + 1.

A polygon with 3 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.

It is an arithmetic number, because the mean of its divisors is an integer number (2).

It is a (trivial) narcissistic number.

It is a Proth number, since it is equal to 1 ⋅ 21 + 1 and 1 < 21.

3 is the 2-nd triangular number.

3 is a deficient number, since it is larger than the sum of its proper divisors (1).

3 is an equidigital number, since it uses as much as digits as its factorization.

With its successor (4) it forms an eRAP, since the sums of their prime factors are consecutive (3 and 4).

With its predecessor (2) it forms an eRAP, since the sums of their prime factors are consecutive (2 and 3).

3 is an evil number, because the sum of its binary digits is even.

The product of its digits is 3, while the sum is 3.

The square root of 3 is about 1.7320508076. The cubic root of 3 is about 1.4422495703.

The spelling of 3 in words is "three", and thus it is an aban number, an iban number, an oban number, and an uban number.