• 3 can be written using four 4's:
• 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.
It is the 3-rd Fibonacci number F3.
It is a double factorial (3 = 3 !! = 1 ⋅ 3 ).
3 is nontrivially palindromic in base 2.
3 is an esthetic number in base 3, because in such base its adjacent digits differ by 1.
It is a weak prime.
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.
It is a Chen prime.
It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) 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 the 2-nd Hogben number.
It is the 3-rd Perrin number.
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 Pierpont prime, being equal to 21 ⋅ 30 + 1.
A polygon with 3 sides can be constructed with ruler and compass.
It is a (trivial) narcissistic number.
3 is the 2-nd triangular number.
3 is an equidigital number, since it uses as much as digits as its factorization.
3 is an evil number, because the sum of its binary digits is even.
The square root of 3 is about 1.7320508076. The cubic root of 3 is about 1.4422495703.