0 is the additive identity
1 is the multiplicative identity
2 is the only even prime
3 is the number of spatial dimensions we live in.
5 is the number of Platonic solids. (The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are exactly five such solids : the cube, dodecahedron, icosahedron, octahedron, and tetrahedron, as was proved by Euclid in the last proposition of the Elements. The Platonic solids are sometimes also called "cosmic figures")
6 is the smallest perfect number.
7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
10 is the base of our number system.
11 is the largest known multiplicative persistence. (Multiply all the digits of a number by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative persistence, and the final digit obtained is called the multiplicative digital root of .
For example, the sequence obtained from the starting number 9876 is (9876, 3024, 0), so 9876 has an multiplicative persistence of two and a multiplicative digital root of 0.)
16 is the only number of the form x^y = y^x with x and y different integers
18 is the only number that is twice the sum of its digits
25 is the smallest square that can be written as a sum of 2 squares.
26 is the only positive number to be directly between a square and a cube
28 is the 2nd perfect number