4444

4444 = 2² x 11 x 101.

4444 is a number that cannot be written as a sum of three squares.

121 × (1 + 2 + 1) = 484 = 22²

^{12,321 × (1 + 2 + 3 + 2 + 1) = 110,889 = 3332}

^{12,34,321 × (1 + 2 + 3 + 4 + 3 + 2 + 1) = 19,749,136 = 4,4442}

4444 is 32324 in base 6 and 15646 in base 7.

The classic "four fours" problem states: "Given no more than four instances of the digit 4, represent all integers using a finite number of mathematical symbols and operators in common use."

Source: Numeropedia