199

199 is a prime number.

199 is the 11th Lucas number.

197 and 199 form a twin prime pair.

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

199 is the smallest number with an additive persistence of 3: 1 + 9 + 9 = 19; 1 + 9 = 10; 1 + 0 = 1.

The Cape May Lighthouse in New Jersey has 199 steps in the tower's cast-iron spiral staircase.

Source: Number Gossip

481

481 = 13 x 37.

481 has two representations as a sum of two squares: 481 = 9² + 20² = 15² + 16².

481 is the hypotenuse of two primitive Pythagorean triples: 481² = 31² + 480² = 319² + 360².

481 is an octagonal number.

The Great Pyramid of Giza in Egypt is 481 feet high.

Source: WolframAlpha

604

604 = 2² x 151.

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

604 and the two numbers before it and after it are all products of exactly three primes: 602 = 2 x 7 x 43; 603 = 3 x 3 x 67; 604 = 2 x 2 x 151; 605 = 5 x 11 x 11; 606 = 2 x 3 x 101.

604 is 2444 in base 6 and 424 in base 12.

Nebula NGC 604 was discovered by William Herschel in 1784. It is 3 million light years away. Note that 604 x 1784 + 3 is prime.

Source: Prime Curios!

67

67 is a prime number.

67 has a unique representation as a sum of three squares: 67 = 3² + 3² + 7².

67 is the largest prime that is not the sum of distinct squares.

67 is the maximum number of regions into which 11 lines divide a plane.

67 is the only number such that the common alphabetical value of its Roman representation (LXVII) is equal to its reversal: 12 + 24 + 22 + 9 + 9 = 76.

67 is the smallest prime that contains all 10 digits when raised to the 10th power: 67¹⁰ = 1,822,837,804,551,761,449.

The chemical element holmliun has the atomic number 67.

Source: Number Gossip

5497

5497 = 23 x 239.

5497 is 41241 in base 6, 7477 in base 9, and 2009 in base 14.

5497 is the number of lattice points within a sphere of radius 12.

5497 is a semiprime (product of two primes) such that 239 mod 23 = 9.

NGC 5497 is a galaxy in the constellation Bootes.

Source: On-Line Encyclopedia of Integer Sequences

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

3563

3563 = 7 x 509.

3563 is a semiprime (product of two primes) such that 509 mod 7 = 5.

3563 is a term in the sequence created by starting with 1, then repeatedly reversing the digits and adding 76 to get the next term.

NGC 3563 is a galaxy in the constellation Leo.

Source: On-Line Encyclopedia of Integer Sequences