184

184 = 2³ x 23.

184 has a unique representation as a sum of three squares: 184 = 2² + 6² + 12².

184 is the maximum number of regions into which 14 circles divide the plane.

184 is the smallest number that can be written as q * p^q + r * p^r, where p, q, and r are distinct primes: 184 = 3 x 2³ + 5 x 2⁵.

184 is the difference of two square numbers: 184 = 25² - 21².

In nuclear physics, 184 is believed to be a magic number.

Source: Prime Curios!

80

80 = 2⁴ x 5.

80 has a representation as a sum of two squares: 80 = 4² + 8².

80 is the smallest number with exactly seven representations as a sum of three distinct primes: 80 = 2 + 5 + 73 = 2 + 7 + 71 = 2 + 11 + 67 = 2 + 17 + 61 = 2 + 19 + 59 = 2 + 31 + 47 = 2 + 37 + 41.

80 is 2222 in base 3.

80 is the smallest number that is diminished by taking its sum of letters (writing out its English name and adding the letters using a = 1, b = 2, c = 3, . . .): EIGHTY = 5 + 9 + 7 + 8 + 20 + 25 = 74.

Around the World in Eighty Days is a novel by Jules Verne.

Source: Number Gossip

218

218 = 2 x 109.

218 has a representation as a sum of two squares: 218 = 7² + 13².

218 is the number of simple directed graphs of four nodes.

218 is 1333 in base 5, 1002 in base 6, 262 in base 9, and 118 in base 14.

218 is the number of votes required in the United States House of Representatives to achieve a majority.

Source: Number Gossip

166

166 = 2 x 83.

166 is a centered triangular number.

166 is the smallest number such that the number and its reversal are both congruent to 1 mod p for the same set of distinct odd primes: 166 = 661 = 1 mod (3, 5, 11).

166 is the smallest Smith number that is prime when reversed (661), turned upside down (991), and reversed-then-turned-upside-down (199). You get the next case by inserting a zero between the digits: 10606.

U-166 was the only German submarine lost in the Gulf of Mexico.

Source: Prime Curios!

772

772 = 2² x 193.

772 has a representation as a sum of two squares: 772 = 14² + 24².

772 is the sum of six distinct positive pentatope numbers.

772 is the sum of six positive cubes in exactly three ways.

772 is a structured truncated icosahedral number.

Telephone area code 772 serves that state of Florida.

Source: On-Line Encyclopedia of Integer Sequences

576

576 = 2⁶ x 3².

576 has a unique representation as a sum of three squares: 576 = 8² + 16² + 16².

576 is the number of 4 x 4 Latin squares.

576 is the smallest square such that it remains a square when its leading digit is increased by 1: 676 = 26².

576 = (2 + 3 + 5 + 7 + 11)² - (2² + 3² + 5² + 7² + 11²).

New Balance produces a 576 line of fitness walking shoes.

Source: Number Gossip

654

654 = 2 x 3 x 109.

654 has a square that is the sum of a cube and fifth power.

The sum 327 + 654 = 981 is one of only four cases in which the equality n + 2n = 3n uses each of the nine digits 1 to 9 once (n = 192, 219, 273, and 327).

654 is 545 in base 11.

654 is a Smith number. The sum of its digits is equal to the sum of the digits of its prime factors: 6 + 5 + 4 = 2 + 3 + 1 + 0 + 9 = 15.

The Auburn Company produced the Auburn 654 automobile in 1936, the year the company went out of business.

Source: What's Special About This Number?