30

30 = 2 x 3 x 5.

30 is the smallest number with three distinct prime divisors.

30 has a unique representation as a sum of three squares: 30 = 1² + 2² + 5².

30 is a pyramidal number (the sum of all squares of integers from 1 to 4): 30 = 1² + 2² + 3² + 4².

30 is 33 in base 9.

A dodecahedron is a Platonic solid with 30 edges.


Source: Number Gossip

73

73 is a prime number.

73 is the least number of sixth powers needed to represent every possible integer.

73 is the smallest number (besides 1) that is one less than twice its reverse: 2 x 37 – 1 = 73.

73 is the alphanumeric value of the word NUMBER: 14 + 21 + 13 + 2 + 5 + 18 = 73.


Pi Day occurs on the 73rd day of the year (March 14), except during leap years.

Source: Number Gossip

420

420 = 2² x 3 x 5 x 7.

420 is the smallest number divisible by 1 through 7.

420 is the sum of four consecutive primes: 101 + 103 + 107 + 109 = 420.

420 is the smallest argument for which Euler’s prime generating polynomial p(n) = n² + n + 41 has more than two prime factors: p(420) = 176861 = 71 x 53 x 47. For all smaller arguments, p(n) is either prime or semiprime.


In sailing, the 420 (dinghy) is a class of doublehanded racing sailboats.

Source: Prime Curios!

1306

1306 = 2 x 653.

1306 has a representation as a sum of two squares: 1306 = 9² + 35².

1306 is the smallest four-digit number that is the sum of its digits to progressive powers: 1306 = 1¹ + 3² + 0³ + 6⁴.

1306 has the representation 6⁴ + 10.


In the year 1306, Robert the Bruce was crowned King of Scotland.

Source: Number Gossip

634

634 = 2 x 317.

634 is a Smith number. The sum of its digits equals the sum of the digits appearing in its prime divisors: 6 + 3 + 4 = 2 + 3 + 1 + 7 = 13.

The fifth root of 634 has a decimal part that begins with the digits 634.

634 has a representation as a sum of two squares: 634 = 3² + 25².

634 Ute is an asteroid discovered in 1907.

Source: Number Gossip

116

116 = 2² x 29.

116! + 1 is a prime number.

116 has a representation as a sum of two squares: 116 = 4² + 10².

116 is a composite number that when added to the sum of its prime factors becomes prime: 116 + 2 + 2 + 29 = 149.

The Hundred Years' War between France and England lasted 116 years, with periodic truces, from 1337 to 1453.

Source: Prime Curios!

28

28 = 2² x 7.

28 is the second perfect number. It is the only even perfect number of the form x³ + 1.

28 is the sum of the first five prime numbers: 2 + 3 + 5 + 7 + 11 = 28.

28 is the seventh triangular number.

28 is the smallest number with three representations as a sum of four squares: 28 = 1² + 1² + 1² + 5² = 1² + 3² + 3² + 3² = 2² + 2² + 2² + 4².

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

28 is 44 in base 6.


A standard domino set contains 28 dominoes.

Source: Number Gossip