34

34 = 2 x 17.

34 is the ninth Fibonacci number.

34 is the smallest number with the property that it and its neighbors have the same number of divisors (four): 33 = 3 x 11; 34 = 2 x 17; 35 = 5 x 7.

The rows and columns of a 4 x 4 magic square always total 34.

34 has a representation as a sum of two squares: 34 = 3² + 5².

34 is the smallest number with four representations as a sum of two primes: 34 = 3 + 31 = 5 + 29 = 11 + 23 = 17 + 17.

34 is 22 in base 16.

34 is a heptagonal number.


34 is the atomic number of the element selenium.

Source: Number Gossip

726

726 = 2 x 3 x 11².

726 is the start of a record-breaking run (smallest set) of six consecutive integers (from 726 to 731) with a distinct number of prime factors (from 1 to 6).

726 is 1011010110 in base (binary), 10401 in base 5, 600 in base 11, and 141 in base 25.

726 is the sum of nonconsecutive factorial numbers: 726 = 3! + 6! = 6 + 720.


Introduced in 1952, the IBM 726 was one of the first practical high-speed magnetic tape systems for electronic digital computers.

Source: Prime Curios!

92

92 = 2² x 23.

92 is a pentagonal number.

92 is the maximum number of regions into which 13 lines divide a plane.

92 is the maximum number of regions into which 10 circles divide a plane.

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


The snub dodecahedron is an Archimedean solid with 92 faces.
Source: Wolfram MathWorld

501

501 = 3 x 167.

501 is the sum of the first 18 prime numbers.

501 is the number of partitions of five items into ordered lists.

501 is the sum of 11 positive fifth powers: 501 = 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵.

Telephone area code 501 covers Little Rock, Arkansas.

Source: What's Special About This Number?

3079

3079 is a prime number.

3079 is a number that cannot be written as a sum of three squares.

3079 is a prime of the form n² - n - 1, for n = 56.

3079 is a centered 18-gonal number.

3079 is a prime p such that p - 1 and p + 1 are divisible by cubes: 3078 = 2 x 3⁴ x 19 and 3080 = 2³ x 5 x 7 x 11.

NGC 3079 is a spiral galaxy, found in the direction of the constellation Ursa Major about 55 million light years from Earth.

Chandra X-ray Observatory image of NGC 3079.

Source: Chandra X-ray Observatory

Image: NASA/CXC/U.North Carolina/G.Cecil

187

187 = 11 x 17.

The 187th prime number is 1117, which can be written with the digits of 187. This is the smallest prime with this property.

187 = 59 + 61 + 67 (sum of three consecutive primes).

187 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 (sum of 9 consecutive primes).

187 = 2³ + 3³ + 3³ + 5³ (sum of cubes).


187 is the number of odd days in a leap year.

Source: Prime Curios!

19

19 is a prime number.

19 has a unique representation as a sum of three squares: 19 = 1² + 3² + 3².

19 is the fourth centered triangular number.

19 is the largest prime number that is a palindrome in Roman numerals (XIX).

17 and 19 form a twin prime pair.

Go is played by two players who alternately place black and white pieces on the vacant intersections of a grid of 19 by 19 lines.

Source: Number Gossip