521

521 is a prime number.

521 has a representation as a sum of two squares: 521 = 11² + 20².

521 is the 13th Lucas number.

521 and 523 for a twin prime pair.

521 is the hypotenuse of a primitive Pythagorean triple: 521² = 279² + 440².

521 has the representation 521 = 2⁹ + 9.

521 is the exponent of the Mersenne prime 2⁵²¹ - 1.

521 is the smallest prime whose reversal is a cube: 125 = 5³.

Galaxy cluster Abell 521 is located about 2.9 billion light-years from Earth.

Source: Prime Curios!

843

843 = 3 x 281.

843 is the 14th Lucas number.

843 is a divisor of 53⁴ - 1.

843 is 31023 in base 4, 11333 in base 5, 3523 in base 6, 2313 in base 7, and 1513 in base 8, all ending in 3. 843 is 443 in base 14, 223 in base 20, and 123 in base 28.

843 is palindromic in base 2: 1101001011.

Telephone area code 843 covers coastal South Carolina, including Charleston, Myrtle Beach, and Hilton Head Island.

Source: WolframAlpha

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

76

76 = 2² x 19.

76 has a unique representation as the sum of three squares: 76 = 2² + 6² + 6².

76 is the ninth Lucas number. Lucas numbers are the sequence of integers obtained when each successive element is the sum of the previous two elements, starting with 1 and 3.

76 is the number of integer partitions of 21 into distinct parts. The partitions of an integer are the number of ways of writing that integer as a sum of positive integers without regard to order with the constraint that all integers in a given partition are distinct.

Meredith Wilson's song "Seventy-six Trombones" is a highlight of the musical The Music Man.

Source: Wolfram MathWorld

18

18 = 2 x 3²

18 has a representation as a sum of two squares: 18 = 3² + 3².

18 = 9 + 9 and 81 = 9 x 9.

18 is the only number that is twice the sum of its digits: 18 = 2(1 + 8).

The cube together with the 4th power of 18 use all the digits 0 to 9 once each: 18³ = 5832 and 18⁴ = 104,976.

18 is the smallest number with two representations as a sum of three primes: 18 = 2 + 3 + 13 = 2 + 5 + 11.

18 is the sixth Lucas number.

18 is the number of integer partitions of 13 into distinct parts.

18 is 33 in base 5.

18 is the voting age in many countries.

Source: Number Gossip