106

106 = 2 x 53.

106 has a representation as a sum of two squares: 106 = 5² + 9².

106 is a divisor of 23⁴ - 1.

106 = 25 + 26 + 27 + 28.

15 straight cuts through a pizza can produce as many as 106 pieces.

106 is a centered pentagonal number and a centered heptagonal number.

The sum of the first 106 digits of pi is a prime.

Messier 106 is a bright spiral galaxy in the constellation Canes Venatici.

Source: Prime Curios!

951

951 = 3 x 317.

951 is 1110110111 in base 2 (binary) and 2526 in base 7.

951 is a centered pentagonal number.

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

Asteroid 951 Gaspra was photographed in 1991 by the Galileo spacecraft.

Source: WolframAlpha

601

601 is a prime number.

599 and 601 form a twin prime pair.

601 has a representation as a sum of two squares: 601 = 5² + 24².

601 is the hypotenuse of a primitive Pythagorean triple: 601² = 240² + 551².

601 is a centered pentagonal number.

601 is the lesser member p of the least sexy prime pairs (p, p + 6) such that all numbers in between have the same number of prime divisors (counted with multiplicity).

The Minivac 601 Digital Computer Kit was a product created by Claude Shannon and sold by Scientific Development Corporation as early as 1961.

Source: Number Gossip

856

856 = 2³ x 107. It is the product of the cube of a prime and a different prime.

856 is a nonagonal number. It is also a centered pentagonal number.

856 is 11411 in base 6 and 2332 in base 7.

856 is a member of the Fibonacci-like sequence that begins with 1 and 9: 1, 9, 10, 19, 29, 48, 77, 125, 202, 327, 529, 856, 1385, . . .

NWA 856 is a Mars meteorite found in Morocco in 2001.

Source: Positive Integers

681

681 = 3 x 227.

The sum of the digits of 681 is five times the number of digits: 6 + 8 + 1 = 15 = 3 x 5.

681 is the sum of 11 positive 5th powers: 681 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.


681 is a centered pentagonal number.


The galaxy NGC 681, more than 55 million light years away, resembles the striking Sombrero Galaxy (M104).

Source: Wolfram MathWorld

526

526 = 2 x 263.

526 is the number of ways to cut an 8-by-8 chessboard into two pieces with equal areas using a cut that travels only up and right.

526 is a Smith number. It a composite number such that the sum of its digits is equal to the sum of its prime factors: 5 + 2 + 6 = 2 + 2 + 6 + 3 = 13.

526 and 527 are both the products of two primes: 526 = 2 x 263 and 527 = 17 x 31.


526 is a centered pentagonal number.


Source: What’s Special About This Number?