255

255 = 3 x 5 x 17.

255 = 11111111 in base 2.

255 is the largest value representable as an 8-bit binary number. Eight bits, otherwise known as a byte, is a very common size for storing "small" values in computer memories. Consequently, 255 appears as a bound or an otherwise magic number in many computer-related tasks. For example, 255 is the maximum amount of red, green, or blue that goes into an RGB color, as well as the maximum content of any of the four octets of an IP address.

255 is the least odd integer greater than 3 that is not the sum of two distinct powers of two and a prime.

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

255 is 3333 in base 4.

255 is a Mersenne number: 255 = 2⁸ - 1.


Source: Number Gossip

249

249 = 3 x 83.

The sum of the digits of 249 equals five times the number of digits: 2 + 4 + 9 = 15 = 3 x 5.

249 is a number not divisible by any of its digits.

249 is a Blum number. A natural number n is a Blum integer if n = pq is a semiprime (the product of two prime numbers) for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t.

249 Ilse is an asteroid with an unusually slow rotation period, discovered in 1885.

Source: The On-Line Encyclopedia of Integer Sequences

146

146 = 2 x 73.

The absolute difference between any two digits of 146 is a prime number (2, 3, 5).

146 is 222 in base 8.

146 is an octahedral number, which has the form (2n³ + n)/3.

146 is an untouchable number: No integer's proper divisors add up to 146.

146 has a representation as a sum of two squares: 146 = 5² + 11².


The Grand Union Canal Race is a 146-mile ultramarathon from Birmingham to London.

Source: Prime Curios!

91

91 = 7 x 13.

91 is the first non-trivial odd composite number. Every smaller composite is either even, a familiar square, ends in 5, has a digit sum that is a multiple of 3, or is obviously divisible by 11.

91 is the sum of the squares of the first six integers: 1² + 2² + 3² + 4² + 5² + 6² = 91. It is the 13th triangular number.

91 is the sum of the first 13 positive integers: 1 + 2 + 3 + . . . + 11 + 12 + 13 = 91.

91 has a unique representation as a sum of three squares: 91 = 1² + 3² + 9².

91 is 111 in base 9.

91 cents is the total amount of money one has, given one each of a penny, nickel, dime, quarter, and half dollar.
Source: Number Gossip

51

51 = 3 x 17.

51 is the smallest number that can be written with all the digits from 1 to 5 (without repetition) as a sum of prime numbers: 2 + 3 + 5 + 41 = 51. Note that the highest digit (5) and the lowest digit (1) are the digits of 51.

51 is a pentagonal number, a number of the form n(3n - 1)/2, and a centered pentagonal number (one of the few numbers to be both).

51 is 110011 in base 2 (binary) and 33 in base 16.

51 is the sixth Motzkin number.

Area 51 is a nickname for a secret military base located in the southern portion of Nevada in the western United States.

Source: Prime Curios!

47

47 is a safe prime number. A safe prime has the form 2p + 1, where p is also a prime.

There are 47 occurrences of 47 in the first thousand prime numbers.

4³ + 7³ = 407.

47 is the smallest number n for which 666ⁿ has a digit sum of 666.

The atomic number of silver is 47.

Sources: Number Gossip; Prime Curios!

711

711 = 3² x 79.

711 is the concatenation of the fourth and fifth primes.

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

711 is a divisor of 80² - 1.

711 is the sum of ten positive fifth powers: 711 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

711 is the phone number of the Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.

The logo for a chain of convenience stores.

#711 was a comics superhero created by George Brenner and published by Quality Comics from 1941 to 1943.

In the 1950 movie 711 Ocean Drive, a telephone repairman in Los Angeles uses his knowledge of electronics to help a bookie set up a betting operation.

Source: WolframAlpha