957

957 = 3 x 11 x 29, which makes 957 a sphenic number. A sphenic number is a positive integer that is the product of three distinct prime numbers.

957 is 12312 in base 5, 4233 in base 6, and 2535 in base 7.

957 is the product of three distinct primes such that the sum of the three primes is also a prime: 3 + 11 + 29 = 43, a prime.

957 is a number such that its base 2 (binary) representation is the juxtaposition of two identical strings: 1110111101.


The asteroid 957 Camelia was discovered in 1921.

Source: Positive Integers

164

164 = 2² x 41.

164 is the smallest concatenation of two squares in two ways: 1 and 64; 16 and 4.

164 is 20002 in base 3 and 202 in base 9.

164 has a representation as a sum of two squares: 164 = 8² + 10².

164 is a divisor of 81² - 1.

164 is the highest possible score of a word in the game Scrabble: playing “Quartzy” across triple-word square with “z” on a double-letter square and a premium of 50 for using all seven letters on the rack.

Source: Number Gossip

201

201 = 3 x 67.

201ⁿ + 2 is a prime number, for n = 14, 15, and 16.

The square of 201 is one of four square numbers using the same digits: 102² = 10404, 120² = 14400, 201² = 40401, and 210² = 44100.

201 is a Niven (or Harshad) number, which is divisible by the sum of its digits.

201 Penelope is a large asteroid discovered in 1879.

Source: Prime Curios!

302

302 = 2 x 151.

The square of 302 is one of three square numbers using the same digits: 148² = 21904, 203² = 41209, and 302² = 91204.

302 is the number of ways to play the first three moves in checkers.

302 is a number n such that n and n + 1 have the same number of divisors: 303 = 3 x 101.

302 is the telephone area code for the state of Delaware.

Source: What’s Special About This Number?

503

503 is a prime number.

503 is the smallest prime that is the sum of the cubes of the first n primes: 2³ + 3³ + 5³ +7³ = 503.

5! + 0! + 3! is a three-digit Mersenne prime.

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


503 is Clark Kent's Metropolis apartment number in the "Superman" series.

Source: Prime Curios!

905

905 = 5 x 181.

Most odd integers can be written as the sum of a prime and a power of two in at least one way. Ones that cannot are called obstinate numbers. They form an infinite set but are not all that common. The first composite obstinate number is 905. So 905 is the smallest composite number that is not the sum of a prime and a power of two.

905 is the sum of seven consecutive primes: 109 + 113 + 127 + 131 + 137 + 139 + 149 = 905.

905 has two representations as a sum of two squares: 905 = 8² + 29² = 11² + 28².

905 is the hypotenuse of two Pythagorean triples: 905² = 464² + 777² = 616² + 663².


A Neptune-Pluto conjunction occurred in Taurus in the year 905.

Source: Prime Curios!

889

889 = 7 x 127. It is a product of distinct Mersenne primes.

889 is an odious number because it has an odd number of ones in its binary expansion: 1101111001.

889 is a number such that the sum of its divisors is a square: 1 + 7 + 127 + 889 = 135 = 32 x 32.

889 is the sum of eight positive fifth powers: 889 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵.

In the Dewey Decimal System for classifying books, 889 is the code for literature in medieval and modern Greek

Source: Number Gossip