57

57 = 3 x 19.

57 is 111 in base 7.

57 is the sum of the 7th through 12th numbers: 7 + 8 + 9 + 10 + 11 + 12 = 57.

As a semiprime (a product of two primes), 57 is a Blum integer because its two prime factors, 3 and 19, are both Gaussian primes.

"57 Varieties" was the slogan of Pittsburgh's H. J. Heinz Company. In its early days, the company wanted to advertise the great number of choices of canned and bottled foods it offered for sale. Although the company had more than 60 products in 1892, the number 57 was chosen because the number "5" was Henry John Heinz's lucky number and the number "7" was his wife's lucky number.

Source: Wikipedia

194

194 = 2 x 97.

194 has a representation as a sum of two squares: 194 = 5² + 13².

194 is the smallest number with five representations as a sum of three squares: 194 = 1² + 7² + 12² = 3² + 4² + 13² = 3² + 8² + 11² = 5² + 5² + 12² = 7² + 8² + 9².

194 is a number n such that n⁴ + 1 is prime: 1,416,468,497 is prime.

194 Prokne is a large, dark, main-belt asteroid discovered in 1879.

Source: What's Special About This Number?

271

271 is a prime number.

269 and 271 form a twin prime pair.

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

271 is the sum of eleven consecutive primes: 271 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.

271 is a Google number. The nth Google number is the first n-digit prime found in the decimal expansion of e. This sequence of numbers was originally featured in an unusual job ad placed by Google. The first few numbers in the sequence are

2,

71,

271,

4523,

74713,

904523, . . .

271 is a centered hexagonal number.

Source: Number Gossip

929

929 is a prime number.

929 is the smallest palindromic prime whose cube can be expressed as the sum of three odd cubes: 929³ = 69³ + 447³ + 893³.

929 has a representation as a sum of two squares: 929 = 20² + 23².

929 is the hypotenuse of a primitive Pythagorean triple: 929² = 129² + 920².

The Mazda 929 automobile was introduced in 1973.

Source: Prime Curios!

799

799 = 17 x 47.

799 is the smallest number with a composite sum of digits (7 + 9 + 9 = 25) and a prime sum of cubes of digits (7³ + 9³ + 9³ = 1801).

799 is the smallest number whose sum of digits is 25.

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

799 is the sum of 11 positive fifth powers: 799 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

NGC 799 is a spiral galaxy in the constellation Cetus.

Source: Number Gossip

357

357 = 3 x 7 x 17.

357 is the only three-digit number such that 2*357³⁵⁷ - 1 is prime.

357 is the smallest three-digit number with its digits being three distinct odd primes that is not prime, nor do any of the permutations of its digits represent a prime number.

357 is the larger of the only two sphenic numbers (product of three distinct primes) consisting of three distinct prime digits.

357 is a divisor of 50² - 1.

The .357 Magnum is a revolver cartridge.

Source: Prime Curios!

93

93 = 3 x 31.

93 has the unique representation 93 = 2² + 5² + 8² as a sum of three squares.

93 is 1011101 in base 2 and 333 in base 5.

93 is a cake number. The nth cake number is the maximum number of pieces into which a (cylindrical) cake can be cut with n planar cuts. The first 10 cake numbers are 2, 4, 8, 15, 26, 42, 64, 93, 130, 176. There are 39 cake numbers below 10,000.

The chemical element niobium has one stable isotope, which has 93 neutrons.

Source: Number Gossip