698

698 = 2 x 349.

698 has a representation as a sum of two squares: 698 = 13² + 23².

698 is 221212 in base 3, 22322 in base 4, and 585 in base 11.

698 is the smallest of three consecutive integers divisible by three consecutive primes respectively: 698 = 2 x 349, 699 = 3 x 233, 700 = 5 x 140.

NGC 698 is a galaxy in the constellation Fornax.

Source: Positive Integers

512

512 = 2⁹.

512 has a representation as a sum of two squares: 512 = 16² + 16².

512 is the number of integer partitions of 34 into distinct parts.

512 is the smallest integer (except 1) that is the cube of the sum of its digits: 512 = (5 + 1 + 2)³.

512 is 1000000000 in base 2, 20000 in base 4, 1331 in base 7, 1000 in base 8, 242 in base 15, and 200 in base 16.

512 is the three-digit start in the Dewey Decimal Classification System of call numbers for books in algebra and number theory.

Source: Number Gossip

488

488 = 2³ x 61.

488 has a representation as a sum of two squares: 488 = 2² + 22².

488³ = 116,214,272 = (1 - 1 + 62 + 1 + 427 - 2)³.

488 is 200002 in base 3, 404 in base 11, and 148 in base 20.

IEEE-488 is a short-range digital communications bus specification, originally created for use with automated test equipment.

Source: Numeropedia

323

323 = 17 x 19.

323 is the smallest palindrome that is the product of a pair of twin primes.

323 is the smallest palindrome that is not divisible by any of its digits.

323 is the 8th Motzkin number. These numbers enumerate various combinatorial objects.

323 Brucia was the first asteroid to be discovered by the use of astrophotography.

Source: Number Gossip

293

293 is a prime number.

293 is a Sophie Germain prime because 2 x 293 + 1 = 587, which is also a prime.

293 has a representation as a sum of two squares: 293= 2² + 17².

293 is the hypotenuse of a primitive Pythagorean triple: 293² = 68² + 285².

293 Brasilia is a large asteroid discovered in 1893.

Source: Prime Curios!

103

103 is a prime number.

103 is the smallest three-digit prime with distinct digits.

101 and 103 form a twin prime pair.

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

103 is the total number of prime numbers that can be displayed on a 12-hour digital clock.

The play Proof, by David Auburn, revolves around a mysterious proof involving prime numbers, left behind in 103 notebooks by a young woman's brilliant father.

Source: Prime Curios!

58

58 = 2 x 29.

58 has a representation as a sum of two squares: 58 = 3² + 7².

58 is the maximum number of regions into which eight circles divide the plane.

58 is the smallest Smith number with a prime sum of digits. A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors: 5 + 8 = 2 + 2 + 9 = 13.

58 is the number of commutative semigroups of order 4.

The chemical element cerium has the atomic number 58.

Source: Number Gossip