343

343 = 7 x 7 x 7.

343 = (3 + 4)³.

342³⁴³ + 343³⁴² is prime.

343 is the sum of the first five odd Fibonacci primes: 343 = 3 + 5 + 13 + 89 + 233.

343 can be expressed using the first six odd primes: 7(3 + 5 + 11 + 13 + 17).

343 + 656 = 999 = 323 + 676.

343 is 1331 in base 6 and 292 in base 11.

343 = 18⁰ + 18¹ + 18².

The Willow Grove exit on the Pennsylvania Turnpike started out as exit 27 (the cube of an odd prime). With a change in exit numbers, Willow Grove is now exit 343, another cube of an odd prime.

Source: Prime Curios!

1000

1000 = 2 x 2 x 2 x 5 x 5 x 5. 1000 is a perfect cube.

1000 can be expressed using the first three primes: 2³ x 5³.

The 147th prime (853) plus 147 equals 1000.

2⁹⁹⁹ + 1239 is the smallest 1000-bit prime.

1000 is 2626 in base 7. It is 1331 in base 9.

1000 has two representations as a sum of two squares: 1000 = 10² + 30² = 18² + 26².

T-1000 was the shape-changing robot from the 1991 film Terminator 2: Judgment Day.

Source: Prime Curios!

216

216 = 2 x 2 x 2 x 3 x 3 x 3.

216 = 6³ is a perfect cube. 216 = 6^{(2 + 1)}.

216 = 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6.

216 is the smallest cube that can be written as the sum of three cubes: 216 = 5³ + 4³ + 3³.

216 is the smallest number that can be expressed as the difference of the sums of the squares of successive twin primes: 216 = (13² + 11²) - (7² + 5²).

216 is 1331 in base 5.

216 is the sum of a twin prime pair: 216 = 107 + 109.

In the film Pi, Max Cohen becomes obsessed with a 216-digit number in his quest to find a numeric equation behind existence.

Source: Prime Curios! and Wikipedia

1331

1331 is a perfect cube.

1331 = 11³ = (13 – 3 + 1)³ = (1 + 3 x 3 – 1)³.

1331 is that smallest cube (other than 1) containing only odd digits. It is also the smallest cube having every digit it contains exactly twice

1331 = 19² + 21² + 23².

1331 = 11³ = 439 + 443 + 449 is the smallest solution of three consecutive primes summing to the third power of a prime.

A partial solar eclipse occurred on July 5 in the year 1331.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.

27

27 = 3³, a perfect cube.

27 is the largest number that is the sum of the digits of its cube: 27³ = 19683; 1 + 9 + 6 + 8 + 3 = 27.

27 is the only number that is three times the sum of its digits.

27 is 11011 in base 2 (binary) and 33 in base 8.

27 is the smallest number with two representations as a sum of three squares: 27 = 1² + 1² + 5² = 3² + 3² + 3².

27 is the number of integer partitions of 15 into distinct parts.

The chemical element cobalt has atomic number 27.

Source: Number Gossip

125

125 is a perfect cube, 5³.

125 is the smallest cube that is also the sum of two squares in two different ways: 125 = 11² + 2² = 10² + 5².

5³ – 2⁷ = 5 – 2. The only known matching pattern is 13³ – 3⁷ = 13 – 3.

125 is the hypotenuse of a primitive Pythagorean triple: 125² = 44² + 117².

Space Shuttle mission STS-125 was the final servicing mission to the Hubble Space Telescope.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.