4347

4347 = 3 x 3 x 3 x 7 x 23.

4347 is a heptagonal number (A000566). It is also a pentagonal number (A049452).

4347 is the concatenation of the 27th and 28th primes (A045533).

4347 is a value of n for which 2n and 5n together use each of the digits 1 to 9 exactly once.

4347 is the number of regions in a regular 63-gon that are octagons (A067155).

4347 divides 22¹⁸ - 1.

Source: Number Gossip

7740

7740 = 2 x 2 x 3 x 3 x 5 x 43.

7740 is a pentagonal number (A049452). It is a pentagonal number that is not the difference of two larger pentagonal numbers (A136113), but it is the sum of two other positive pentagonal numbers (A136117).

7740 is 55500 in base 6 (A097252).

7740 is the number of primes less than 13! (A133228).

7740 is the sum of the interior angles of a 45-sided polygon in degrees (A066164).

7740 divides 49⁶ - 1.

Source: Number Gossip

5735

5735 = 5 x 31 x 37.

5735 is a pentagonal number (A049452 and A014632).

5735 is a number divisible by 5 that is the difference between two different positive cubes in at least one way (A038853).

5735 is a number whose set of base 11 digits is {3, 4} (A032835): 4344.

5735 is a number n such that 2n + 1, 3n + 2, and 4n + 3 are primes (A126995).

5735 divides 26⁶ - 1.

5735 is a number that cannot be written as a sum of three squares.

Source: Number Gossip

8400

8400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7.

8400 is a number with four distinct prime factors {2, 3, 5, 7} (A147571).

8400 is a pentagonal number (A000326).

8400 is the number of ways of writing 31 as the sum of seven triangular numbers (A226252).

8400 is 1100 in base 20.

8400 is a number that can be expressed as the difference of the squares of primes in just three distinct ways (A090782).

8400 divides 43⁴ - 1.

8400 is the number of legal queen moves in chess.

Source: Number Gossip

651

651 = 3 x 7 x 31.

651 is a pentagonal number and a nonagonal number. It is the smallest number that is both pentagonal and nonagonal.

651 is 10101 in base 5 and 3003 in base 6.

651 is the number of binary trees of height 4.

651 has a fourth power that is the sum of four fourth powers.

101,556 = 372 x 273 = 651 x 156.

Source: Number Gossip

1080

1080 = 2 x 2 x 2 x 3 x 3 x 3 x 5.

1080 is a pentagonal number (A000326).

1080 is the smallest number with 18 divisors. The sum of the divisors of 1080 is a square (A006532).

1080 is the sum (in degrees) of the internal angles of an eight-sided polygon.

1080 is a number that can be expressed as the difference of the squares of primes in just two distinct ways (A090788).

Source: What's Special About This Number?

376

376 = 2 x 2 x 2 x 47.

376 is a pentagonal number.

376 is an automorphic (or curious) number: 376² = 141376, which ends with the digits 376. Indeed, all powers of 376 (or powers of any number ending in 376) end with 376.

There are 376 Smith numbers among the first 10,000 positive integers.

376 = 1⁷ + 3⁵ + 5³ + 7¹.

Source: Number Gossip

782

782 = 2 x 17 x 23.

782 is a pentagonal number (A000326).

782 is a number whose sum of divisors is a fourth power (A006532): 1 + 2 + 17 + 23 + 34 + 46 + 391 + 782 = 1296 = 6⁴.

The sum of the squares of the first 782 primes is a prime (A098561).

782 is a divisor of 47⁴ - 1.

Source: Number Gossip

1426

1426 = 2 x 23 x 31.

1426 is the number of integer partitions of 42 into distinct parts.

1426 is a pentagonal number.

1426 is the smallest number n such that the sum of the divisors of n equals the product of the squares of the digits of n: 1 + 2 + 23 + 31 + 46 + 62 + 713 + 1426 = 2304 = 1² x 4² x 2² x 6².

1426 is 474 in base 18.

1426 is the sum of the totient function for the first 68 integers.

Source: Number Gossip

715

715 = 5 x 11 x 13.

715 is the tenth pentatope number. It is also a pentagonal number (A000326), a hendecagonal number (A051682), and a hexagonal pyramidal number (A002412).

715 is 222111 in base 3, 23023 in base 4, and 1313 in base 8.

715 is the number of intersections of diagonals in the interior of a regular 13-gon (A006561).

715 is the smallest positive number that can be written as a sum of distinct Fibonacci numbers in 26 ways.

Source: Number Gossip

330

330 = 2 x 3 x 5 x 11.

330 is the eighth pentatope number. It is also a pentagonal number.

330³ + 330³ + 330⁰ is a prime number.

330 is the sum of six consecutive primes: 330 = 43 + 47 + 53 + 59 + 61 + 67.

330 is the sum of five consecutive squares: 330 = 6² + 7² + 8² + 9² + 10².

Source: Prime Curios!

247

247 = 13 x 19. Its digits sum to the smallest prime factor: 2 + 4 + 7 = 13.

247 is a pentagonal number.

247 is the smallest possible difference between two integers that together contain each digit exactly once: 247 = 50,123 - 49876.

247² is one of six square numbers that use the same digits: 247² = 61,009; 130² = 16.900; 140² = 19,600; 310² = 96,100; 103² = 10,609; and 301² = 90,601.

247 Eukrate is a large, dark asteroid discovered in 1885.

Source: Prime Curios!

477

477 = 3² x 53,

477 has a representation as a sum of two squares: 477 = 6² + 21².

477 is a pentagonal number.

477 is the smallest number that is the sum of different primes by using twice all the digits greater than 0: 477 = 89 + 83 + 67 + 61 + 53 + 47 + 41 + 29 + 5 + 2.

477 is the smallest number whose cube contains four 3s: 477³ = 108,531,333.

Masonic Funeral Music in C by Wolfgang Amadeus Mozart is cataloged as KV 477.

Source: Number Gossip

287

287 = 7 x 41.

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

287 is a pentagonal number.

287 is the sum of consecutive primes in three different ways: 287 = 89 + 97 + 101 = 47 + 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

287 is the sum of the first three NSW primes: 287 = 7 + 41 + 239.

287 Nephthys is a large asteroid discovered in 1889.

Source: Prime Curios!

532

532 = 2² x 7 x 19.

532 has a unique representation as a sum of three squares: 532 = 8² + 12² + 18².

532 is 444 in base 11.

532 is a divisor of 11⁶ - 1.

532 is a pentagonal number.

532 is the smallest even number differing by a composite number from both of its prime neighbors.

532 was the first year in which the Anno Domini calendar was used for numbering the years.

Source: Number Gossip

590

590 = 2 x 5 x 59.

590 is a pentagonal number.

590 plus 590 ones is a prime. This is the only three-digit number with this property.

590 is a number n such that n concatenated with n + 2 gives the product of two numbers that differ by 1: 590592 = 768 x 769.

590 Tomyris is an asteroid discovered in 1906.

Source: Prime Curios!

852

852 = 2² x 3 x 71.

852 is a pentagonal number.

852 is the number of 6-colorable connected graphs with seven vertices.

852 is a Smith number.

NGC 852 is a galaxy in the constellation Eridanus.

Source: What's Special About This Number?

925

925 = 5² x 37.

925 has three representations as a sum of two squares: 925 = 5² + 30² = 14² + 27² = 21² + 22².

925 is the hypotenuse of two primitive Pythagorean triples: 925² = 43² + 924² = 533² + 756².

925 is 1021021 in base 3 and 4141 in base 6.

925 is a pentagonal number.

Asteroid 925 Alphonsina was discovered in 1920.

Source: Wolfram MathWorld

425

425 = 5² x 17.

425 has three representations as a sum of two squares: 425 = 5² + 20² = 8² + 19² = 13² + 16².

425 is the hypotenuse of two primitive Pythagorean triples: 425² = 87² + 416² = 297² + 304².

425 is a pentagonal number, a number of the form n(3n - 1)/2, where n = 17.

425 is the number of subsets of {1, 2, 3, . . . 11} that have an integer average.

425 is the telephone area code for suburbs to the north and east of Seattle, Washington.

Source: What's Special About This Number?

2501

2501 = 41 x 61.

2501 is the product of the only two primes (41 and 61) that can be the last two digits of a perfect fourth power. If you replace the 5 by a 4, you get a fourth power: 2401 = 7⁴.

2501 is a pentagonal number, having the form n(3n – 1)/2. In this case, n = 41.

2501 has two representations as a sum of two squares: 2501 = 1² + 50² = 10² + 49².

2501 is the hypotenuse of two primitive Pythagorean triples: 2501² = 100² + 2499² = 980² + 2301².


Project 2501, from the film and manga Ghost in the Shell, is an artificial intelligence program that develops sapience.

Source: Prime Curios!