8128

8128 = 2 x 2 x 2 x 2 x 2 x 2 x 127.

8128 is a perfect number (2^{7 - 1}(2⁷ - 1)), associated with the Mersenne prime 127 = 2⁷ - 1 (A000396). It is the largest perfect number whose index (4) is equal to the number of digits.

8128 is the 127th triangular number; it is the sum of the first 127 integers. 8128 is the 64th hexagonal number. It is also a centered nonagonal number (A060544).

8128 divides 63¹⁴ - 1.

Source: Number Gossip

561

561 = 3 x 11 x 17.

561 is 1000110001 in base 2 (binary) (A006995).

561 is the 33rd triangular number (A000217), the sum of the first 33 integers. It is also a hexagonal number (A000384) and a dodecagonal number (A051624).

561 is the smallest Carmichael number (A002997).

561 is a centered icosahedral number (cuboctahedral number) (A005902).

Source: Number Gossip

120

120 = 2 x 2 x 2 x 3 x 5.

120 has a unique representation as a sum of three squares: 120 = 2² + 4² + 10².

120 = 5!

120 is the 15th triangular number. It is the sum of the first 15 positive integers.

120 is the eighth tetrahedral number.

120 is a hexagonal number.

120 = 3¹ + 3² + 3³ + 3⁴.

120 is the smallest composite number of the form x! whose digit sum (1 + 2 + 0 = 3) and x (5) are both primes.

120 is the smallest three-digit number that may be expressed as the difference between squares of consecutive primes in tow different ways: 120 = 31² - 29² = 17² - 13².

The great rhombicosidodecahedron is an Archimedean solid with 120 vertices, 180 edges, and 62 faces.

Source: Prime Curios!

946

946 = 2 x 11 x 43.

946 is the 43rd triangular number (A000217). It is the sum of all integers from 1 to 43.

946 is also a hexagonal number (A000384), a centered nonagonal number, and a hexagonal pyramidal number (A002412).

946 is the only three-digit number such that the reversal of the concatenation of the first 946 natural numbers is a prime.

946 is the largest known number n such that n is the sum of two consecutive primes but not the sum of two sums of two consecutive primes.

Source: Prime Curios!

231

231 = 3 x 7 x 11. It is the 22nd number that is the product of three distinct primes.

231 is 11100111 in base 2 (binary).

231 is the number of integer partitions of 16.

231 is the 21st triangular number. It is the smallest triangular number in which the sum of the external digits equals the sum of the internal digits.

231 is a hexagonal number and an octahedral number.

231 = 2² + 3² + 7² + 13².

The U.S. liquid gallon is defined as 231 cubic inches.

Source: Number Gossip

496

496 = 2 x 2 x 2 x 2 x 31.

496 is the 31st triangular number. It is the sum of all integers from 1 to 31. It is also a hexagonal number and a centered nonagonal number.

496 is the smallest triangular number such that the sum of its digits cubed is prime: 4³ + 9³ + 6³ = 1009.

496 is the third perfect number, associated with the Mersenne prime 31. It is the largest perfect number with all different digits. It is the smallest perfect number such that the sum of its digits is prime: 4 + 9 + 6 = 19.

496 = 1³ + 3³ + 5³ + 7³.

Source: Number Gossip

919

919 is a prime number.

919 is the 18th centered hexagonal number (hex number).

919 is the smallest palindromic number whose sum of digits (19) shows up as a substring of the number.

919 is the smaller number in the smallest pair of prime numbers that are mutually the sums of the same powers of each other's digits: 919 = 1³ + 4³ + 5³ + 9³ and 1459 = 9³ + 1³ + 9³.

919 is the largest known palindromic prime for which the next prime (929) is also palindromic.

919 is the smallest palindromic prime equal to the difference of consecutive cubes:919 = 18³ - 17³.

Source: Prime Curios!

153

153 = 3² x 17.

153 is the 17th triangular number. It is also a hexagonal number.

153 = 1! + 2! + 3! + 4! + 5!

153 is palindromic in base 2 (binary): 10011001. It is 2121 in base 4 and 99 in base 16.

153 is the smallest number greater than 1 such that the sum of the cubes of its digits equals itself: 153 = 1³ + 5³ + 3³.

153 has a representation as a sum of two squares: 153 = 3² + 12².

In the Bible, Simon Peter is said to have caught 153 fish (John 21:11).

Source: Number Gossip

378

378 = 2 x 3³ x 7.

378 is the 27th triangular number. It is also a hexagonal number and the smallest Smith triangular number.

378 is the smallest three-digit number in which the sum of the digits is equal to the sum of the prime factors: 3 + 7 + 8 = 2 + 3 + 3 + 3 + 7 = 18.

378 is a cake number.

378 Holmia is an asteroid discovered in 1893.

Source: Number Gossip

861

861 = 3 x 7 x 41.

861 is the 41st triangular number. It is also a hexagonal number.

861 = 7 + 77 + 777.

144,648 = 861 x 168 = 492 x 294.

The USS Harwood (DD 861) was a destroyer in the U.S. Navy just after World War II.

Source: What's Special About This Number?

703

703 = 19 x 37.

703 is the 37th triangular number. It is also a hexagonal number.

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

703 is 3131 in base 6.

703 is the smallest number requiring 73 fifth powers for its Waring representation.

703 is one of the telephone area codes for northern Virginia.

Source: Wikipedia

325

325 = 5² x 13.

325 is the 25th triangular number (the sum of the first 25 integers): 1 + 2 + 3 + . . . + 25 = 325.

325 is a hexagonal number.

In base 2, 325 is the palindromic number 101000101; in base 4, it is 11011; and in base 8, it is 505.

325 is the smallest number to be the sum of two squares in three different ways: 325 = 1² + 18² = 6² + 17² = 10² + 15².

325 is the hypotenuse of two primitive Pythagorean triples: 325² = 36² + 323² = 204² + 253².

Currently undergoing restoration, the USS LST-325, launched in 1942, participated in the invasion of Sicily in 1943 and in June 1944 landed at Omaha Beach.

Source: Positive Integers

26

26 = 2 x 13.

26 is the only integer sandwiched between a square (25) and a cube (27).

26 is the smallest non-palindromic number whose square is palindromic: 26² = 676.

26 is equal to the sum of the digits of its cube: 26³ = 17,576 and 1 + 7 + 5 + 7 + 6 = 26.

26 (together with 11) cannot be represented as the sum of less than six hexagonal numbers from the sequence 1 6 15 28 45 . . . .

26 has a representation as a sum of two squares: 26 = 5² + 1².

26 is the smallest number with three representations as a sum of three distinct primes: 26 = 2 + 5 + 19 = 2 + 7 + 17 = 2 + 11 + 13.


26 is the atomic number of iron and the number of letters in the English alphabet.

Source: Number Gossip

435

435 = 3 x 5 x 29.

435 is a triangular number and a hexagonal number.

435 is the number of ordered partitions of 16 into distinct parts.

435 is the sum of seven positive fifth powers: 435 = 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 3⁵.

The United States House of Representatives has 435 members.

Source: The On-Line Encyclopedia of Integer Sequences