114

114 = 2 x 3 x 19.

114 is the smallest number with 10 representations as a sum of two primes: 114 = 5 + 109 = 7 + 107 = 11 + 103 = 13 + 101 = 17 + 97 = 31 + 83 = 41 + 73 = 43 + 71 = 47 + 67 = 53 + 61.

114 has the representation 2⁷ - 14.

114 is 222 in base 7.

114² = 12996 = (129 - 9 - 6)².

114 is the number of different ways to color the faces of a cube with three colors.

114 appears in the Padovan sequence.

114 Kassandra is a large, dark asteroid discovered in 1871. The asteroid is featured in the 2009 film Meteor: Path to Destruction, in which it is split in two by a comet and set on a collision course with Earth.

Source: Numeropedia

513

513 = 3³ x 19.

513 is 1000000001 in base 2 and 1001 in base 8. It is 20001 in base 4 and 201 in base 16.

513 is a triangular matchstick number.

513 is a sum of two positive cubes: 513 = 8³ + 1³.

513 appears in the sequence generated when you start with 1 and repeatedly reverse the digits and add 16 to get the next term.

513 are the first three digits in the Dewey Decimal Classification System call numbers for library books in arithmetic.

Source: On-Line Encyclopedia of Integer Sequences

612

612 = 2² x 3² x 17.

612 has a representation as a sum of two squares: 612 = 6² + 24².

612 is a number whose square (374544) and cube (229220928) use different digits.

612 can be represented as two consecutive sums of consecutive numbers: 612 = 64 + 65 + . . . + 71 + 72 = 73 + 74 + . . . + 79 + 80.

612 is 4422 in base 5 and 1144 in base 8; it is 2500 in base 6 and 750 in base 9; it is 211200 in base 3 and 21210 in base 4 and 220 in base 17.

612 is a telephone area code for Minneapolis/St. Paul, Minnesota.

Source: Numeropedia

819

819 = 3² x 7 x 13.

819 is 1100110011 in base 2 (binary) and 333 in base 16.

819 is a square pyramidal number.

819 is the largest three-digit number whose square (670761) and cube (549353259) use different digits.

819 is the smallest number such that it and its successor (820) are both the product of two primes and the square of a prime: 820 = 2² x 5 x 41.

In 1944, René Barthélemy developed an 819-line television standard.

Source: Number Gossip

25

25 = 5², a perfect square.

25 has a representation as a sum of two squares: 25 = 3² + 4². It is the smallest square that can be written as a sum of two squares.

25 is the hypotenuse of a primitive Pythagorean triple: 25² = 7² + 24².

25 is the sum of the first five odd numbers: 25 = 1 + 3 + 5 + 7 + 9.

25 = 3 + 4 + 5 + 6 + 7.

25 is an octahedral number.

Every square number is the sum of two triangular numbers: 25 = 10 + 15.

Pachisi, the Hindu word for 25, is one of the national games of India.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

810

810 = 2 x 3⁴ x 5.

810 has a representation as a sum of two squares: 810 = 9² + 27².

810 has the representation 3⁶ + 81.

810 is a value of n for which n - 1 (809) and n + 1 (811) are twin primes, and so are 2n - 1 (1619) and 2n + 1 (1621).

810 is 1100 in base 9.

The Intel i810 chipset was released in early 1999.

Source: What's Special About This Number?

498

498 = 2 x 3 x 83. 498 is the product of three distinct Sophie Germain primes.

498 is the number of necklaces possible with eight beads, each being one of three colors.

498 is 3443 in base 5.

The digit 9 occurs in the 498th position of the decimal expansion of pi.

498 is a number n such that 2n + 1 and 4n + 1 are primes: 997 and 1993.

498 Tokio is an asteroid discovered in 1900.

Source: What's Special About This Number?

176

176 = 2⁴ x 11.

176 has a unique representation as a sum of three squares: 176 = 4² + 4² + 12².

176 is the number of integer partitions of 15.

176 is the smallest number that is both a pentagonal number and an octagonal number.

Each internal angle of a regular 90-sided polygon is 176 degrees.

Gliese 176 is a red dwarf star in the constellation Taurus.

Source: Number Gossip

241

241 is a prime number.

241 has a representation as a sum of two squares: 241 = 4² + 15².

239 and 241 form a twin prime pair.

241 is the hypotenuse of a primitive Pythagorean triple: 241² = 120² + 209².

241 is 111 in base 15.

241 is the smallest prime p such that p plus the reversal of p equals a palindromic prime: 241 + 142 = 383.

Reel Big Fish wrote a song entitled "241", in which the number is repeated as the only lyric.

Source: Prime Curios!

883

883 is a prime number.

881 and 883 form a twin prime pair.

8ⁿ + 8ⁿ + 3ⁿ is prime for n = 0 to 4: 3, 19, 137, 1051, and 8273.

883 is a number n whose fifth root has a decimal part that begins with the digits of n: 3.883221296. . .

883 is 733 in base 11 and 373 in base 16.

Actress Penélope Cruz has 883 tattooed on her right ankle.

Source: Prime Curios!

975

975 = 3 x 5² x 13.

975 is 1111001111 in base 2 (binary).

975 is 33033 in base 4, 4303 in base 6, 1303 in base 9, and 303 in base 18.

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

975 is the number of 11-ominoes that contain one hole.

The Wright R-975 Whirlwind was a radial engine developed in the United States by Wright Aeronautical.

Source: What's Special About This Number?

778

778 = 2 x 389.

778 has a representation as a sum of two squares: 778 = 7² + 27².

778 is the number of ways a 5 x 1 rectangle can be surrounded by 5 x 1 rectangles.

778 is a Smith number. The sum of its digits is equal to the sum of the digits of its prime factors: 7 + 7 + 8 = 2 + 3 + 8 + 9.

778 is a telephone area code for British Columbia.

Source: What's Special About This Number?

677

677 is a prime number.

677 has a representation as a sum of two squares: 677 = 1² + 26².

677 is the sum of three consecutive squares: 677 = 14² + 15² + 16².

677 is the hypotenuse of a primitive Pythagorean triple: 677² = 52² + 675².

677 Aaltje is an asteroid named for a Dutch singer.

Source: Prime Curios!

88

88 = 2³ x 11.

88 has a unique representation as a sum of three squares: 88 = 4² + 6² + 6².

88 = 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13.

88 is the sixth number that stays the same when written upside down.

88 is the smallest number such that its square has all its digits twice: 88² = 7744.

A modern piano has 88 keys, 52 white and 36 black, spanning more than seven octaves.

88 is the number of constellations in the sky, as defined by the International Astronomical Union.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

773

773 is a prime number.

773 has a representation as a sum of two squares: 773 = 17² + 22².

773 is the hypotenuse of a primitive Pythagorean triple: 773² = 195² + 748².

773 is the largest three-digit unholey prime; its digits have no holes.

773 is the smallest prime such that adding a preceding or trailing digit will always result in a composite if we omit the case where the leading digit is zero.

773 is a telephone area code for Chicago.

Source: Prime Curios!