694

694 = 2 x 347.

694 is a centered triangular number (A005448).

694 and 695 are consecutive semiprimes (A070552). 694 is a semiprime with only semiprime digits (A107342).

694 is 1010110110 in base (binary). 694 is the smallest pandigital number in base 5 (10234), containing all possible digits.

694 is the number of different arrangements (up to rotation and reflection) of 7 non-attacking rooks on a 7 x 7 chessboard.

694 is the number of partitions of 34 in which no part occurs only once (A007690).

Source: Number Gossip

571

571 is a prime number.

569 and 571 form a twin prime pair.

571 is a centered triangular number.

571 is the index of a prime Fibonacci number.

571 is 4241 in base 5. It is 1444 in base 7.

571 is a divisor of 90¹⁰ - 1.

U-571 is a 2000 film about a World War II German submarine captured by a disguised U.S. submarine.

The USS Nautilus (SSN-571) was the world's first operational nuclear-powered submarine.

Source: Prime Curios!

409

409 is a prime number.

409 is a centered triangular number.

409 has a representation as a sum of two squares: 409 = 3² + 20².

409 is the hypotenuse of a primitive Pythagorean triple: 409² = 120² + 391².

409 is the smallest prime that, along with both its prime neighbors, uses non-prime digits: 401, 409, 419.

409 is the number of primes less than 10,000 that form members of twin prime pairs.

Source: Prime Curios!

274

274 = 2 x 137.

274 has a representation as a sum of two squares: 274 = 7² + 15².

274 is a centered triangular number.

274 is the maximum number of regions into which 17 circles divide the plane.

(274 - 2)² + (274 - 7)⁷ + (274 - 4)⁴ is a prime.

The 274th Lucas number plus 274 is a prime.

274 is the sum of five positive cubes: 274 = 3(2³) + 2(5³).

Source: Prime Curios!

361

361 = 19 x 19.

361 is a centered triangular number (A005448). It is also a centered octagonal number (A016754) and a centered decagonal number (A062786).

The representations of 361 in bases 2, 3, 4, 5, 6, 8, 9, and 10 all end in 1. It is 551 in base 8 and 441 in base 9. It is 121 in base 18.

361 is a square that remains a square when the last digits is removed (A023110).

361 and 361² (130321) have the same digit sum (A058369): 3 + 6 + 1 = 10 = 1 + 3 + 0 + 3 + 2 + 1.

The game of Go is played on a grid of 19 x 19 lines, which produces 361 intersections on the game board.

Source: On-Line Encyclopedia of Integer Sequences

976

976 = 2⁴ x 61.

976 is a decagonal number. It is also a centered triangular number.

976 has a square formed by inserting a block of digits inside the original number: 976² = 952,576.

976 has a representation as a sum of two squares: 976 = 20² + 24².

976 is a divisor of 11⁴ - 1.

976-EVIL is a 1989 horror film directed by Robert Englund.

Source: What's Special About This Number?

166

166 = 2 x 83.

166 is a centered triangular number.

166 is the smallest number such that the number and its reversal are both congruent to 1 mod p for the same set of distinct odd primes: 166 = 661 = 1 mod (3, 5, 11).

166 is the smallest Smith number that is prime when reversed (661), turned upside down (991), and reversed-then-turned-upside-down (199). You get the next case by inserting a zero between the digits: 10606.

U-166 was the only German submarine lost in the Gulf of Mexico.

Source: Prime Curios!

316

316 = 2² x 79.

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

316 is a centered triangular number. It is also a centered heptagonal number.

316 has a digit product that is the digit sum of (3¹)⁶ = 729: 3 x 1 x 6 = 18; and 7 + 2 + 9 = 18.

316 is the telephone area code for the city of Wichita, Kansas.

Source: What's Special About This Number?

460

460 = 2² x 5 x 23.

460 has a unique representation as a sum of three squares: 460 = 6² + 10² + 18².

460 is a centered triangular number.

460 is the sum of twelve consecutive primes: 460 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

460 Scania is an asteroid discovered in 1900.

Source: Wikipedia

109

109 is a prime number.

109 has a representation as a sum of two squares: 109 = 3² + 10².

107 and 109 form a twin prime pair.

109 is the hypotenuse of a primitive Pythagorean triple: 109² = 60² + 91².

109 is a centered triangular number.

109 is the smallest number that contains more digits than its square: 109² = 11881.

109 is the smallest number that is palindromic in bases 5 (414) and 9 (131).

109 is the atomic number of the element meitnerium.

Source: Number Gossip

901

901 = 17 x 53.

901 has two representations as a sum of two squares: 901 = 1² + 30² = 15² + 26².

901 is the hypotenuse of two primitive Pythagorean triples: 901² = 60² + 899² = 451² + 780².

901 is a centered triangular number.

901 is the sum of the digits of the first 100 positive integers.

901 is a telephone area code in the state of Tennessee.

Source: Number Gossip

514

514 = 2 x 257.

514 is a centered triangular number.

514!/415! + 1 is a prime number.

514 is 20002 in base 4, 4024 in base 5, 1333 in base 7, and 1002 in base 8.


514 is a telephone area code that covers all of the island of Montreal, Quebec.

Source: Prime Curios!

85

85 = 5 x 17.

85 is a Smith number because the sum of its digits is equal to sum of the digits in its prime factorization: 8 + 5 = 13 = 5 + 1 + 7.

85 is a centered triangular number. Such a number can be represented by a dot in the center, with all other dots surrounding the center in successive triangular layers. The first few triangular numbers are: 1, 4, 10, 19, 31, 46, 64, 85, 109, . . .

85 is the largest known n for which 1² + 2² + 3² + . . . + n² = 1 + 2 + 3 + . . . + m has a solution.

There are 85 ways to tie a tie, according to a book by Thomas Fink and Yong Mao.

Sources: Wolfram MathWorld ; What's Special About This Number?