167

167 is a prime number.

167 cannot be written as a sum of three squares.

167 is the smallest number whose fourth power begins with four identical digits: 167⁴ = 777796321.

167 = 2 * 3⁴ + 5.

167 is the smallest multidigit prime such that the product of the digits is equal to the number of digits times the sum of the digits: 1 x 6 x 7 = 3(1 + 6 + 7) = 42.

At the start of backgammon, each player has a pip count of 167.

Source: Prime Curios!

842

842 = 2 x 421.

842 has a representation as a sum of two squares: 842 = 1² + 29².

842 is a semiprime sandwiched between semiprimes: 841 = 29², 842 = 2 x 421, 843 = 3 x 281.

842 is a centered square number.

The largest swordfish ever caught (in 1936) weighed 842 pounds.

Source: On-Line Encyclopedia of Integer Sequences

474

474 = 2 x 3 x 79.

474 is a nonagonal number.

474 is a member of the Fibonacci-like sequence starting with 1 and 8: 1, 8, 9, 17, 26, 43, 69, 112, 181, 293, 474, . . .

474 is 3344 in base 5.

474 is the sum of eight consecutive primes: 474 = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73.

Mathematician and architect Anthemius of Tralles was born in the year 474 and collaborated in building the Hagia Sophia in Constantinople.

Source: On-Line Encyclopedia of Integer Sequences

820

820 = 2² x 5 x 41.

820 has two representations as a sum of two squares: 820 = 6² + 28² = 12² + 26².

820 is the 40th triangular number.

820 is a divisor of 81² - 1.

810 is 1111 in base 9.

Muhammad ibn Musa al-Khwarizmi presented the first systematic solution of linear and quadratic equations in the year 820 in The Compendious Book on Calculation by Completion and Balancing.

Source: WolframAlpha

215

215 = 5 x 43.

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

215 is 3113 in base 4 and 555 in base 6.

215³ = 9,938,375 = (99 + 38 + 3 + 75)³.

215 = 31³ - 1.

215 is a telephone area code for the city of Philadelphia.

Source: Numeropedia

158

158 = 2 x 79.

158 is the maximum number of regions into which 13 circles divide the plane.

158 is the smallest number such that the sum of the number and its reverse is a nonpalindromic prime: 158 + 851 = 1009, and 1009 is a nonpalindromic prime.

158 is the sum of the first nine Mersenne prime exponents: 2 + 3 + 5 + 7 + 13 + 17 + 19 + 31 + 61 = 158.

Episode 158 (Season 8) of The Simpsons is titled "Bart after Dark" and features a mock-up of the Beatles album cover "Sgt. Pepper's Lonely Hearts Club Band."

Source: Number Gossip

891

891 = 3⁴ x 11.

891 is an octahedral number.

891 is the smallest number that is the reversal of the sum of its proper substrings: 8 + 9 + 1 + 89 + 91 = 198.

891 is 031323 in base 4 and 1200 in base 9.

NGC 891 is a spiral galaxy in the constellation Andromeda, discovered by William Herschel in 1784.

Source: Number Gossip