265

265 = 5 x 53.

2, 6, and 5 are the sixth, seventh, and eighth decimal digits of pi.

265 has two representations as a sum of two squares: 265 = 3² + 16² = 11² + 12².

265 is the hypotenuse of two primitive Pythagorean triples: 265² = 23² + 264² = 96² + 247².

265 is a centered square number.

Greek mathematician Archimedes, who is studying in Alexandria in the year 265 BC, devised a screw for raising water

Source: Wikipedia

415

415 = 5 x 83.

4, 1, and 5 are the second, third, and fourth decimal digits of pi.

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

415 is the tenth Iccanobif number, where each term is the reverse of the sum of the previous two numbers.

415 is the telephone area code for San Francisco.

Source: What's Special About This Number?

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?

568

568 = 2³ x 71.

568 has a unique representation as a sum of three squares: 568 = 10² + 12² + 18².

568 is the smallest number whose seventh power can be written as a sum of seven seventh powers.

568 is 1441 in base 7, 161 in base 21, and 131 in base 22.

In the world of structured cabling systems, the number 568 refers to the order in which the individual wires inside a CAT 5 cable are terminated.

Source: What's Special About This Number?

375

375 = 3 x 5³.

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

375 is a 5-smooth number. The product of its prime factors equals its sum of digits: 5 x 3 = 3 + 7 + 5 = 15.

Its odd powers end with 375, and its even powers end with 625.

The year 2010 is the 375th anniversary of the founding of the town of Newbury, Massachusetts.

Source: Prime Curios!

183

183 = 3 x 61.

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

183 is 111 in base 13.

183 is the smallest number n so that n concatenated with n + 1 is square: 183184 = 428².

183 Istria is a stony main belt asteroid, discovered in 1878.

Source: Number Gossip

991

991 is a prime number.

991 is the largest three-digit permutable prime. In other words, 991, 919, and 199 are all primes.

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

991 is the maximum number of regions into which 44 lines divide a plane.

991² = 982081 and 982 + 0 + 8 + 1 = 991.

Florida angler Allen Ogle caught a 991-pound hammerhead shark May 30, 1982.

Source: Prime Curios!