546

546 = 2 x 3 x 7 x 13.

546 is 666 in base 9 and 222 in base 16.

546 is 202020 in base 3, 20202 in base 4, and 4141 in base 5.

546! - 1 is a prime number.

The sum 273 + 546 = 819 is one of only four cases in which the equality n + 2n= 3n uses each of the nine digits from 1 to 9.

BS 546 is an old British standard for domestic air conditioner power plugs and sockets.

Source: Prime Curios!

40

40 = 2³ x 5.

40 has a representation as a sum of two squares: 40 = 2² + 6².

A regular 40-gon is constructible with straightedge and compass.

40 is 1111 in base 3.

40 can be partitioned in 31,185 ways.

40 is the number of equivalent hyperspheres in five dimensions that can touch an equivalent hypersphere without any intersection. Hence, 40 is the kissing number in five dimensions.

According to the Bible, rain fell for 40 days and 40 nights during Noah's flood.

40 is the only number in English whose letters are in alphabetical order.

Source: WolframAlpha

516

516 = 2² x 3 x 43.

516 is the number of partitions of 32 in which no part occurs only once.

516 is the sum of two distinct powers of 2: 516 = 2⁹ + 2².

516 is a refactorable number. The number of divisors (4) of 516 divides 516.

The digit 6 occurs in the 516th position in the decimal expansion of pi.

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

Source: What's Special About This Number?

745

745 = 5 x 149.

745 has two representations as a sum of two squares: 745 = 4² + 27² = 13² + 24².

745 is the hypotenuse of two Pythagorean triples: 745² = 216² + 713² = 407² + 624².

745 is a divisor of 44⁴ - 1.

745 is the smallest number whose square begins with three 5s: 745² = 555,025.

The German submarine U-745 was lost at sea on Jan. 30, 1945.

Source: What's Special About This Number?

333

333 = 3² x 37.

333 has a representation as a sum of two squares: 333 = 3² + 18².

333 = 101 + 11 + 2 + 3 + 41 + 5 + 61 + 7 + 83 + 19, where each term is the smallest prime containing 0, 1, 2, ..., and 9, respectively.

333¹²² + 122³³³ is a prime number.

The Sikorsky Model S-333 is a light turbine-powered helicopter.

Source: Number Gossip

9293

9293 is a prime number. It is also a Sophie Germain prime because 2 x 9293 + 1 = 18587, which is also a prime.

9293 reversed is also a prime: 3929. 9293 is the largest number formed from two consecutive two-digit numbers that is also a prime when reversed.

9293 has a representation as a sum of two squares: 9293 = 58² + 77².

9293 is the hypotenuse of a primitive Pythagorean triple: 9293² = 2565² + 8932².

9293 Kamogata is a main-belt asteroid discovered in 1982.

Source: Prime Curios!

379

379 is a prime number.

379 is a divisor of 51³ - 1.

379 is the maximum number of regions into which 27 lines divide the plane.

379 is the smallest multidigit prime such that its largest digit is equal to the largest digit of the sum of its digits.

379 is the sum of the seven smallest primes whose last digit is 7: 379 = 7 + 17 + 37 + 47 + 67 + 97 + 107.

It was not until page 379 in the first edition of their pivotal Principia Mathematica (a 1910 text deriving logic and mathematics from an axiomatic basis) that Alfred North Whitehead and Bertrand Russell were able to prove the key lemma, which would later allow them to prove that 1 + 1 = 2.

Source: Prime Curios!