149

149 is a prime number.

149 and 151 form a pair of twin primes.

149 has a representation as a sum of two squares: 149 = 7² + 10².

149 is the hypotenuse of a primitive Pythagorean triple: 149² = 51² + 140².

149 is the concatenation of the first three positive squares.

149 is the smallest number whose square starts with three identical digits: 149² = 22201.

149 is the smallest prime that retains the end (unit) digit of its predecessor (139).

149 is the smallest number that is the sum of proper substrings of its reverse: 149 = 1 + 4 + 9 + 94 + 41.

149 Medusa is an asteroid discovered in 1875.

Source: Number Gossip

351

351 = 3³ x 13.

351 is the 26th triangular number. It is the sum of the first 26 numbers. Hence, it is also the numeric value of all the letters of the English alphabet, taken together.

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

351 is a divisor of 53² - 1.

351 is the smallest number so that it and its immediate neighbors are each the product of four or more primes: 350 = 2 x 5 x 5 x 7; 351 = 3 x 3 x 3 x 13; 352 = 2 x 2 x 2 x 2 x 2 x 11.

The 1971 Ford Mustang Boss 351 was equipped with a powerful 351-cubic-inch V-8 engine.

Source: Number Gossip

874

874 = 2 x 19 x 23.

874 is a heptagonal number.

874 is the number of positive integer solutions to (1 + 1/a)(1 + 1/b)(1 + 1/c)(1 + 1/d)(1 + 1/e) = 2.

874 = 0! + 1! + 2! + 3! + 4! + 5! + 6!

874² = 763876 = (7 - 6 - 3 + 876)²

USS Duncan (DDR 874) was a U.S. Navy destroyer, launched in 1945.

Source: What's Special About This Number?

742

742 = 2 x 7 x 53.

742 is a decagonal number.

742 is the maximum number of regions into which 38 lines divide a plane.

742 is the smallest number that is one more than triple its reverse: 742 = 3 x 247 + 1.

742 is the eighth Keith number.

GJ 742 (Gliese-Jahreiss 742) is a white dwarf star located about 43 light years from Earth in the constellation Draco.

Source: What's Special About This Number?

625

625 = 5⁴. It is a perfect fourth power.

Two fourth powers use the same digits: 5⁴ = 625 and 4⁴ = 256.

625 has two representations as a sum of two squares: 625 = 7² + 24² = 15² + 20².

625 is the hypotenuse of a primitive Pythagorean triple: 625² = 336² + 527².

625 is a centered octagonal number.

625 is an automorphic number.

According to a 2010 White House news release, 625 people lost their health insurance every hour in 2009.

Source: What's Special About This Number?

856

856 = 2³ x 107. It is the product of the cube of a prime and a different prime.

856 is a nonagonal number. It is also a centered pentagonal number.

856 is 11411 in base 6 and 2332 in base 7.

856 is a member of the Fibonacci-like sequence that begins with 1 and 9: 1, 9, 10, 19, 29, 48, 77, 125, 202, 327, 529, 856, 1385, . . .

NWA 856 is a Mars meteorite found in Morocco in 2001.

Source: Positive Integers

714

714 = 2 x 3 x 7 x 17.

The sum of the prime factors of 714 is 2 + 3 + 7 + 17 = 29, and the sum of the prime factors of 715 (5 x 11 x 13) is 5 + 11 + 13 = 29. These numbers are known as Ruth-Aaron pairs.

714 is the smallest number that has equal numbers of every digit in bases 2 and 5: 1011001010 and 10324.

510,510 = 2 x 3 x 5 x 7 x 11 x 13 x 17 (the first seven prime numbers) = 714 x 715 (two consecutive numbers) = 13 x 21 x 34 x 55 (four consecutive Fibonacci numbers).

714 is the sum of twelve consecutive prime numbers: 714 = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83.

Babe Ruth hit 714 home runs in his baseball career.

Source: Prime Curios!