# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 127

• 127 is the number of prime days in a leap year
• 127 is the smallest prime whose Zeckendorf expansion is palindromic
• 127 is the first odd prime Motzkin number
• 127 is the sum of factorials of the first three odd numbers: 127 = 1! + 3! + 5!
• ASCII characters are numbered from 0 to 127 — this also means 127 is the largest integer that can be represented by a signed byte
• 127 is the smallest non-trivial odd number that is not expressible as a prime plus a power of 2 (submitted by Andy Edwards)
• 127 is the smallest Friedman prime number (Friedman numbers can be written using their own digits and a given set of operations): 127 = -1 + 27. Moreover is it the smallest orderly Friedman number, where the digits are used in their proper order
• 127 is the largest Mersenne prime with all different digits
• 127 is the smallest prime whose internal digits form a prime