# 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 73

• Pi Day occurs on the 73rd day of the year (March 14) on non-leap years
• 73 is the largest integer with the property that all permutations of all its substrings are primes
• In the context of Waring's problem, all positive integers can we written as the sum of no more than 73 sixth powers
• 73 is the largest two-digit Unholey prime: such primes do not have holes in their digits
• 73 is the smallest number (besides 1) which is one less than twice its reverse
• 73 is the smallest prime whose square (5329) is the concatenation of two multi-digit primes
• 73 is the smallest number with the property that it and its neighbors can be written as a sum of 2 nonzero squares
• 73 is the alphanumeric value of the word NUMBER: 14 + 21 + 13 + 2 + 5 + 18 = 73
• 73 is the smallest Prime that is the sum of three distinct positive cubes
• A classic positive definite quadratic form represents all prime numbers if and only if it represents all prime number up to 73