# 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 97

- 97 is the smallest prime that has a prime alphabetical value in its Roman numerals-based representation (XCVII): 24 + 3 + 22 + 9 + 9 = 67
- There are 97 leap days every 400 years in the Gregorian Calendar
- 97 is the largest two-digit prime
- 97 is the smallest prime occurring only once in its decade
- 97 is the smallest prime p such that p and p+4 are sandwiching three consecutive non-squarefree numbers (submitted by Massimo Kofler)

## Common Properties of 97

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

A number is *odd* if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

The number n is *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

A *prime* is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.

Prime numbers are opposite to composite numbers.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.