# 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 367

- 367 is the largest number whose square has strictly increasing digits
- 367 is the smallest prime p such that σ(p+1) = σ(p-1)
- 367 is the smallest lucky-indexed prime that is also a prime-indexed lucky number
- 367 is smallest lucky number such that the next lucky number (385) has the same digital sum
- 367 is the smallest prime such that the total frequency of every decimal digit in the set of all primes up to it and inclusive is odd