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 373
- 373 is the greatest prime such that all substrings are prime
- 373 is the largest and only palindromic prime with all substrings prime
- 373 is the smallest prime whose cube is interprime (interprime number is the average of two successive primes 3733 = 51895117 with surrounding primes 51895093 and 51895141)
- 373 is the smallest prime that can be written as a sum of squares of five consecutive primes
Common Properties of 373
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.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
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.
A palindrome is a number that reads the same forward or backward.
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.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.