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 157
- 157 is the smallest apocalyptic power
- 157 is the smallest prime whose binary and ternary representations are also prime when read in decimal
- 157 is the smallest prime which is the sum of ten consecutive composite numbers
- 157 is the smallest emirp whose binary conversion remains an emirp when read in decimal
- 157 is the smallest multi-digit prime of the form 2p + p3, where p is prime
Common Properties of 157
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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.
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.