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 420
- 420 is the smallest number divisible by 1 through 7
- 420 is the smallest long leg of more than one primitive Pythagorean triangle
- 420 is the smallest number n such that n2+n+41 (Euler's "prime generating polynomial") has more than 2 prime factors
- 420 is the smallest perimeter of exactly 5 different Pythagorean triangles
Rare Properties of 420
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 420
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.