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 2310
- 2310 is the product of the first 5 primes
- 2310 is the largest primorial with all digits distinct: 0, 1, 2 and 3
- 2310 is the smallest number such that the number of its distinct prime factors equals the sum of the distinct prime factors of three preceding numbers
Rare Properties of 2310
The p-primorial is the product of all primes less than or equal to p. It is sometimes denoted by p#.
Compare to compositorials and factorials.
- ...,
- 6,
- 30,
- 210,
- 2310,
- 30030,
- 510510,
- 9699690,
- ...
Common Properties of 2310
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.
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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.
A number is said to be square-free if its prime decomposition contains no repeated factors.