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 2946
- 2946 is the smallest number n such that in the list of the first n primes there are more primes with the remainder 1 mod 4 than with the remainder 3 mod 4
Common Properties of 2946
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 odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
A number is said to be square-free if its prime decomposition contains no repeated factors.
The untouchable numbers are those that are not the sum of the proper divisors of any number.