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 4567

4567 is the largest prime with consecutive increasing digits

Common Properties of 4567

Apocalyptic power

The number n is called an apocalyptic power if 2ⁿ contains the consecutive digits 666 (in decimal).

...,
4559,
4563,
4566,
4567,
4568,
4570,
4572,
...

Deficient

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.

...,
4562,
4563,
4565,
4567,
4568,
4569,
4570,
...

Evil

The number n is evil if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

...,
4561,
4562,
4564,
4567,
4568,
4571,
4573,
...

Lucky

To build the lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ... . The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, ... . The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, ... . The next number remaining is 9, so delete every ninth number, etc.

Those numbers were lucky they weren't crossed out.

...,
4539,
4551,
4561,
4567,
4569,
4573,
4587,
...

Odd

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.

...,
4561,
4563,
4565,
4567,
4569,
4571,
4573,
...

Prime

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.

...,
4547,
4549,
4561,
4567,
4583,
4591,
4597,
...

Square-free

A number is said to be square-free if its prime decomposition contains no repeated factors.

...,
4562,
4565,
4566,
4567,
4569,
4570,
4571,
...

Tanya Khovanova

Number Gossip

Unique Properties of 4567

Common Properties of 4567