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 823

823 is the smallest prime p such that p and prime(p) end with the same two digits
823 is the first start of a decreasing run of length 4 for the Euler phi function

Common Properties of 823

Apocalyptic power

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

...,
819,
820,
822,
823,
824,
826,
828,
...

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.

...,
818,
819,
821,
823,
824,
825,
826,
...

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.

...,
801,
805,
819,
823,
831,
841,
855,
...

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.

...,
817,
819,
821,
823,
825,
827,
829,
...

Odious

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

Guess what evil numbers are.

...,
817,
818,
820,
823,
824,
827,
829,
...

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.

...,
809,
811,
821,
823,
827,
829,
839,
...

Square-free

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

...,
818,
821,
822,
823,
826,
827,
829,
...

Twin

A prime number is called a twin prime if there exists another prime number differing from it by 2.

...,
809,
811,
821,
823,
827,
829,
857,
...

Tanya Khovanova

Number Gossip

Unique Properties of 823

Common Properties of 823