Number Gossip

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Unique Properties of 645

645 is the smallest Smith number which is also a base-2 pseudoprime
645 is the largest 3-digit pseudoprime to base 2
645 is the smallest Fermat pseudoprime to base 2 which are not an Euler pseudoprime to base 2

Common Properties of 645

Composite

A positive integer greater than 1 that is not prime is called composite.

Composite numbers are opposite to prime numbers.

...,
640,
642,
644,
645,
646,
648,
649,
...

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.

...,
639,
641,
643,
645,
646,
647,
649,
...

Evil

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

Guess what odious numbers are.

...,
639,
640,
643,
645,
646,
649,
650,
...

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.

...,
631,
639,
643,
645,
651,
655,
673,
...

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.

...,
639,
641,
643,
645,
647,
649,
651,
...

Smith (Joke)

A composite number is called a Smith number if the sum of its digits equals the sum of all the digits appearing in its prime divisors (counting multiplicity).

In 1984, when Albert Wilansky called his brother-in-law, named Smith, he noticed that the phone number possesses the property described here. Are they called joke numbers, because they were named after an innocent unsuspecting brother-in-law :-) ?

...,
627,
634,
636,
645,
648,
654,
663,
...

Square-free

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

...,
641,
642,
643,
645,
646,
647,
649,
...

Tanya Khovanova

Number Gossip

Unique Properties of 645

Common Properties of 645