Number Gossip

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Unique Properties of 619

619 is the only strobogrammatic prime with distinct digits
619 is the smallest strobogrammatic prime which is not a palindrome
619 is of the form 6! - 5! + 4! - 3! + 2! - 1!

Common Properties of 619

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.

...,
614,
615,
617,
619,
621,
622,
623,
...

Evil

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

Guess what odious numbers are.

...,
612,
615,
616,
619,
621,
622,
624,
...

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.

...,
601,
613,
615,
619,
621,
631,
639,
...

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.

...,
613,
615,
617,
619,
621,
623,
625,
...

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.

...,
607,
613,
617,
619,
631,
641,
643,
...

Square-free

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

...,
615,
617,
618,
619,
622,
623,
626,
...

Twin

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

...,
599,
601,
617,
619,
641,
643,
659,
...

Tanya Khovanova

Number Gossip

Unique Properties of 619

Common Properties of 619