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 787

787 is the smallest prime formed from the concatenation of n, n+1, and n
787 is the smallest prime p such that 2p + 1 is abundant

Rare Properties of 787

Palindromic prime

A palindromic prime is a prime which is a palindrome.

In base 2 Mersenne primes are palindromic primes.

...,
383,
727,
757,
787,
797,
919,
929,
...

Common Properties of 787

Apocalyptic power

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

...,
747,
748,
749,
787,
800,
807,
819,
...

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.

...,
782,
783,
785,
787,
788,
789,
790,
...

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.

...,
769,
777,
781,
787,
801,
805,
819,
...

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.

...,
781,
783,
785,
787,
789,
791,
793,
...

Odious

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

Guess what evil numbers are.

...,
781,
782,
784,
787,
789,
790,
793,
...

Palindrome

A palindrome is a number that reads the same forward or backward.

...,
757,
767,
777,
787,
797,
808,
818,
...

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.

...,
761,
769,
773,
787,
797,
809,
811,
...

Square-free

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

...,
782,
785,
786,
787,
789,
790,
791,
...

Undulating

Undulating numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.

...,
757,
767,
777,
787,
797,
808,
818,
...

Tanya Khovanova

Number Gossip

Unique Properties of 787

Rare Properties of 787

Common Properties of 787