Number Gossip

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Unique Properties of 151

151 is the smallest palindromic prime no squarefree neighbors
151 is the smallest palindromic prime that is not a Chen prime

Rare Properties of 151

Palindromic prime

A palindromic prime is a prime which is a palindrome.

In base 2 Mersenne primes are palindromic primes.

...,
11,
101,
131,
151,
181,
191,
313,
...

Common Properties of 151

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.

...,
147,
148,
149,
151,
152,
153,
154,
...

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.

...,
133,
135,
141,
151,
159,
163,
169,
...

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.

...,
145,
147,
149,
151,
153,
155,
157,
...

Odious

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

Guess what evil numbers are.

...,
145,
146,
148,
151,
152,
155,
157,
...

Palindrome

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

...,
121,
131,
141,
151,
161,
171,
181,
...

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.

...,
137,
139,
149,
151,
157,
163,
167,
...

Square-free

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

...,
145,
146,
149,
151,
154,
155,
157,
...

Twin

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

...,
137,
139,
149,
151,
179,
181,
191,
...

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.

...,
121,
131,
141,
151,
161,
171,
181,
...

Tanya Khovanova

Number Gossip

Unique Properties of 151

Rare Properties of 151

Common Properties of 151