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 171

If you write n consecutive digits starting with 1 and following 9 by 0, the smallest n that will give you a prime number is 171

Common Properties of 171

Composite

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

Composite numbers are opposite to prime numbers.

...,
168,
169,
170,
171,
172,
174,
175,
...

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.

...,
167,
169,
170,
171,
172,
173,
175,
...

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.

...,
159,
163,
169,
171,
189,
193,
195,
...

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.

...,
165,
167,
169,
171,
173,
175,
177,
...

Odious

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

Guess what evil numbers are.

...,
164,
167,
168,
171,
173,
174,
176,
...

Palindrome

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

...,
141,
151,
161,
171,
181,
191,
202,
...

Triangular

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.

Compare to square, pentagonal and tetrahedral numbers.

...,
120,
136,
153,
171,
190,
210,
231,
...

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.

...,
141,
151,
161,
171,
181,
191,
202,
...

Tanya Khovanova

Number Gossip

Unique Properties of 171

Common Properties of 171