# 111 (number)

111 is the natural number following 110 and preceding 112.

 List of numbers — Integers << 110 111 112 113 114 115 116 117 118 119 >>
Cardinalone hundred and
eleven
Ordinal111th
Factorization[itex]111 = 3 \cdot 37[itex]
Roman numeralCXI
Binary1101111

## In mathematics

One hundred eleven is R3 or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 x 37, therefore all triplets (numbers like 222 or 666) in base ten are of the form 3n x 37.

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. "111" is not prime in base ten, but is prime in base two, where 111 = 7 in base ten. It is also prime in these other bases 3 to 100: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, and 99. 111 is also prime in base 111 (= 1243310).

The smallest magic square using only prime numbers (and 1) has a magic constant of 111:

31  73   7
13  37  61
67   1  43


A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111:

24  16  33  23  10   5
11  15  28   8  13  36
20  14   2  31  25  19
1  18   6  29  27  30
21  22   7  17  32  12
34  26  35   3   4   9


(The square has this magic constant because 1+2+3+...+34+35+36 = 666, and 666 / 6 = 111).

This number is also the magic constant of n-Queens Problem for n = 6, an enneagonal number and a Harshad number.

111 is the lowest positive integer requiring six syllables to name in American English, or seven syllables (including "and") in British English.

## In other fields

The number 111 is sometimes called a "nelson", after Admiral Nelson.

One hundred eleven is also:

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy