# 111 (number)

 ← 110 111 112 →
Cardinalone hundred eleven
Ordinal111th
(one hundred eleventh)
Factorization3 × 37
Divisors1, 3, 37, 111
Greek numeralΡΙΑ´
Roman numeralCXI
Binary11011112
Ternary110103
Quaternary12334
Quinary4215
Senary3036
Octal1578
Duodecimal9312
Vigesimal5B20
Base 363336

111 (One hundred [and] eleven) is the natural number following 110 and preceding 112.

## In mathematics

111 is a perfect totient number.[1]

111 is R3 or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like 222 or 777) in base ten are of the form 3n × 37. As a repunit, it also follows that 111 is a palindromic number.

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 1112 = 710. It is also prime in these other bases up to 128: 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, 99, 101, 105, 110, 111, 117, 119 (sequence A002384 in the OEIS)

In base 18, the number 111 is 73 (= 34310) which is the only base where 111 is a perfect power.

The smallest magic square using only 1 and prime numbers 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 to 36 also has a magic constant of 111:

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

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

111 is also the magic constant of the n-Queens Problem for n = 6.[2] It is also a nonagonal number.[3]

In base 10, it is a Harshad number.[4]

## Nelson

In cricket, the number 111 is sometimes called "a Nelson" after Admiral Nelson, who allegedly only had "One Eye, One Arm, One Leg" near the end of his life. This is in fact inaccurate - Nelson never lost a leg. Alternate meanings include "One Eye, One Arm, One Ambition" and "One Eye, One Arm, One Arsehole".

It is particularly known as a score in cricket. A score of 111 or multiples thereof (222 = "double nelson", 333 = "triple nelson" and so on) is considered unlucky by some in English cricket. To combat the bad luck those watching are supposed to lift their feet off the ground, famously the international umpire David Shepherd, had a whole retinue of peculiar mannerisms - hops, shuffles, jiggles and so on since an umpire cannot sit down and raise his feet - that he would indulge in if the score was ever a "Nelson" multiple. Particularly if the number of wickets also matched - 111/1, 222/2 etc.

111 is also: