118 (number)

118 ( one hundred and eighteen ) is a natural number located between the numbers 117 and 119 .

In Math

118 is an even three-digit number.
The number 118 is a semisimple number ^[1] .
118 is the smallest of the numbers, which can be written in four ways as the sum of three different numbers, which, when multiplied by each other, produce the same result: $118=14+50+54=15+40+63=18+30+70=21+25+72$ ${\ displaystyle 118 = 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72}$ ; the multiplied numbers from each triple are equal to 37,800 ^[2] ^[3] .
Also, 118 is the smallest three-digit compound number for which all numbers resulting from the permutation of numbers ( 181 and 811 ) are simple ^[3] .
118 is the sum of the cubes of three positive numbers: $118=3^{3}+3^{3}+4^{3}$ ${\ displaystyle 118 = 3 ^ {3} + 3 ^ {3} + 4 ^ {3}}$ ^[3] ^[4] .
The number 118 is a 21-coal and centered 39-coal number ^[5] .
If a natural number $N\geqslant 118$ ${\ displaystyle N \ geqslant 118}$ then the interval $[N,4N/3]$ ${\ displaystyle [N, 4N / 3]}$ contains a prime number in each of the forms: $4n+1$ ${\ displaystyle 4n + 1}$ , $4m-1$ ${\ displaystyle 4m-1}$ , $6k+1$ ${\ displaystyle 6k + 1}$ and $6j-1$ ${\ displaystyle 6j-1}$ where $n,m,k,j\in \mathbb {N}$ ${\ displaystyle n, m, k, j \ in \ mathbb {N}}$ ^[2] .

↑ sequence A001358 in OEIS .
↑ ¹ ² David Wells. 118 // The Penguin Dictionary of Curious and Interesting Numbers (English) . - 1st ed. - Penguin Books , 1987. - p. 119-120. - 229 s. - ISBN 0-14-008029-5 .
↑ ¹ ² ³ 118 in MAA NumberADay
↑ sequence A003072 in OEIS .
↑ The Number 118 .