181 (number)

Template:Infobox number 181 (one hundred [and] eighty-one) is the natural number following 180 and preceding 182.

In mathematics

181 is prime, and a palindromic, strobogrammatic, and dihedral number in decimal. 181 is a Chen prime.

181 is a twin prime with 179, equal to the sum of five consecutive prime numbers: 29 + 31 + 37 + 41 + 43.

181 is the difference of two consecutive square numbers 91² – 90², as well as the sum of two consecutive squares: 9² + 10².

As a centered polygonal number, 181 is: Template:Bulletlist 181 is also a centered (hexagram) star number, as in the game of Chinese checkers.

Specifically, 181 is the 42nd prime number and 16th full reptend prime in decimal, where multiples of its reciprocal $\frac{1}{181}$ inside a prime reciprocal magic square repeat 180 digits with a magic sum $M$ of 810; this value is one less than 811, the 141st prime number and 49th full reptend prime (or equivalently long prime) in decimal whose reciprocal repeats 810 digits. While the first full non-normal prime reciprocal magic square is based on $\frac{1}{19}$ with a magic constant of 81 from a $18\times 18$ square, a normal $19\times 19$ magic square has a magic constant $M_{19}=19\times 181$; the next such full, prime reciprocal magic square is based on multiples of the reciprocal of 383 (also palindromic).Template:Efn

181 is an undulating number in ternary and nonary numeral systems, while in decimal it is the 28th undulating prime.

External links

• Prime curiosities: 181
• Number Facts and Trivia: 181
• Number Gossip: 181

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