181 (number) explained

Number:	181
Factorization:	prime
Prime:	42nd
Divisor:	1, 181

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

In mathematics

181 is prime, and a palindromic,^[1] strobogrammatic,^[2] and dihedral number^[3] in decimal. 181 is a Chen prime.^[4]

181 is a twin prime with 179,^[5] equal to the sum of five consecutive prime numbers:^[6] 29 + 31 + 37 + 41 + 43.

181 is the difference of two consecutive square numbers 91² – 90²,^[7] as well as the sum of two consecutive squares: 9² + 10².^[8]

As a centered polygonal number,^[9] 181 is:181 is also a centered (hexagram) star number, as in the game of Chinese checkers.

\tfrac{1}{181}

inside a prime reciprocal magic square repeat 180 digits with a magic sum

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

\tfrac{1}{19}

with a magic constant of 81 from a

18 x 18

square,^[12] a normal

19 x 19

magic square has a magic constant

M₁₉=19 x 181

;^[13] the next such full, prime reciprocal magic square is based on multiples of the reciprocal of 383 (also palindromic).^[14]

181 is an undulating number in ternary and nonary numeral systems, while in decimal it is the 28th undulating prime.^[15]

In other fields

181 is also:

181 Eucharis is a large K-type Main belt asteroid
Minuscule 181 (in the Gregory–Aland numbering), α 101 (Soden), is a Greek minuscule manuscript of the New Testament
Mir-181 microRNA precursor is a small non-coding RNA molecule
Route 181: Fragments of a Journey in Palestine-Israel, winner of the 2005 Yamagata International Documentary Film Festival

External links

Notes and References

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Web site: Sloane, N. J. A. . Neil Sloane . Centered polygonal numbers . . OEIS Foundation . 2023-11-02 .
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Book: Andrews, William Symes . Magic Squares and Cubes . . Chicago, IL . 1917 . 176, 177 . 9780486206585 . 1136401 . 1003.05500 . 0114763 .
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