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: 181 is also a centered (
hexagram)
star number, and
16th full reptend prime in
decimal, where multiples of its
reciprocal \tfrac {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 \tfrac {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). 181 is an
undulating number in
ternary and
nonary numeral systems, while in
decimal it is the
28th undulating prime. ==References==