• Deleting all the even digits from 2²⁰⁹ we obtain a prime of 30 digits.

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209 has 4 divisors (see below), whose sum is σ = 240. Its totient is φ = 180.

The previous prime is 199. The next prime is 211. The reversal of 209 is 902.

209 is nontrivially palindromic in base 6, base 9 and base 13.

209 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

209 is an esthetic number in base 6, base 8 and base 15, because in such bases its adjacent digits differ by 1.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4, and also a brilliant number, because the two primes have the same length.

It is a cyclic number.

It is not a de Polignac number, because 209 - 2⁴ = 193 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (11), and also a Moran number because the ratio is a prime number: 19 = 209 / (2 + 0 + 9).

It is a magnanimous number.

It is an Ulam number.

It is a d-powerful number, because it can be written as 2⁷ + 0 + 9² .

It is a Duffinian number.

209 is an undulating number in base 6, base 9 and base 13.

209 is a modest number, since divided by 9 gives 2 as remainder.

It is the 19-th Perrin number.

It is a Curzon number.

It is a plaindrome in base 12 and base 15.

It is a nialpdrome in base 8 and base 16.

It is a self number, because there is not a number n which added to its sum of digits gives 209.

It is not an unprimeable number, because it can be changed into a prime (229) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2 + ... + 20.

It is an arithmetic number, because the mean of its divisors is an integer number (60).

It is a Proth number, since it is equal to 13 ⋅ 2⁴ + 1 and 13 < 2⁴.

It is an amenable number.

209 is a deficient number, since it is larger than the sum of its proper divisors (31).

209 is a wasteful number, since it uses less digits than its factorization.

209 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30.

The product of its (nonzero) digits is 18, while the sum is 11.

The square root of 209 is about 14.4568322948. The cubic root of 209 is about 5.9344721404.

Subtracting from 209 its product of nonzero digits (18), we obtain a palindrome (191).

Adding to 209 its reverse (902), we get a palindrome (1111).

The spelling of 209 in words is "two hundred nine", and thus it is an aban number.