### Properties of the number 2113:

2111 and 2113 form a twin prime pair.2113 has 10 antidivisors and 2112 totatives.

2113 has a prime digit sum 7 in base 10.

2113 has a semiprime digit product 6 in base 10.

2113 has a triangular digit product 6 in base 10.

2113 has an oblong digit product 6 in base 10.

2113 has sum of divisors equal to 2114 which is a sphenic number.

2113 = 32

^{2}+ 33

^{2}is the sum of at least 2 consecutive positive squares in 1 way.

2113 = 1057

^{2}- 1056

^{2}is the difference of 2 nonnegative squares in 1 way.

2113 is the difference of 2 positive pentagonal numbers in 1 way.

2113 = 32

^{2}+ 33

^{2}is the sum of 2 positive squares in 1 way.

2113 = 5

^{2}+ 18

^{2}+ 42

^{2}is the sum of 3 positive squares.

2113

^{2}= 65

^{2}+ 2112

^{2}is the sum of 2 positive squares in 1 way.

2113

^{2}is the sum of 3 positive squares.

2113 is a divisor of 439

^{6}- 1.

2113 = '2' + '113' is the concatenation of 2 prime numbers.

2113 = '21' + '13' is the concatenation of 2 Fibonacci numbers.

2113 is an emirp in (at least) the following bases: 2, 11, 19, 21, 25, 26, 29, 31, 34, 37, 40, 42, 43, 45, 49, 51, 53, 55, 56, 64, 71, 76, 81, 84, 85, 89, 95, 97, and 100.

2113 is palindromic in (at least) the following bases: 33, 44, -18, -48, -64, -66, -88, and -96.

2113 in base 14 = aad and consists of only the digits 'a' and 'd'.

2113 in base 17 = 755 and consists of only the digits '5' and '7'.

2113 in base 20 = 55d and consists of only the digits '5' and 'd'.

2113 in base 26 = 337 and consists of only the digits '3' and '7'.

2113 in base 32 = 221 and consists of only the digits '1' and '2'.

2113 in base 33 = 1v1 and consists of only the digits '1' and 'v'.

2113 in base 43 = 166 and consists of only the digits '1' and '6'.

2113 in base 44 = 141 and consists of only the digits '1' and '4'.

2113 in base 45 = 11h and consists of only the digits '1' and 'h'.

### The number 2113 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A001844: Centered square numbers: 2n(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.

A005108: Class 4+ primes (for definition see A005105).

A027862: Primes of the form n^2 + (n+1)^2.

A053001: Largest prime < n^2.

A061068: Primes which are the sum of a prime and its subscript.

A069489: Primes > 1000 in which every substring of length 3 is also prime.

A090707: Primes whose decimal representation is a valid number in base 4 and interpreted as such is again a prime.

A107008: Primes of the form x^2+24*y^2.

A211684: Numbers > 1000 such that all the substrings of length = 3 are primes (substrings with leading '0' are considered to be nonprime).

A211685: Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime).

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