Number of the day: 2113

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 = 32² + 33² is the sum of at least 2 consecutive positive squares in 1 way.
2113 = 1057² - 1056² is the difference of 2 nonnegative squares in 1 way.
2113 is the difference of 2 positive pentagonal numbers in 1 way.
2113 = 32² + 33² is the sum of 2 positive squares in 1 way.
2113 = 5² + 18² + 42² is the sum of 3 positive squares.
2113² = 65² + 2112² is the sum of 2 positive squares in 1 way.
2113² is the sum of 3 positive squares.
2113 is a divisor of 439⁶ - 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).