Prime Curios!: 2113

2113
(another Prime Pages' Curiosity)

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2113 = 1^5 + 2^5 + 2^5 + 4^5 + 4^5 = (2^5)^2 + (2^5 + 1)^2.

2113 is the largest prime factor of 2^22+1.

2113 + sigma(2113) + sigma(sigma(2113)) = 1+2+3+...+125 = (5^(3*2) + 5^3)/2.

2113 is the 41st prime p, for which p^2 - p + 1 is also prime: 2113^2 - 2113 + 1 = 4462657 which is prime, note that 41 is also prime.

2113 is the smallest 4 digit prime and the 7th prime of the form pi(p)+p: 1831 is prime, and 2113 =

(1831) + 1831.

2113, when written in base 5/2, is prime: 2*(5/2)^3 + 1*(5/2)^2 + 1*(5/2) + 3 = 43 is prime; There are 2113 different ways (permutations) of achieving the score of 24 under American football rules.

2113 is the 43rd prime of the form

(

(p)), where p-2 and p are twin primes: 205661 and 205663 are twin primes, and 2113 =

(

(205663)).

The sum of the 35 primes <= 2113 == the sum of the 31 primes > 2113: 1867+1871+...+2111+2113 = 2129+2131+...+2351+2357.

2113 is the smallest prime with an equal number of even and odd prime digits that is also the reverse concatenation of two consecutive Fibonacci numbers: 2113 has 1 even prime digit, 1 odd prime digit, and is the reverse concatenation of two consecutive Fibonacci numbers: 21 and 13. [Noll]

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