… as a base-three number. 2012 in base 3 is 59 in base 10.
2012 is also prime as a base-five number.
Update: Here’s some Mathematica code to find other bases where 2012 is prime.
f[n_] := 2 n^3 + n + 2 For[n = 3, n < 100, n++, If[PrimeQ[f[n]], Print[n]]]
Related posts:
Odd numbers in odd bases
Prime words
Prime telephone numbers
Sonnet primes
And also in base 25, I believe (2012b25 == 31277)
And base 13.
Only, you, John! I have enjoyed the style and content of your blog like no other. Please keep it coming!
Heh… heh… heh… Base 13 is the same base where Douglas Adams’ notorious “What is six times nine” actually *is* 42.
Fun! Here it is in functional style,
Select[Range[3, 100], PrimeQ[2 #^3 + # + 2] &]
Hmm.. a little off-topic, but I wonder if any famous physical or mathematical constants look “nicer” in other base-representations?
A shock! then surprise!!!