Question 918753: The question asks: "The 2 digit number AB, with A not equal to 0, represents a prime if the numeration base is 8,10, or 12. Find AB." My trouble is that I'm not really sure when a number is prime in base 8 and 12. Could you at least give me some examples of primes in them?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Seems like an awkwardly-written problem, but what I'm getting from it is, if N = AB, then when N is written in base 8, those two digits form a prime number (when evaluated in base 10). For example, 59_10 = 73_8, and 73 (in base 10) is also prime. However 59 in base 12 is 5A.
Since prime checking is not the most efficient algorithm, there's not really an efficient way to do it, that I know of. One thing to note is, N_10 is prime, and it follows that the base-8 and base-12 representations of N cannot have digits summing to a multiple of 3. I wrote a small program to find the 2-digit numbers (in base 10) that work:
19 (23 in base 8, 17 in base 12)
43 (53 in base 8, 37 in base 12)
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