document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #557242 by richard1234(7193) $\"\"$ $\"About$

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.\r
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\n" ); document.write( "\n" ); document.write( "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:\r
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\n" ); document.write( "\n" ); document.write( "19 (23 in base 8, 17 in base 12)
\n" ); document.write( "43 (53 in base 8, 37 in base 12) \n" ); document.write( "

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