Prime Number PuzzleDate: 09/27/2001 at 20:56:08 From: Pat Subject: Prime number word problem I am the product of four primes, and the sum of these numbers is thirty. My three digits are prime and differant. Who am I? I couldn't come up with any combination without using one (1,5,11,13 for 715) How do I do this? Can I use a prime number twice in my set, like 2,2,3,3,7,13 because I am using only four primes even though I am using them more then once? Date: 09/28/2001 at 14:12:39 From: Doctor Ian Subject: Re: Prime number word problem Hi Pat, The main thing here is to proceed systematically. For example, you know that you're looking for a 3-digit number, with distinct prime digits. How many of those are there? Not very many. The digits have to be 2, 3, 5, or 7, and they can't repeat, so you need to find all the permutations of the 3-element subsets of this set: 2-- => 23- => 235 237 25 => 253 257 27- => 273 275 3-- => 32- 35- 37- 5-- => 52- 53- 57- 7-- => 72- 73- 75- I'll leave it for you to fill in the rest of the table. The number of possibilities is 4*3*2 = 24, which isn't too awful. Once you have the 24 numbers, you can break them into prime factors. Keep the ones that have four prime factors; and of those, keep the ones whose factors add up to 30. Maybe there will be only one of those, maybe not. By the way, note that 1 is _not_ a prime number, so it won't appear as a digit in the number, or as one of the prime factors. In case you don't feel like working out the prime factorization of 24 different 3-digit numbers, you can look them up here: Prime Factorization - Cenius.net http://www.cenius.fsnet.co.uk/refer/maths/articles/p/primefactorization1000_ref.html I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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