Three Primes
Find three different two-digit prime numbers where the average of any two is a prime , and the average of all three is a prime.
Labels: mathemagic, SharedPuzzle
posted by Zaux at
2:50 PM
Tuesday, January 5, 2010
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19 Comments:
You cant.
The only pair of numbers that will have an average as a prime number is 3 and 7 being 5.
Are Gaussian primes allowed? (Not that I've checked if that'll do it).
I guess that the question was meant to be for 3 integers, not 3 primes. I'll have a go on that basis.
au contraire ... there is
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Chris ... there are 25 primes between 1 and 100 ... 3 meet the criteria stated
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Hi Zaux,thanks for confirming that the question is correct so quickly. I believe you are right.
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Hi Zaux. I see I wasn't quick enough deleting my post. I decided the sentence was non-sensical.
I've made a good start on the problem. I should be posting an analytical solution soon.
Hi Zaux, I thought I'd cracked it, but made a silly, but cataclysmic error. As I've got less than 4 hours kip time available before getting up for a course, I have to stop.
Good problem though. Thank you.
Answer: 5, 17, 29.
5-17avg.=11
17-29avg.=23
Good job anonymous ... was not aware that 5-17-29 worked.
11-47-71 also works
Hi Zaux,
I think you gave away the answer too quickly.
5-17-29 does not qualify as 5 is not a two-digit prime.
Hi Wiz ... you're right .. I did give it away too quickly ... was in wee hours of the morning when I read the post.. and was too quickly convinced. Thanks!
Rant mode on: I'm disappointed that no-one (including self) came up with a nice logical exposee. Who cares what the triplets are? (No doubt it'll turn out to explain the big-bang because I said that). Using computers or plain grunt is a cop-out. I accept that writing a programmatic solution is interesting, but it's not what I consider a proper answer - this site is Trick of Mind, not Komputer Kiddies Korner (OK I made that up). If you must program, then why not publish the program you made? That would be a vast improvement on just a bunch of numbers.
I accept that some problems will need computer assistance, but it's usually obvious when that is the case, so those problems are fair game. But I don't tend to like that sot of problem much anyway.
Rant mode off.
Good problem Zaux.
Cam, you've restored my faith, thank you. I'll certainly look through your solution.
I goofed mine so badly that, after having spent too long on a flawed argument, I decided to have a bash at the "Odd Streak of Heads" problem (posted 5/01/2010). I've just posted my "solution" there.
Hi Cam, I just started reading your solution. I can't believe that I didn't use modulo arithmetic when I tried to solve it. I feel really silly now.
Hi Cam. I think you did a pretty fine job of that. Thanks for publishing your reasoning. I felt a bit mean writing my rant. I'm sure that you appreciate the method far more than the result.
Hi Cam. Of course I'm aware of the enormous value of using computers to solve problems. In some cases it's the only practical way to do it. But it sems obvious to me (and I'm sure to you) that the method is the real thing that's been sought, not simply some, ususually uninteresting, number.
If no-one posted their reasoning, I'd stop coming here. But, of course I appreciate the humour etc.
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