3 May 2013

Prize Maths Quiz: Constructing a Set of Primes (PMQ17)

Thanks to http://alphapixel.com/content/prime-number-diagrams-python-and-svg
The Question

Using each of the non-zero digits only once, it is possible to construct a set of only prime numbers. The set {3, 41, 659, 827} is one possibility, with the sum of its members being equal to 1530.

What is the smallest possible sum that such a set of primes can have? Find one such set.

Just remember that the digits 1 to 9 inclusive must all be used but only once. Also note that you should not need to consult any tables of primes for the above question. However, such a list may well be useful for the extension exercises below.

Extension Exercises

If we restrict our required sets to those with just three 3-digit primes, find the two sets with the minimum and maximum possible sums. Again, use just the non-zero digits once each.

You may discuss the question below, but no full answers, please, until the competition has closed!

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How to Enter

Send your complete solution by email to pmq17cardano@giftedmaths.comThis email address shall be removed after the competition closes to avoid spam. This PMQ17 competition closes on MONDAY 6 May at 23:59 GMT - one extra weekday from now on.

The Prize

The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
Use the official server clock in the right column to avoid late entries.
All emails and email addresses sent to us will be deleted after the winners have been processed.
DO NOT submit your entries to the comments section at the bottom of this post.
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Enjoy the challenge!
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