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Twins I (Posted on 2013-01-20) Difficulty: 3 of 5

Let N, a number greater than 5, be the smaller member of a twin prime pair (e.g. {11,13} {17,19} etc.)

It is easily shown that if m=6 then N mod(m) = 5 - though, of course, 5 is itself the smaller member of a twin prime pair.

More interestingly:
(a) for what other values of m is every possible value of N mod(m) also the smaller member of a twin prime pair?
(b) Explain the phenomenon.

No Solution Yet Submitted by broll    
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Hints/Tips Examples Comment 1 of 1

One example is m=12, when every prime pair, the smaller member of which is 11 or more, is worth either 5 or 11, mod 12.

Another is 18, where every such prime pair is worth 5, 11, or 17, mod 18.

Then there is ...?

And the reason is ...?

  Posted by broll on 2013-01-22 07:41:59
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