

Sexy primes - beerglass
http://en.wikipedia.org/wiki/Sexy_prime

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jgrahamc
It's fairly easy to see that the only sexy prime quintuple will be the one
that contains 5 (see last part of the Wikipedia page) by imagining the number
line as follows.

Now line up multiples of 5 and see if it's possible to fit them around these
primes. There's always one multiple of 5 that lines up with a prime in the
quintuple and hence one prime must be divisible by 5 and the only prime number
divisible by 5 is 5.

    
    
      p.....p.....p.....p.....p
            +     +     +     +
            6     1     1     2
                  2     8     4
    
      5....5....5....5....5....5
      .5....5....5....5....5....
      ..5....5....5....5....5...
      ...5....5....5....5....5..
      ....5....5....5....5....5.
    

Another way to think of that is as follows. Suppose that p is not divisible by
5 then one of p+1, p+2, p+3, p+4 must be. But p+6 = p+1+5, p+12=p+2+10,
p+18=p+3+15, p+24=p+4+20, so whichever one it is there's a prime that's also
divisible by 5. Similar reasoning works from the other numbers.

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baby
I would do this : (I use "=" as "congruous to")

if p = 1 [5]:

    
    
      p + 6x4 = 1 + 6x4 = 25 = 0 [5]
    

if p = 2 [5]:

    
    
      p + 6x3 = 2 + 6x3 = 20 = 0 [5]
    

and so on...

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hopeless
Of course, everyone knows the sexy primes are the 35/1.4, 50/1.4, 85/1.4 and
135/2.8

Sorry but photographic prime lenses beat mathematical prime numbers!

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beerglass
Good one! <http://en.wikipedia.org/wiki/Prime_lens> for those interested in
what @hopeless in talking about

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dmvaldman
I propose primes that differ by 12 be called sexy twin cousin primes

