4 ms·

Sexy primes

• hopeless 14y ago
  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!
  • ibotty 14y ago
    while i definitely prefer sexy prime numbers to sexy prime lenses. your comment is on top! a shame it got downvoted.
  • beerglass 14y ago
    Good one! http://en.wikipedia.org/wiki/Prime_lens http://en.wikipedia.org/wiki/Prime_lens for those interested in what @hopeless in talking about
• dmvaldman 14y ago
  I propose primes that differ by 12 be called sexy twin cousin primes
• deleted 14y ago
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• jgrahamc 14y ago
  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.
  • baby 14y ago
    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...
• deleted 14y ago
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