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  1. Many of you might not know who Terrence Tao is, but suffice it to say he's *smart as hell*. A mathematician and Fields Medal winner, Tao's primary love (forgive the pun) is prime numbers. And yet, he makes a pretty blatant boo-boo in this clip on The Colbert Report - see if you can spot it: Here's a question for mathemeticians: 13 is number that can be paired with a sexy prime on either side of it (19 and 7) - is this a special genre of sexy prime? Does it have a name? Actually, now that I think about it, you have 5, 11, 17, 23, and 29, making five consecutive numbers that are sexy primes: Has this been proven to be the greatest number of consecutive sexy primes, or does it remain unproven? Or, does nobody give a shit? ETA: Actually, I know for a fact that {5, 11, 17, 23, 29} is the largest possible sequence of sexy primes. It would be impossible to come up with a sequence of 6, and there aren't any other sequences of 5. I can explain it more easily than I can prove it: Any other number ending in 5 is not prime (obviously, since it would be divisible by 5). Therefore, the sequence must start with a number ending in 1. So, the numbers would be X1, X7, X3, X9, and ... you're back to a number ending in 5 again at the 5th number in the sequence, so this is the *only* occurrence of 5 consecutive sexy primes there is. How's that! Did I just win a Fields Medal? What this does, is make 17 a unique number, in that it has *2* sexy primes on either side of it - out of every number in the universe, this is the only number with this property. That's a big deal. I think.
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