According to [Encyclopaedia Britannica][1],
"Greek mathematician Euclid (flourished c. 300 bce) gave the oldest known proof that there exist an infinite number of primes, and he conjectured that there are an infinite number of twin primes,"
which makes the twin prime conjecture remarkably old.

  [1]: http://www.britannica.com/EBchecked/topic/1556762/twin-prime-conjecture