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Good news for anyone working on the conjecture that there are an infinite number of primes that are two units apart (like, for example, 3 and 5 or 17 and 19). Yitang Zhang, of the University of New Hampshire, has whittled the provable difference between these primes down from infinity to 70 million, and he did it using provable methods: http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989