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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest 4digit super2 emirp. [Loungrides] The larger prime of any twin prime pair can be expressed as P + 2n^2, where P is any prime. Having checked up to 9931, all twin primes up to 10^5, they can also be expressed as P = 2n^2  Q, where P is the larger of any twin prime pair and Q is the larger of another twin prime. Can you find a counterexample to this? [Homewood]
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