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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) In 1990, Balog proved there are arbitrarily large sets of primes for which the means of each pair of entries is a distinct prime. For example, {71, 1163, 1283, 2663, 4523, 5651, 9311, 13883, 13931, 14423, 25943, 27611}Granville believes there may be sets like this of infinite length!
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