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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) If we use 3 instead of 2 in the formula for perfect numbers we get 3^{2}(3^{2}  1) = 72, which lies between a twin prime pair. [Gundrum] 72 is the only number of the form p^{q} * q^{p} that lies between a twin prime pair, where p and q are distinct primes. [Kulsha] The maximum difference between two consecutive fivedigit primes (31397 and 31469). [Gallardo] The smallest number that can be expressed as a sum of two primes, each ending with the digit 1, in two different ways (72 = 11 + 61 = 31 + 41). [Schlesinger] 72 is the smallest number that can be expressed as the difference of the squares of consecutive primes in two distinct ways: {19^{2}  17^{2}} and {11^{2}  7^{2}}. [King] The smallest number that can be written in two ways as the sum of a set of four distinct primes such that the sum of any three in either set is prime: {5, 11, 13, 43} and {11, 13, 19, 29}. [Honaker , Noe , Porter]
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