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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The prime 769 equals sqrt(590593+sqrt(590593sqrt(590593+sqrt(590593...)))).Note 590593 is a prime. [Caldwell] prime(769) = prime(7)*prime(6)*prime(9) + phi(769). The prime 769 is the only known number (up to 2*10^9) with this property. [Firoozbakht] The smaller of only two 3digit primes p, (emirp), such that p^2 is a concatenation of three doubledigit primes, i.e., 591361 = 769^2. The other such prime is 823. [Loungrides] (n*2*3*769*2^33)*2^(769*2^3)1 is always divisible by a prime p between 3 and 773 for any n>0. [Cami]
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