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# 769

The prime 769 equals

sqrt(590593+sqrt(590593-sqrt(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 3-digit primes p, (emirp), such that p^2 is a concatenation of three double-digit primes, i.e., 591361 = 769^2. The other such prime is 823. [Loungrides]

(n*2*3*769*2^3-3)*2^(769*2^3)-1 is always divisible by a prime p between 3 and 773 for any n>0. [Cami]

(There are 4 curios for this number that have not yet been approved by an editor.)

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