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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]
(There are 6 curios for this number that have not yet been approved by an editor.)
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