131071

This number is a prime.

+ 131071 is the largest known prime of form 2^(2^k+1)-1, where k = 4. [Luhn]

+ The concatenation of first four happy numbers in reverse order is prime. [Gupta]

+ Pietro Cataldi verified that 131071 is a Mersenne prime in the year 1588. Did the defeat of the Spanish Armada have something to do with it?

+ The largest nth Mersenne prime with n digits. [Beedassy]

+ 131071 is the 35th Fibonacci 17-step number, the first odd prime of this type. Note that 2^17-1 = 131071, making it the 6th Mersenne prime. [Loungrides]

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