# 2207

This number is a prime.

The largest known prime Lucas number to have a composite index. [Dobb]

Largest known prime of the sequence a(0) = 3; thereafter, a(n) = a(n-1)^2 - 2. We start with the prime 3. Then 3^2-2 = 7 is prime. Next 7^2-2 = 47 is prime. Finally, 47^2-2 = 2207 is prime. [Post]

The largest number in a Collatz trajectory is 250504 for 2207 different numbers. [Gaydos]

If you type 2, 2, 0, 7, √, √, √, √ (i.e., repeat the square root of 2207 four times) on a calculator you'll get a good approximation of the golden ratio (phi). [Petrov]

(There are 2 curios for this number that have not yet been approved by an editor.)

Printed from the PrimePages <primes.utm.edu> © G. L. Honaker and Chris K. Caldwell