# 647

The smallest prime that may be written as 2*a*^{2} - 1, and also as 3*b*^{3} - 1. [Hartley]

A man described as looking like a plump Moses asked the following questions during a 1987 joint American Mathematical Society/Mathematical Association of America conference in San Antonio, Texas: "What about 647? Is it prime?" (from *The Man Who Loved Only Numbers* by Paul Hoffman)

647 equals the sum of all two-digit even semiprimes plus one. [Silva]

The largest prime whose digits form an acute-angle scalene triangle with prime perimeter. [Loungrides]

The largest 3-digit number n such that 3^n-2^n is prime, 3^647-2^647. [Loungrides]

The only prime of form p^(p+1)+q^(q+1)-1, where p, q are consecutive primes, i.e., 2^3*3^4-1. [Loungrides]

647 must be a common number to use as a big number in cartoons! In the SpongeBob SquarePants episode "Mermaid Man vs. SpongeBob", SpongeBob says that he has not seen Mermaid Man do the Spine Blaster since Episode 647. In the Scooby-Doo episode "Night of the Living Burger", Velma says that this is the 647th time that Freddie was wrong about Red Herring. 647 is a prime number. [Jacobs]