647

This number is a prime.

The smallest prime that may be written as 2a² - 1, and also as 3b³ - 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]

Argam names are only available for 647-smooth numbers (i.e., no prime factors exceed 647), unless you wish to use any of the extended variants. Argam (AHR-gam, also spelt as arqam, singular form: ragam/raqam) is a numeral set invented and developed by entrepreneur and coder Michael De Vlieger to express numbers written in large number bases. [Leonardis]

π(647)=118. Note that 647 occurs at position 118 of π. See PC777643. [Sariyar]