The number two (2) is the second positive integer and the first prime number. It is even, and is the only even prime (the primes other than 2 are called the odd primes). The number 2 is also equal to its factorial since . A quantity taken to the power 2 is said to be squared. The number of times k a given binary number is divisible by 2 is given by the position of the first , counting from the right. For example, 12 = 1100 is divisible by 2 twice, and 13 = 1101 is divisible by 2 zero times.

The only known solutions to the congruence

are n = 4700063497 (Guy 1994), 8365386194032363 (J. Crump 2000), and

(P.-L. Montgomery 1999; Sloane's A050259). In general, the least n satisfying

for k = 2, 3, ... are n = 3, 4700063497, 6, 19147, 10669, 25, 9, 2228071, ... (Sloane's A036236).

 

1, Binary, 3, Ruler Function, Squared, Two-Ears Theorem, Two-Form, Two-Graph, Two-Scale Expansion, Two-Sheeted Hyperboloid, Zero