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 
a given binary number 
is divisible by 2 is given by the position of
the first 
, counting from the right. For example,
is divisible by 2 twice, and 
is divisible by 2 zero times.
The only known solutions to the congruence
 |
are summarized in the following table (OEIS A050259). M. Alekseyev explored all solutions below 
on Jan. 27 2007, finding no other solutions in
this range.
 | reference |
| 4700063497 | Guy (1994) |
| 3468371109448915 | M. Alekseyev (pers. comm., Nov. 13, 2006) |
| 8365386194032363 | Crump (pers. comm., 2000) |
| 10991007971508067 | Crump (2007) |
| 63130707451134435989380140059866138830623361447484274774099906755 | Montgomery (1999) |
In general, the least 
satisfying
 |
for 
, 3, ... are 
, 4700063497, 6, 19147, 10669, 25, 9, 2228071, ... (OEIS
A036236).
The chorus of the song "Power of Two" by the Indigo Girls (Swamp Ophelia, 1994), includes the lines "Adding up the total of a love that's true; Multiply life by the power of two."
