## $2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$.

What is the sum of the digits of the number $2^{1000}$?

### This is a non-trivial problem and requires a bit of programming as it’s quite complicated to compute manually.

The problem is essentially asking you to find the sum of the digits of the number 2^1000.

In Python, you can implement the following steps:

1. Calculate the number 2^1000.

2. Convert that number to a string for easy manipulation.

3. Use a for loop to traverse through each digit in the string number and convert it back to an integer.

4. Add all the integers together.

Here is Python code that would provide an answer:

“`python

number = 2**1000

str_num = str(number)

sum_of_digits = sum(int(digit) for digit in str_num)

print(sum_of_digits)

“`

Running this code would give the result of 1366. Thus, the sum of the digits of the number 2^1000 equals 1366.

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