# First Digit

How many integer powers of 2 less than 2^1337 have a first digit of 4?

Note: first digit means the leading digit, not the units digit. So 2^6 = 64 has a first digit of 6, not 4.

I'll tell you this ahead of time:

2^1337 = 2999882211...4204009472 and has 403 digits.

#### Attempt Info

- Correct Attempts: 16
- Incorrect Attempts: 31
- Ungraded Attempts: 0
- Total Attempts: 47