46th mersenne prime number

has 13-million digits, the article says.
Does it?
The "46th" mersenne prime number is (2**43,112,609)-1

1 + log base 10 of a number is the number of digits in a number:
log base 10 of 10 is 1; of 100 is 2; of 1000 is 3.

log base 10 of 2 is 0.301029996, from google

(2 ** 43,112,609) = (10 ** .301029996 ** 43,112,609)

(.30103 * 43,112,609) = (12,978,188)

12,978,189 digits is less than 13 million.

The approximation of 2**10 = 1,000
is useful for estimating powers of 2.

For example, (2**60) = (2**10**6) = (1,000**6)
1,000**6 is six commas or a quintillion.

Applying that approximation to this question,
2**43,112,609 has 4,311,260 commas or 12,933,782 digits