"Mersenne primes — named for their discoverer, 17th century French mathematician Marin Mersenne — are expressed as 2P-1, or two to the power of "P" minus one. P is itself a prime number. For the new prime, P is 43,112,609."

I think the last sentence is a mistake. If Mersenne primes are expressed as 2^P - 1, then the Mersenne prime is 2^43,112,609 - 1. as it's bigger than P.

The textual definition of everything is correct. There's just an error in the formatting of 2^p - 1.

A Mersenne prime is a prime of the form 2^n - 1 for some n. The new biggest Mersenne prime is 2^(43,112,609) - 1. An interesting coincidence is that the power itself, 43,112,609, is also prime.

The definition given by the improper formatting of numbers in the article: (2 * 43,112,609) - 1 = 86225217 = 3 * 13 * 2210903 and so is not prime.

2^n - 1 is the Mersenne prime, not the exponent, right? (Even though the exponent is always prime).

So therefore, the new prime should be 2^43,112,609 - 1, and not just 43,112,609