That specific format -- two to the power of n minus one -- is what’s called a Mersenne prime.
这种特定格式——二的 n 次方减一——就是所谓的梅森素数。
英语百科
Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number that can be written in the form Mn = 2 − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. The first four Mersenne primes (sequence A000668 in OEIS) are 3, 7, 31, and 127.