David Slowinski

A short mathematical monograph about Mersenne primes-numbers of the form 2^p ? 1-and the long-running effort to identify which of them are truly prime. Centered on the "32nd Mersenne prime" that falls within the set of exponents originally claimed by the 17th-century scholar Marin Mersenne, it recounts the historical context of Mersenne's prediction and outlines the reasoning and computations used to confirm primality, offering a concise snapshot of how conjecture, theory, and extensive calculation meet in the search for record-breaking primes.