It has been conjectured that there exist an infinite number of Mersenne primes. Fitting a line through the origin to the asymptotic number of Mersenne primes with for the first 49 (known) Mersenne primes gives a best-fit line with , illustrated above. If the line is not restricted to pass through the origin, the best fit is . It has been conjectured (without any particularly strong evidence) that the constant is given by , where is the Euler-Mascheroni constant (Havil 2003, p. 116; Caldwell), a result related to Wagstaff's conjecture
As the title suggest, the exhibit theme wrests on the notoriety of Venice as a center of romantic liaisons, seductions and scandals, the likes of Casanova and the many courtesans that frequented the city. Yet, Venice was much more than that. It was a cauldron of intellectual activity, of industry, literature, and music. It was a society that for many years ensured the peace, prosperity and freedom of its people. And it was also a very pious city, one steeped in Roman Catholicism where many churches were built by its richest and most influential citizens.