On Numbers: On Prime Numbers (Unsourced)

"A prime number, which exceeds a multiple of four by unity, is only once the hypotenuse of a right triangle." (Pierre de Fermat)

"God may not play dice with the universe, but something strange is going on with the prime numbers." (Paul Erdős)

"If [the Riemann Hypothesis is] not true, then the world is a very different place. The whole structure of integers and prime numbers would be very different to what we could imagine. In a way, it would be more interesting if it were false, but it would be a disaster because we've built so much round assuming its truth." (P  Sarnak)

"[...] in one of those unexpected connections that make theoretical physics so delightful, the quantum chorology of spectra turns out to be deeply connected to the arithmetic of prime numbers, through the celebrated zeros of the  Riemann zeta function: the zeros mimic quantum energy levels of a classically chaotic system. The connection is not only deep but also tantalizing, since its basis is still obscure - though it has been fruitful for both mathematics and physics." (Michael V Berry)

"[Looking at the distribution of the primes is like the] the feeling of being in the presence of one of the inexplicable secrets of creation." (Don Zagier) 

"Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate." (Leonhard Euler)

"Observation more than books and experience more than persons, are the prime educators." (Amos B Alcott)

"Prime numbers are the most basic objects in mathematics. They also are among the most mysterious, for after centuries of study, the structure of the set of prime numbers is still not well understood […]" (Andrew Granville) 

"The consequences [of the Riemann Hypothesis] are fantastic: the distribution of primes, these elementary objects of arithmetic. And to have tools to study the distribution of these of objects." (H Iwaniec)

"We found a beautiful and most general proposition, namely, that every integer is either a square, or the sum of two, three or at most four squares. This theorem depends on some of the most recondite mysteries of numbers, and it is not possible to present its proof on the margin of this page." (Pierre de Fermat)