"A prime number is one (which is) measured by a unit alone. Πρῶτος ἀριθμός ἐστιν ὁ μονάδι μόνῃ μετρούμενος."
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are
", eleven years younger than Archimedes, was a native of Cyrene. He... measured the obliquity of the ecliptic and invented a device for finding prime numbers. ...In his old age he lost his eyesight, and on that account is said to have committed suicide by voluntary starvation."
"The primes are the atoms of arithmetic, the indivisible building blocks from which all other numbers are constructed. In their chaotic distribution lies a profound order, a secret language waiting to be deciphered. To study them is to chase the fundamental rhythm of mathematics itself."
"Leonhard Euler stated that 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 human mind would never penetrate."
"There is another lesser-known "quote" of Erdos that I know first-hand he did not say, since I made it up! ... I gave a talk about Erdos and number theory, and I tried to explain how marvelous the Erdos--Kac theorem is... [Overhead Slide] Einstein: "God does not play dice with the universe." I then said orally: "I would like to think that Erdos and Kac replied..." [Overhead Slide] Erdos and Kac: Maybe so, but something is going on with the primes. ...Somehow, the San Diego newspaper picked this up the next day, and attributed it as a real quote of Erdos."
"And this proposition is generally true for all progressions and for all prime numbers; the proof of which I would send to you, if I were not afraid to be too long. Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je nappréhendois dêtre trop long."
"In the spring of 1997, Connes went to Princeton to explain his new ideas to the big guns: Bombieri, Selberg and Sarnak. Princeton was still the undisputed Mecca of the Riemann Hypothesis... Selberg had become godfather to the problem... a man who had spent half a century doing battle with the primes. Sarnak... [had] recently joined forces with ... one of the undisputed masters of the mathematics developed by Weil and Grothendieck. Together they had proved that the strange statistics of random drums that we believe describe the zeros in Riemanns landscape are definitely present in the landscapes considered by Weil and Grothendieck. ...It was Katz who, some years before, had found the mistake in Wiless first erroneous proof of Fermats Last Theorem. And finally there was Bombieri... the undisputed master of the Riemann Hypothesis. He had earned his for the most significant result to date about the error between the true number of primes and Gausss guess - a proof of... the Riemann Hypothesis on average. ...Bombieri, like Katz, has a fine eye for detail."