Prime number

A prime number is one (which is) measured by a unit alone.Πρῶτος ἀριθμός ἐστιν ὁ μονάδι μόνῃ μετρούμενος.

— Prime number

...The difference of two square numbers is always a product, and divisible both by the sum and by the difference of the roots of those two squares; consequently the difference of two squares can never be a prime number.

— Prime number

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 will never penetrate.

— Prime number

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. … Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

— Prime number

Although I firmly believe that there is no such thing as a stupid question, there can indeed be stupid answers. 42 is an example. Not only is this a poor ripoff of Doug Adams' Hitchhiker's Guide, but it isn't even a prime number. Everyone surely knows that numerical answers to profound questions are always prime. (The correct answer is 37.)

— Prime number

We don't naturally have some magic formula to try and find these prime numbers. In fact trying to find where the next prime number is represents one of the biggest mysteries in the whole of mathemaics. ...The challenge if the primes is somehow of the ultimate puzzle in the whole of mathematics.

— Prime number

The Elements contains thirteen books by Euclid, and two, of which it is supposed that Hypsicles and Damascius are the authors. ...The seventh, eighth, ninth books are on the theory of numbers, or on arithmetic. In the ninth book is found the proof to the theorem that the number of primes is infinite.

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, 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.

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Gauss liked to call [number theory] 'the Queen of Mathematics'. For Gauss, the jewels in the crown were the primes, numbers which had fascinated and teased generations of mathematicians.

— Prime number

Armed with his prime number tables, Gauss began his quest. As he looked at the proportion of numbers that were prime, he found that when he counted higher and higher a pattern started to emerge. Despite the randomness of these numbers, a stunning regularity seemed to be looming out of the mist.

— Prime number