“A prime number is one (which is) measured by a unit alone.”

— Euclid, book Elements

Elements, Book 7, Definition 11 (12 in certain editions)
Euclid’s Elements

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Euclid6

Greek mathematician, inventor of axiomatic geometry -323–-285 BC

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“I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.”

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“Which of us has, at this day, the ability to discover those true and vivific numbers whereby the elements are united and bound to one another?”

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“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.”

Pierre de Fermat (1601–1665) French mathematician and lawyer

Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je n'appréhendois d'être trop long.
Fermat (in a letter dated October 18, 1640 to his friend and confidant Frénicle de Bessy) commenting on his statement that p divides a<sup> p−1</sup> − 1 whenever p is prime and a is coprime to p (this is what is now known as Fermat's little theorem).

“A man is rich in proportion to the number of things which he can afford to let alone.”

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Variant: A man is rich in proportion to the number of things he can afford to let alone.
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“God may not play dice with the universe, but something strange is going on with the prime numbers.”

Paul Erdős (1913–1996) Hungarian mathematician and freelancer

Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter http://empslocal.ex.ac.uk/people/staff/mrwatkin//kac-pomerance.txt, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes." <br class="br">Misattributed

“A prime number is one (which is) measured by a unit alone.”

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