Euclid — "A prime number is that which is measured by a unit alone."
A prime number is that which is measured by a unit alone.
Get This Quote & Author's Image Illustrated On:
Click any product to generate a realistic preview. Up to 3 at a time.
* Initial load can take up to 90 seconds — revising the preview in another color is nearly instant.
Kitchen
Apparel
Other
More from Euclid
"A semicircle is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle."
"Give him threepence, since he must make a gain out of what he learns."
"A surface is that which has length and breadth only."
"A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another."
"If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be e…"
Verification
Unverifiable
Found in 1 providers: grok
1 source checked
Understanding this quote
What it means
A prime number can only be divided evenly by 1 and itself — no other whole number divides it cleanly. Numbers like 2, 3, 5, and 7 qualify; 4 does not because 2 also divides it. This captures mathematical irreducibility: a number that cannot be broken into smaller whole-number factors. It is the foundational definition underpinning all of modern number theory and cryptography.
Relevance to Euclid
Euclid's Elements (~300 BCE) systematized all known Greek mathematics into an axiomatic framework built from definitions. This definition opens Book VII, launching his number theory treatment. He later proved infinitely many primes exist — one of history's most elegant proofs. His insistence on precise, minimal definitions before any proof reflects his rigorous character: nothing assumed, everything grounded, building complex truths from simple, unambiguous starting points.
The era
Around 300 BCE, Alexandria had become the intellectual capital of the Mediterranean under Ptolemaic patronage, with the great Library drawing scholars from across the Greek world. Greek mathematics was transitioning from practical measurement to abstract proof. Without algebra or Hindu-Arabic numerals, numbers were conceived geometrically, making precise verbal definitions essential tools — without them, rigorous proof was impossible and knowledge remained merely observational.
AI-generated insights based on extensive research and information for context. Factual errors? Email [email protected].