Infinitude of Primes (The Inexhaustible Supply)

Number Theory Fundamentals · 7:59

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Lyrics

[Verse 1]
Let me tell you 'bout a quest that ancient minds would chase
To count all prime numbers, find the final place
Two, three, five, seven, eleven in a row
But does this sequence end? We need to know

[Chorus]
The primes keep flowing like an endless spring
No cap can hold them, they're an infinite thing
Multiply them all and add just one
A new prime's born, the proof is done
Infinite primes, they never cease
Euclid's wisdom brings us peace

[Verse 2]
Suppose you think you've found them all inside a box
Two, three, five, seven - that's your finite stock
Now multiply these numbers, every single one
Then add a one to what you've done

[Chorus]
The primes keep flowing like an endless spring
No cap can hold them, they're an infinite thing
Multiply them all and add just one
A new prime's born, the proof is done
Infinite primes, they never cease
Euclid's wisdom brings us peace

[Bridge]
This new number's strange, it breaks the mold
Not divisible by primes of old
Either it's prime or has new factors
Contradiction shows our logic matters
No finite net can catch them all
The primes will always break the wall

[Verse 3]
From contradiction comes the truth we seek
The finite assumption makes our logic weak
For every list that claims to be complete
Euclid's method shows it's incomplete

[Chorus]
The primes keep flowing like an endless spring
No cap can hold them, they're an infinite thing
Multiply them all and add just one
A new prime's born, the proof is done
Infinite primes, they never cease
Euclid's wisdom brings us peace

[Outro]
So when you think of numbers in their endless dance
Remember primes will always find a way to advance
An inexhaustible supply that flows forever free
Mathematical infinity for all to see

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