Early history of prime numbers
score:6
This paper (in .pdf) argues against ancient Chinese mathematics being aware of prime numbers.
The Rhind Mathematical Papyrus, dating to the 15-16th century BCE, indicates an Egyptian knowledge of primes evidenced in their fractional system, but it's not definitive proof.
It looks like the Greeks were indeed the first.
Upvote:0
I was a student learning Vedic mathematics a couple of years ago. I remember they talked about prime numbers also being mentioned in the vedas(probably Rig Veda). I tried to find links that mention it. I was only able to find a few references (might be because Vedic maths is not used outside India ?)
here. Also this link and this for some general info on what vedic math is! Also I don't know how old they are(although Vedas are considered to be one of the oldest known texts) but I just wanted to share this!
Upvote:2
Mathematicians are better at mathematics than at history, and have perpetuated an error concerning what Euclid did. They frequently state in textbooks and elsewhere that Euclid's proof that there are infinitely many prime numbers is by contradiction. But it is not. Euclid considered what happens if you multiply finitely many prime numbers and then add 1. For example:
(2 × 11 × 37) + 1 = 815
The number you get cannot be divisible by any of the finitely many prime numbers you started with. 815 cannot be divisible by 2 because 814 is; 815 cannot be divisible by 11 because 814 is; 814 cannot be divisible by 37 because 814 is. (The next prime number after 814 that is divisible by 37 is 814+37; the next after 814 that is divisible by 11 is 814+11; the next after 814 that is divisible by 2 is 814+2.)
Therefore, whichever prime numbers 815 is divisible by, whether it is prime itself or not, cannot be among the finitely many you started with (in this example 2, 11, and 37). (In fact 815 is 5 × 163, and 5 and 163 are prime.) In this way it is seen that every finite list of prime numbers can be extended to a longer finite list of prime numbers.
That is how Euclid prove there are infinitely many prime numbers.
Catherine Woodgold and I wrote a joint paper in which we refuted the historical error and explained some practical reasons why it matters:
Michael Hardy and Catherine Woodgold, "Prime Simplicity", Mathematical Intelligencer, volume 31, number 4, fall 2009, pages 44–52.
I learned only after the paper appeared that the historical error may have originated with Johann Peter Gustav Lejeune Dirichlet. It appears in his posthumous book on number theory.
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