Prime Numbers — Gareth Jones / Serious Science

Mathematician Gareth Jones on number theory, why there are infinitely many of prime numbers and how to calculate the proportion of prime numbers up to any given n.

'Let's take the finite set of prime numbers and multiply them all together and call that integer n. So all the prime numbers we chose divide n. Now look at n+1, apply the fundamental theorem of arithmetic to that. It's a product of prime numbers, so there must be some prime number which divides it. That prime number cannot be one of the finite set we started with, because if it was, it would divide n and it would divide n+1, so it would have to divide their difference which is 1, but one is not divisible by any prime number, so we have produced a new prime number.'

Gareth Jones, Emeritus Professor of Mathematics, University of Southampton

Be the first to find out about our new videos and articles. Learn interesting facts about various topics and people. Discover the answers to the big questions. Be in the know.

[Hallands.]

Please explain what are "the zeros of complex numbers"? What's the connection between known "functions which take the value of zero" and complex numbers?

[CamiloSanchez]

I'll get on it when done with intermediate algebra

[TorGNorge]

I want to become a mathematician as well one day, so it really looks like fun. I am 18 years rn

[dubaiguy]

So interesting but I didn't understand half of what he said... We need a Michio Kaku for mathematicians?

[wiggles]

If you start with 2, and use Euclid's method to get new primes, you get 2, 3, 7, 43, 1807, ... but 1807 is not prime, it is 13*139.

[Nater.]

Prime number equation
[(n-2)!-1]÷n=whole number

[Nater.]

Every prime number satisfy:. number****
Where:
n is natural number

[erentxunlopez]

I already proved the Rhimman Hypothesis and is . . . . .That I cannot prove it.

[mariasenglishlearning]

There is a recent research book that have Practically answered all the questions about Primes in addition to Formulas that give u an infinity of Primes!! Just bought it from Amazon: THE FORMULAS OF NONPRIMES REVEALING ALL THE PRIME NUMBERS

[muhereza_d]

i think i just solved the distribution of primes problem i need to contact a mathematician
to see my solution