I think I found the highest known prime number.

[Avahlanch]

I think I found the highest known prime number. What should I do about this? I've seen on the internet that you could get money?

 

[Deleted member 4993]

What should I do about this? I've seen on the internet that you could get money?

The same place should tell you where you should send your discovery.

May be you can send it to the mathematics department of Harvard University!

 

[stapel]

I think I found the highest known prime number. What should I do about this? I've seen on the internet that you could get money?

In light of Euclid's famously simple proof that there is no "largest" prime (for instance, here), you know that it's impossible to do what you've claimed. So please reply with clarification of your post. Thank you!

 

[JeffM]

In light of Euclid's famously simple proof that there is no "largest" prime (for instance, here), you know that it's impossible to do what you've claimed. So please reply with clarification of your post. Thank you!

But, at any given instant there must be the highest known prime. I suggest that the OP collect his award quickly.

 

[tkhunny]

This depends on one's feelings towards "known". If we know that there is no limit to their number, it is not unclear to imagine that we cannot know, even for a moment, anything that is "highest" in any reasonable definition of the word.

Question for OP. What is the magnitude of this number you claim to have found?

 

[JeffM]

Lookagain pointed out that I misread the cited proof. What I thought was an omission was not omitted.

 

[lookagain]

Actually, the proof cited is flawed.

It assumes the existence of a finite list of all primes. it further assumes that there are L primes in the list, p_1, p_2, etc.

Now it constructs \(\displaystyle \displaystyle u = 1 + v \text {, where } v = \prod_{j=1}^L p_j.\)

Obviously \(\displaystyle \text {For } j = 1,\ ... \ L,\ p_j \ | \ v \implies p_j \ \not | \ v + 1 = u.\)

So far all is well. The proof then concludes that therefore u is prime, but that does not follow.

No, the proof does not conclude that.

The proof concludes that either u is prime, or u has prime factors larger than the supposed largest prime in the list.

 

[JeffM]

No, the proof does not conclude that.

The proof concludes that either u is prime, or u has prime factors larger than the supposed largest prime in the list.

You are correct. Thank you. I missed what I feel is a minor clause in the cited proof. I shall correct my post.