A new prime serie?

[Sariaht]

This is strange... I can sort of proove this.

( n(1/2 + 1/3 + ... + 1/pa) - (1/3 + 2/5 + ... + (a-1)/pa) minus all whole queries ) <= ½

--> n = p

If it's true and I was the first to find the serie; can I name it after me?

In that case i would like to name my equation the EO-equation.


But pa is the last existing prime between the two numbers 1 and n.

Thereby it's a bit difficult to find really big primes, but anyway.

[suyver]

Originally posted by Sariaht
This is strange... I can sort of proove this.

mod1( n(1/2 + 1/3 + ... + 1/pa) - (1/2 + 2/3 + 3/5 + ... + (a-1)/pa) ) <= ½

I must say that I don't really understand what you are trying to say.

What do you mean with mod1( ... )?

By the way, are you aware that both the series 1/2 + 1/3 + 1/5 + ... + 1/pa and the series 1/2 + 2/3 + 3/5 + ... + (a-1)/pa diverge in the limit to infinity? Actually, the second series diverges considerably faster, so the total series ( n(1/2 + 1/3 + ... + 1/pa) - (1/2 + 2/3 + 3/5 + ... + (a-1)/pa) ) goes to -\infty in the limit a\rightarrow\infty...

[Sariaht]

I ment modulus.

mod1(23.5) = .5


If the first prime is two, how ever you think, the risk is fifty fifty for the next two primes to have a factor two.

If the risk is higher than... Well I can't explain it without a new small numbertheory

[Sariaht]

Originally posted by suyver
[B]I must say that I don't really understand what you are trying to say.

What do you mean with mod1( ... )?



modulus 12.34 = .34

(Am I not right in this?)

Anyway what i ment was everything after the dot in tu.vxyz....

So .342563448 in 23.342563448 is modulus 23.342563448.

[Sariaht]

Originally posted by suyver
I must say that I don't really understand what you are trying to say.

What do you mean with mod1( ... )?

By the way, are you aware that both the series 1/2 + 1/3 + 1/5 + ... + 1/pa and the series 1/2 + 2/3 + 3/5 + ... + (a-1)/pa diverge in the limit to infinity? Actually, the second series diverges considerably faster, so the total series ( n(1/2 + 1/3 + ... + 1/pa) - (1/2 + 2/3 + 3/5 + ... + (a-1)/pa) ) goes to -\infty in the limit a\rightarrow\infty...


The n don't cover the second serie, it only covers the first.

Change sign on -\infty

[suyver]

Originally posted by Sariaht
the n don't cover the second serie, it only covers the first.

But the first series diverges for n->oo! If you won't take the limit in the second series as well, then the result will just be +oo.

Originally posted by Sariaht
Change sign on -\infty
I do not understand this.

Anyway: can't you just give an example with the first 10 (or so) primes?

[suyver]

Originally posted by Sariaht
modulus 12.34 = .34

(Am I not right in this?)


Edit: I have been informed that this is an accepted notation (see below).

[Sariaht]

Originally posted by suyver


Sorry, I was wrong.

Good try anyway.

Good night Erik-Olof Wallman

[Hurkyl]

Actually, I've seen "mod 1" used in this way somewhat frequently.

[suyver]

Originally posted by Hurkyl
Actually, I've seen "mod 1" used in this way somewhat frequently.

Thank you, I stand corrected. (I had never seen it.)

[HallsofIvy]

Suyver, note that in the original post it was "mod1()". That might be more often written "( ) mod(1)" but the notation is perfectly reasonable.