Sylvester's Sequence

[kenta]

I have completely factored the 10th Sylvester number, with "ecm -one -I 1 -c 0 1"

Using B1=29896574, B2=106305143196, polynomial Dickson(12), sigma=1602805018
Step 1 took 834376ms
Step 2 took 239259ms
********** Factor found in step 2:

Sylvester(10) = 2287 * 2271427 * 21430986826194127130578627950810640891005487 * P156

see
http://www.research.att.com/~njas/sequences/A091335

[fetofs]

Originally Posted by kenta

I have completely factored the 10th Sylvester number, with "ecm -one -I 1 -c 0 1"

Using B1=29896574, B2=106305143196, polynomial Dickson(12), sigma=1602805018
Step 1 took 834376ms
Step 2 took 239259ms
********** Factor found in step 2:

Sylvester(10) = 2287 * 2271427 * 21430986826194127130578627950810640891005487 * P156

see
http://www.research.att.com/~njas/sequences/A091335

I should think before posting. But, still, I don't know what number you're reffering to. Maybe I am committing some kind of mistake?

EDIT: Yes, I was. I did my calculations again and now they're suddenly correct! What a strange thing...

EDIT2: Congratulations (I forgot to say), but shouldn't you start at a higher B1 than 1? It should've saved you some curves...

[sean]

There's a wiki for the sequence that includes kenta's factor already :-)

http://en.wikipedia.org/wiki/Sylvester%27s_sequence

These numbers arise naturally from Euclid's proof of infinite prime. In this regard they are similiar to the Euclid Mullin sequence.

[alpertron]

According to the history stored on the Wikipedia page, that factor was added on May 26th, 2006. So it was already known.

[Mystwalker]

Maybe he found the factor back then (well, 4-5 days earlier), and only wrote the Mersenneforum posting some days later?
After all, he is a new user, so it sounds reasonable to me that someone pointed him to this forum after some time...

[fetofs]

Originally Posted by Alpertron

According to the history stored on the Wikipedia page, that factor was added on May 26th, 2006. So it was already known.

Sloane attributes the factor to kenta with the date of April 2006.

[sean]

Originally Posted by alpertron

According to the history stored on the Wikipedia page, that factor was added on May 26th, 2006. So it was already known.

I added it to Wikipedia, after I saw it OEIS. In fact, I added all the factors known at the same time.