mersenneforum.org Sylvester's Sequence
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 2006-05-31, 00:01 #1 kenta   May 2006 22 Posts Sylvester's Sequence 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
2006-05-31, 19:40   #2
fetofs

Aug 2005
Brazil

2×181 Posts

Quote:
 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...

Last fiddled with by fetofs on 2006-05-31 at 19:45

 2006-05-31, 21:53 #3 sean     Aug 2004 New Zealand 2×5×23 Posts 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.
 2006-06-01, 12:18 #4 alpertron     Aug 2002 Buenos Aires, Argentina 2×761 Posts According to the history stored on the Wikipedia page, that factor was added on May 26th, 2006. So it was already known.
 2006-06-01, 14:01 #5 Mystwalker     Jul 2004 Potsdam, Germany 3·277 Posts 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...
2006-06-01, 18:38   #6
fetofs

Aug 2005
Brazil

2·181 Posts

Quote:
 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.

2006-06-01, 20:50   #7
sean

Aug 2004
New Zealand

2·5·23 Posts

Quote:
 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.

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