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Old 2007-05-06, 20:55   #3
wblipp
 
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"William"
May 2003
New Haven

237210 Posts
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If you start with two composites of the same size, it's not that unusual to find largest factors of the same size. The simple algebraic factors of your numbers are

31576-1 = (31519-1)*(31519+1)*(31538+1)

(there is a bit more because each of these is divisible by (315-1),(315+1) and (3152+1)).

Your C45s are the largest factors of the two first two terms.

NOTE: YOU ARE WASTING COMPUTER POWER FACTORING THIS WAY. YOU SHOULD MANUALLY SEPARATE OUT THE ALGEBRAIC FACTORS

If you need to study up on algebraic factors, you can check the Cunningham Book. I also made an attempt to explain them in the Elevensmooth Math FAQ

http://elevensmooth.com/MathFAQ.html#Algebraic

Once you learn how algebraic factors work, you will want to be become familiar with Richard Brent's list. He collects factors of an ± 1 witn a and n both < 10,000. Your number is completely factored there; you can find these factorizations much more quickly and save your computing power for factorization not yet known, which you can then email for inclusion in the next update.

If you just want the factors, Dario Alpern's java factoring applet knows about the algebraic factors and knows about Richard Brent's list of factors. So the fastest way to get the factors is to enter

315^76-1

at http://www.alpertron.com.ar/ECM.HTM

Last fiddled with by wblipp on 2007-05-06 at 21:08 Reason: Mention alpertron
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