9042Re: [PrimeNumbers] Largest Ordinary Prime?
- Oct 3, 2002Firstly, congratulations to Paul, Paul, David and Bouk.
Secondly, DAMN. I had this great idea while I was on holiday
about ten days ago. It appears to be much the the same idea that
you guys had a long while earlier ;-)
I used my experience in trying to prove Gigantic GRUs to model
how many digits of prime factors I would expect to extract from
a cyclotomic factor of a given size given the amount of ECM work
I have done on such factors to date (about 7-10 GHz hours on each
composite on average, though some I've just started and a few have
had thousands of hours).
I then generated a list of promising composite exponents c such that
2^c-1 gave a decent chance of being useful in proving 2^a - 2^b +/- 1
where c=a-b. 64680 came out at 19.85%, so your 30% indicates how much
more work you did on it (and a bit of luck). I reckon the best few
exponents of around the same size are: 65520, 75600, 69300, 83160,
73920, 70560 then 64680.
Another thought I had was to use 2^c-1 where it's a Mersenne prime
... or c=2p, 3p etc where 2^p-1 is a Mersenne prime: diminishing
returns but worth a try for small multiples.
Ah well, I'll stick to the GRUs.
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