Firstly, 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.

Good luck,

Andy