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Old 2010-12-10, 06:38   #1
schickel
 
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Lightbulb Special project #1 - Driver escape attempt 2^4*31

OK, here's a twist.....these sequences are at a point where they might escape from 2^4 \cdot 31 on the next line, depending on what form the final factors take:
Code:
None left, try the others....
And these definitely will not escape on the next line, but if they keep 31^n {n > 0, n even}, then they have a chance of escape on the line after or any subsequent line where n stays even, also depending on the form of the other factors:
Code:
632898 2220. sz 111 2^4 * 3^2 * 31^2 * 59 * 307

Last fiddled with by schickel on 2010-12-23 at 09:25 Reason: Subtract another one...and another one
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Old 2010-12-10, 16:03   #2
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470466 loses the 31^2 next line. poking 700700

Last fiddled with by fivemack on 2010-12-10 at 16:07
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Old 2010-12-10, 16:27   #3
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the DB has 576648 at i=722 with 2^4*3*31.

taking 948780
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Old 2010-12-10, 19:02   #4
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700700 now 2^4*5^2*7*31; running it a bit further. Taking 122556.

Last fiddled with by fivemack on 2010-12-10 at 19:02
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Old 2010-12-10, 22:46   #5
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Well, I was getting ready to post another special project, and I thought I'd let everyone see what we're looking for. I was looking at 2^3 * 3 next, and got this on one sequence:
Code:
686922  693. sz 103 2^3 * 3^2 * 13^2 * 557
Code:
686922  694. sz 103 2^5 * 3^2 * 13
Better, except that 2^5 * 3 is still a persistent guide.....although since it's still 3^2, I'm factoring the c84 just in case.

Then we get
Code:
686922  695. sz 103 2^4 * 3^2 * 13 * 66763 * 224423 * 2147273 * 3437717

Last fiddled with by schickel on 2010-12-10 at 23:18 Reason: Add result for curious...
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Old 2010-12-11, 06:17   #6
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Quote:
Originally Posted by schickel View Post
240096 671. sz 114 2^4 * 3^2 * 31^2
The c109 on this has had 100 curves @ 43M. I'm going to let run it at least overnight, but, as I have too much on my plate right now, I won't be able to do a GNFS job on it for a couple of days....
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Old 2010-12-11, 08:13   #7
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122556 at 2^4*5*29*31, abandoning
700700 at 2^4*31, abandoning
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Old 2010-12-11, 09:25   #8
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948780 is now at i=1536, 24*31. unreserving it
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Old 2010-12-15, 05:17   #9
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I knocked this one out:

263862 1397. sz 103 2^4 * 3 * 31 * 59
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Old 2010-12-18, 08:04   #10
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I guess I'll take the last of the first batch: 240096.
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Old 2010-12-19, 07:20   #11
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Quote:
Originally Posted by schickel View Post
I guess I'll take the last of the first batch: 240096.
240096 671. sz 114 2^4 * 3^2 * 31^2 * c109 = p42 * p68

to

240096 672. sz 114 2^4 * 3^2 * 5 * 31

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