1213^[strike]71[/strike]73-1 is at the low end of the guidelines. It has had ECM well beyond the 2/9 level by Oscar aka Lorgix.

Are the two GNFS numbers and polynomials in posts 256-259 acceptable? I'll be generating a dozen more like these, so I want to be sure I've got it right.

The numbers from posts 256-259 are acceptable, thanks :)
Did you mean 12[b]31[/b]^71-1 ?

[QUOTE=debrouxl;412462]The numbers from posts 256-259 are acceptable, thanks :)
Did you mean 12[b]31[/b]^71-1 ?[/QUOTE]

No, I meant 1213^7[B]3[/B]-1. Fixed in the original post

All three latest OP numbers pre-processed and queued, thanks.

Oscar aka Lorgix has ECM'd 1493^73-1 to beyond 2/9 the SNFS size.

--------------------
The C157 from [URL="http://factordb.com/index.php?id=1100000000438761240"]P180+1 [/URL]needs a polynomial.
Yoyo@home has completed ECM to 1/3 of the size.

[URL="http://factordb.com/index.php?id=1100000000127580358"]P180 [/URL]comes from the factor chain
63601^5-1 -> P8
P8^5-1 -> P28
P28^3-1 -> P27
P27^5-1 -> P56
P56^5-1 -> P180

--------------------------
The C155 from [URL="http://factordb.com/index.php?id=1100000000438763094"]P231+1[/URL] needs a polynomial.
Yoyo@home has completed ECM to 1/3 of the size.

Just added 13 more candidates to the 14e queue. Perhaps someone could run a sanity check even though I think I got it right.

Very few remain from the GCW tables once these have finished. Rob Hooft is testing the last few stragglers; he also ran the new additions to > t55.

Paul

Would this be a 14e SNFS number?

P117^2 + P117 + 1

where P117 = (7537^31-1)/7536

Setting a=7537, it expands to a^62 + a^32 -3a^31 + a^2 -3a + 3

so (a^2) * x^6 + (a^2-3a) * x^3 + (a^2-3a+3)

56806369 x^6 + 56783758 x^3 + 56783761

x-7537^10

which is a 241 digit sextic with eight-digit coefficients. ECM hasn't been started - and I won't start it at this time unless the number is suitable for 14e.

[QUOTE=wblipp;413052]Would this be a 14e SNFS number?

P117^2 + P117 + 1

where P117 = (7537^31-1)/7536

Setting a=7537, it expands to a^62 + a^32 -3a^31 + a^2 -3a + 3

so (a^2) * x^6 + (a^2-3a) * x^3 + (a^2-3a+3)

56806369 x^6 + 56783758 x^3 + 56783761

x-7537^10

which is a 241 digit sextic with eight-digit coefficients. ECM hasn't been started - and I won't start it at this time unless the number is suitable for 14e.[/QUOTE]

This is roughly equivalent to a C289 with single digit coefficients.....

[QUOTE=R.D. Silverman;413076]This is roughly equivalent to a C289 with single digit coefficients.....[/QUOTE]
Thanks. That's beyond the 14e range.

Is there some heuristic you used to determine that?

[QUOTE=wblipp;413091]Thanks. That's beyond the 14e range.

Is there some heuristic you used to determine that?[/QUOTE]

I think he's asserting that each digit in the coefficient corresponds to two digits on the number.

I don't think it's that bad - I did test sieving and the yield with 14e is uselessly low, so I agree it's not a 14e number, but the Murphy_E score of 5.927e-14 isn't _that_ dreadful (I'd say it was comparable to high-260-digits with tiny coefficients; it's a bit worse than 10^263-1 and a bit better than 10^271-1)

Perfectly plausible 15e number, possibly with three large primes on one side, if you think it's interesting enough.

Thanks for the additional details.

I've prioritized my ECM towards 14e prep work because of the difficulty in keeping that queue filled. It's my impression that 15e keeps busy without difficulty, so I haven't considered the relative desirability of composites in that range.

The number I really want factored is phi_17(phi_19(11)), but I expect it to be at least five more years before that C301 is attractive to amateurs.