[URL="http://www.mersenneforum.org/showpost.php?p=394989&postcount=59"]7103^61-1 by NFS@Home[/URL] P73*P159

All the ones I reserved are done. The results are in Factordb so I'll not post them here to save space.

Reserving:
183033817^17-1 (for the smaller system that did the last lot)
22469^47-1 (for my main systems)

Once the second is underway I'll be able to reserve some more for them.

Chris

Dubslow attempts to do useful things, take two.

Thanks RichD for making a simpler list.

[code]
1145924053 18 C164
1149989833 18 C164
36529 36 C165
58789 36 C168
46733917 22 C169

84969569171 16 C173
171634701455943275693670846531537378210379003 4 C177
149107399621 16 C179

563035735138626886051 2 C182
3760067 28 C185
28409 42 C188
237250154152941828313706973109892307074156361791 4 C188
4851463 28 C188
29501 42 C188
29567 42 C188
29573 42 C188
29581 42 C188
621011411269 16 C189

39097262657 18 C191
751410597400064602523400427092397 6 C194
828277 36 C199
1394714501 22 C199[/code]

I guess I'll start with 1145924053 18, which is to say (1145924053^19-1)/1145924052. Just to be clear, need I ECM these, or has that been done before being put on the list?

[QUOTE=RichD;394908]Here is a list of the smallest numbers in the file (minus Chris’).
[CODE]...
563035735138626886051 2 C182
[/CODE][/QUOTE]
There is a typo, a line cut short there.
I've done a few of such numbers before, and I can give anyone who wants to do this number the poly.
The real file entry is this:
[CODE]44799264616686550530996315243199966966425091434166776850060158408354539673563035735138626886051 2
38554240555244771684147788725064564814504311491620196795613705424279432517684827556228587498335690427233900622512289362773643459318294309417509353966389207077852814775292681545055967 4407[/CODE]
Now, where did the enormous value come from? It is actually x = (1429^31-1)/1428
You have to use that, to make the usable snfs poly (because you cannot use neither x^2+x+1 nor x^3-1).
After simplifying:
? (a^31-1)^2+(a^31-1)*(a-1)+(a-1)^2
a^62 + a^32 - 3*a^31 + a^2 - 3*a + 3
? a=1429
1429
? a^2*X^6 + (a^2- 3*a)*X^3 + (a^2 - 3*a + 3)
2042041*X^6 + 2037754*X^3 + 2037757
with X=a^10. Note that a quintic poly will not be able to take care of the middle term (unless with a huge coeff.).
The poly is:
[CODE]#opn2000: s(44799264616686550530996315243199966966425091434166776850060158408354539673563035735138626886051^2)
n: 38554240555244771684147788725064564814504311491620196795613705424279432517684827556228587498335690427233900622512289362773643459318294309417509353966389207077852814775292681545055967
m: 35507679231807726011177575666201
# m = 1429^10
c6: 2042041
c3: 2037754
c0: 2037757
skew: 1
type: snfs
lss: 0[/CODE]
With SNFS difficulty of 195, it is relatively easy. Sieve on the -a side. You can also try 3LP, if you want.
You can also try a quartic with X=1429^15.

Similarly, you can factor other sigma(a^2) cofactors.

For sigma(a^4), simply use x^4+x^3+x^2+x+1 poly, -- there is nothing better.

How do you determine to sieve on the algebraic side (or 3LP)?

By test sieving.

Okay, allow me a rephrase: what makes you think "Hmm, maybe, for this particular number/polynomial, I should consider testing the opposite of the conventional wisdom"? Or do you test sieve the algebraic side on all your SNFS jobs?

[QUOTE=Dubslow;395071]Okay, allow me a rephrase: what makes you think "Hmm, maybe, for this particular number/polynomial, I should consider testing the opposite of the conventional wisdom"? Or do you test sieve the algebraic side on all your SNFS jobs?[/QUOTE]

When the algebraic poly shows up with large coefficient(s) and/or higher than normal degree.

[QUOTE=Dubslow;395071]"...the opposite of the conventional wisdom"?[/QUOTE]
It is elementary, Watson.
If you [I]have[/I] to use an snfs poly of a degree higher than the "optimal degree for the input size" (which was 5 for this difficulty-190 input but we [I]have[/I] to use 6 or 4), then 1) do indeed consider the other side, 2) the more the degree is off (e.g a 230 with an obligatory quartic), the more reason to test uneven limits and/or 3LP. Homework: check why deg-4 poly works worse that deg-6.

Even more generally, any 500 core-hour job deserves a half an hour preparation. "15 minutes could save you 15% or more" on your sieving. A larger job deserves a larger still prep. The side of sieving is just one of half a dozen parameters that one can tune. If you are not doing that, then you are missing all the fun. Trial sieve frequently to get better skills -- except for boring projects (for boring snfs projects no skills are needed).

183033817^17-1 is done:
r1=75638527492663794617660215394226170244578350977509 (pp50)
r2=20977721849008094239599117843558973978221936566053008221323686368946956204920623229 (pp83)

Reserving:
36529^37-1

Chris

[URL="http://factordb.com/index.php?id=1100000000348566756"]9343^61-1[/URL] = p63*p106