Fast Breeding (guru management)

[swellman]

Thanks for the background information. I'll work through it when I have some time. While I don't think 3 LPs are used very often, it seems like a good arrow to have in the quiver.

[unconnected]

One more number for 14e queue - c161 from alq sequence 3366:i2157

# norm 1.255546e-15 alpha -7.005172 e 1.142e-12 rroots 3
n: 71036057950123876011499496054766486217442762401833218657006056374323500079536001800187028848173670371826017382578418890816300844307416796958559595699606519909223
skew: 5818826.06
c0: -2227129036898757153425469105217531782725
c1: 655253516040010442018169509654896
c2: 118199593615005806305609615
c3: -43834689600223666222
c4: -404552652404
c5: 840840
Y0: -9668366369049929360705998428426
Y1: 268134514635675169
rlim: 41800000
alim: 41800000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6
lss: 0

[Dubslow]

Originally Posted by swellman

Thanks for the background information. I'll work through it when I have some time.

It's only around 15 lines or so.

Originally Posted by swellman

While I don't think 3 LPs are used very often, it seems like a good arrow to have in the quiver.

I agree. Good to know, good to have a reference floating around somewhere, but not necessary at the front of the mind.

[Max0526]

Hope it's not too late.
unconnected's poly optimized by CADO-NFS:

Msieve v. 1.52 (SVN 958)
R0: -9668366027525121127644085946943
R1: 268134514635675169
A0: -44827242285777982437223994216770965080
A1: 54612925324116628758297883016524
A2: -35861060043695668021061855
A3: -32254620229650701134
A4: 4950366316996
A5: 840840
skew 3510308.24, size 1.038e-015, alpha -6.435, combined = 1.169e-012

[RichD]

Two OPNs are ready as sextics. One from the t480 file and the other from the t490 file. This will also reduce the t500 file from 15 to 13 numbers.

18041^53-1 SNFS-230
21492^53-1 SNFS-234

[swellman]

C202_140_102

n: 3910659131819658723845854640229275791390440937895363277440313255688252073643851034588806659533980211325236912690368523362885460741680593596193988726663080566944631998915441928362770350499447220149491817
# 140^102+102^140, difficulty: 239.66, anorm: 2.04e+038, rnorm: -4.06e+045
# scaled difficulty: 240.88, suggest sieving rational side
# size = 3.616e-012, alpha = 0.000, combined = 3.132e-013, rroots = 0
type: snfs
size: 239
skew: 4.6723
c6: 1
c0: 10404
Y1: -1879810409774061983350381163649003258651
Y0: 363485178105010937500000000000
rlim: 134000000
alim: 134000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7

[VBCurtis]

One for 14e:

n: 113896911958072613417084980874908908746973542471460633482362069439033932389702739476186505894601951134672990859123293770471676698292533355335535984543225198595853603259689794881267488790526158252341054695099979992565220710131
m: 2722258935367507707706996859454145691648
# 13*2^784-1 difficulty: 237 
type: snfs
skew: 1.03
c6: 13
c0: -4
rlim: 67000000
alim: 67000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7

I'm afraid I don't quite understand what y0 and y1 represent on these snfs jobs; I've always fed factmsieve the .poly file with the "m" value, and it fires right up.

[jyb]

Originally Posted by VBCurtis

I'm afraid I don't quite understand what y0 and y1 represent on these snfs jobs; I've always fed factmsieve the .poly file with the "m" value, and it fires right up.

Y0 and Y1 are the coefficients of the rational polynomial, which is assumed to be of degree 1. So that polynomial is just Y1*x + Y0. If you specify the value of m directly, as in your case, then Y1 is assumed to be 1 and Y0 is assumed be be -m (or -1 and m, respectively).

Giving the coefficients in this way may be more convenient than specifying m because it can allow you to avoid any modular inversions. For your number above it wouldn't make any difference, but it comes up when the number has more of a homogeneous form.

For example, to find a sextic polynomial for something like a^131 - b^131, you would multiply by ab to get b*a^132 - a*b^132, which is bx^6 - ay^6, where x = a^22 and y = b^22. Dividing both sides by y^6 gives you a polynomial in the single variable (x/y). So now your 'm' value is a^22/b^22. If you want to specify that directly, you need to do a modular inversion of b mod n (or of b^22 mod n if that's easier for some reason). But your rational polynomial, instead of being x - a^22/b^22, can instead be (b^22)*x - a^22. So you can just set Y1 = b^22 and Y0 = -a^22 and leave out m.

[RichD]

Originally Posted by RichD

21492^53-1 SNFS-234

The number should be 21491^53-1. (not 21492)

All OPN are p^q-1 where both p & q are prime.

[jyb]

Originally Posted by RichD

The number should be 21491^53-1. (not 21492)

All OPN are p^q-1 where both p & q are prime.

Fixed.

[RichD]

Thank you,

I would have felt really bad if that got most of the way through sieving...