Fast Breeding (guru management) - Page 32

swellman · 2016-01-07, 13:14

Last three of my collection of low SNFS xyyx numbers with slow sieving speeds. Suggested polys follow. Please note the first number is sieved on the -a side. All ECM'd to t50+.

C185_144_74

C172_128_61

C170_122_63

Code:

n: 39008604262848745579512062604674171098658120040273939593068321451388166360937120729911152962290502345179090892337319446509715962615808960350672509116150372872390462033586749747916063169
# 144^74+74^144, difficulty: 225.82, anorm: 2.88e+038, rnorm: 1.89e+043
# scaled difficulty: 225.82, suggest sieving algebraic side
# size = 2.982e-011, alpha = 0.000, combined = 1.426e-012, rroots = 0
type: snfs
size: 225
skew: 5.2415
c6: 1
c0: 20736
Y1: -4738381338321616896
Y0: 43335257111193343900365036083324748961
rlim: 33600000
alim: 33600000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6

Code:

n: 8753199056024756823225646471617282276146491396249291925486956888261102122823686440715759020969339967419006403488131835707229870727510696654315862636366998112494209937882361
# 128^61+61^128, difficulty: 228.82, anorm: 1.73e+038, rnorm: -5.81e+043
# scaled difficulty: 233.32, suggest sieving rational side
type: snfs
size: 228
skew: 3.5070
c6: 2
c0: 3721
Y1: -31040344686800426926132378247220037261
Y0: 2361183241434822606848
rlim: 31200000
alim: 31200000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6

Code:

n: 16024551089267513719266493828993031940369135219121692406298527831741941487021250786389848891789448748267356690051852199986182759987009368455258740751659707415080278598561
# 122^63+63^122, difficulty: 222.64, anorm: 3.27e+034, rnorm: 1.43e+049
# scaled difficulty: 225.08, suggest sieving rational side
# size = 5.607e-016, alpha = 0.000, combined = 8.560e-013, rroots = 1
type: snfs
size: 222
skew: 10.2141
c5: 49
c0: 5447544
Y1: -10872213398722912904482816
Y0: 45845260162545276902907549795287406637985283
rlim: 30600000
alim: 30600000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6

chris2be8 · 2016-01-07, 17:40

Are those the best polys? I would have adjusted them to minimize the coefficients.

I would make C185_144_74

Code:

n: 39008604262848745579512062604674171098658120040273939593068321451388166360937120729911152962290502345179090892337319446509715962615808960350672509116150372872390462033586749747916063169
# 144^74+74^144, difficulty: 225.82, anorm: 2.88e+038, rnorm: 1.89e+043
# scaled difficulty: 225.82, suggest sieving algebraic side
# size = 2.982e-011, alpha = 0.000, combined = 1.426e-012, rroots = 0
type: snfs
size: 225
skew: 5.2415
c6: 9
c0: 4
# Y1 = -2^24*3^24*6
Y1: -28430288029929701376
# Y0 = 37^24
Y0: 43335257111193343900365036083324748961
rlim: 33600000
alim: 33600000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6

Which has much smaller coefficients.

Chris

swellman · 2016-01-08, 16:03

Quote:

Originally Posted by chris2be8

Are those the best polys? I would have adjusted them to minimize the coefficients.

These polys were generated by YAFU. It seems to do a reasonable job of narrowing the list of possible polys, then test sieving the best three for final selection.

Quote:

I would make C185_144_74

Code:

n: 39008604262848745579512062604674171098658120040273939593068321451388166360937120729911152962290502345179090892337319446509715962615808960350672509116150372872390462033586749747916063169
# 144^74+74^144, difficulty: 225.82, anorm: 2.88e+038, rnorm: 1.89e+043
# scaled difficulty: 225.82, suggest sieving algebraic side
# size = 2.982e-011, alpha = 0.000, combined = 1.426e-012, rroots = 0
type: snfs
size: 225
skew: 5.2415
c6: 9
c0: 4
# Y1 = -2^24*3^24*6
Y1: -28430288029929701376
# Y0 = 37^24
Y0: 43335257111193343900365036083324748961
rlim: 33600000
alim: 33600000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6

Which has much smaller coefficients.

Chris

Your poly sieves about 5% slower than the one I proposed. However I appreciate your input - blind trust in black box results is never a good thing. Maybe I just got lucky in this case!

wblipp · 2016-01-11, 01:00

These have had ECM to at least 2/9 SNFS size by yoyo@home. Those with base larger than 10^4 have had additional ECM.

6883^61-1
12269^61-1
12479^61-1

wblipp · 2016-01-11, 15:01

Here are two more that have had ECM to 1/3 their size by yoyo@home, but need a polynomial

C164 from P207+1

P207 is the largest factor of 1036950426156829^17-1
1036950426156829 is the largest factor of 9868152717977503^3-1
9868152717977503 is the largest factor of 16694867096928847^3-1
16694867096928847 is the largest factor of 1453121857811448551^3-1
1453121857811448551 is the largest factor of 3348577^5-1
3348577 is the larger factor of 3169^3-1
3169 is the larger factor of 97^3-1

----------------------------------------------

C166 from P172+1

P172 is the largest factor of 687015720002749009^11-1
687015720002749009 is the largest factor of 829007553280001^3-1
829007553280001 is the larger factor of 22406023^5-1
22406023 is (4733^3-1)/4732

fivemack · 2016-01-11, 16:46

I will throw 16 threads for a few days at the C164

fivemack · 2016-01-12, 14:45

Sorry, I have over-committed myself and turn out not to have spare cycles to throw at the C164.

wombatman · 2016-01-12, 15:16

I'll take a run at the C164.

wombatman · 2016-01-13, 03:46

Highest scoring poly for the C164 (A1 tested up to 3M):

Code:

polynomial selection complete
R0: -26885225424716159133281397018875
R1: 40687377600901
A0: 1506690899496724904947942882250050668
A1: 23822949827861961108337023238148
A2: 51009084356172000817547053
A3: 6062887903033652013
A4: -10683664797135
A5: 1284780
skew 1997202.06, size 6.261e-016, alpha -5.159, combined = 8.554e-013 rroots = 5
elapsed time 03:35:16

wblipp · 2016-01-14, 04:50

6883^61-1 has had ECM to 2/9 the SNFS size by yoyo@home

wblipp · 2016-01-18, 03:38

9199^59-1 has had ECM to 2/9 the SNFS size by yoyo@home

---------------------
C161 from P201+1 has had ECM to 1/3 size by yoyo@home, but needs a polynomial

P201 is the largest factor of P51^5-1
P51 is the largest factor of P50^3-1
P50 is the largest factor of P35^3-1
P35 is the largest factor of P33^3-1
P33 is the largest factor of P30^3-1
P30 is the largest factor of 129574807^7-1
129574807 is the largest factor of 99995282631947^3-1
99995282631947 is the larger factor of 19^17-1

2016-01-11, 15:01	#346
wblipp "William" May 2003 New Haven 2×7×13² Posts	Here are two more that have had ECM to 1/3 their size by yoyo@home, but need a polynomial C164 from P207+1 P207 is the largest factor of 1036950426156829^17-1 1036950426156829 is the largest factor of 9868152717977503^3-1 9868152717977503 is the largest factor of 16694867096928847^3-1 16694867096928847 is the largest factor of 1453121857811448551^3-1 1453121857811448551 is the largest factor of 3348577^5-1 3348577 is the larger factor of 3169^3-1 3169 is the larger factor of 97^3-1 ---------------------------------------------- C166 from P172+1 P172 is the largest factor of 687015720002749009^11-1 687015720002749009 is the largest factor of 829007553280001^3-1 829007553280001 is the larger factor of 22406023^5-1 22406023 is (4733^3-1)/4732 Last fiddled with by wblipp on 2016-01-11 at 15:02

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2016-01-11, 01:00	#345
wblipp "William" May 2003 New Haven 93E₁₆ Posts	These have had ECM to at least 2/9 SNFS size by yoyo@home. Those with base larger than 10^4 have had additional ECM. 6883^61-1 12269^61-1 12479^61-1

2016-01-11, 16:46	#347
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³×11×73 Posts	I will throw 16 threads for a few days at the C164

2016-01-12, 14:45	#348
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³·11·73 Posts	Sorry, I have over-committed myself and turn out not to have spare cycles to throw at the C164.

2016-01-12, 15:16	#349
wombatman I moo ablest echo power! May 2013 13×137 Posts	I'll take a run at the C164.

2016-01-14, 04:50	#351
wblipp "William" May 2003 New Haven 2×7×13² Posts	6883^61-1 has had ECM to 2/9 the SNFS size by yoyo@home

2016-01-18, 03:38	#352
wblipp "William" May 2003 New Haven 2·7·13² Posts	9199^59-1 has had ECM to 2/9 the SNFS size by yoyo@home --------------------- C161 from P201+1 has had ECM to 1/3 size by yoyo@home, but needs a polynomial P201 is the largest factor of P51^5-1 P51 is the largest factor of P50^3-1 P50 is the largest factor of P35^3-1 P35 is the largest factor of P33^3-1 P33 is the largest factor of P30^3-1 P30 is the largest factor of 129574807^7-1 129574807 is the largest factor of 99995282631947^3-1 99995282631947 is the larger factor of 19^17-1