Last Three
 

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]


[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]

[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
[/code]

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[B]
c6: 9
c0: 4
# Y1 = -2^24*3^24*6
Y1: -28430288029929701376
# Y0 = 37^24[/B]
Y0: 43335257111193343900365036083324748961
rlim: 33600000
alim: 33600000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6
[/code]
Which has much smaller coefficients.

Chris

[QUOTE=chris2be8;421471]Are those the best polys? I would have adjusted them to minimize the coefficients.[/QUOTE]

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[B]
c6: 9
c0: 4
# Y1 = -2^24*3^24*6
Y1: -28430288029929701376
# Y0 = 37^24[/B]
Y0: 43335257111193343900365036083324748961
rlim: 33600000
alim: 33600000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6
[/code]
Which has much smaller coefficients.

Chris[/QUOTE]

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!

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

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

[URL="http://factordb.com/index.php?id=1100000000438704895"]C164[/URL] from P207+1

[URL="http://factordb.com/index.php?id=1100000000126871264"]P207[/URL] is the largest factor of [URL="http://factordb.com/index.php?id=1100000000438406629"]1036950426156829^17-1[/URL]
1036950426156829 is the largest factor of [URL="http://factordb.com/index.php?query=%289868152717977503^3-1%29%2F9868152717977502"]9868152717977503^3-1[/URL]
9868152717977503 is the largest factor of [URL="http://factordb.com/index.php?query=%2816694867096928847^3-1%29%2F16694867096928846"]16694867096928847^3-1
[/URL]16694867096928847 is the largest factor of [URL="http://factordb.com/index.php?query=%281453121857811448551^3-1%29%2F1453121857811448550"]1453121857811448551^3-1[/URL]
1453121857811448551 is the largest factor of [URL="http://factordb.com/index.php?id=1100000000125956641"]3348577^5-1[/URL]
3348577 is the larger factor of [URL="http://factordb.com/index.php?query=%283169^3-1%29%2F3168"]3169^3-1[/URL]
3169 is the larger factor of [URL="http://factordb.com/index.php?query=%2897^3-1%29%2F96"]97^3-1[/URL]

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

[URL="http://factordb.com/index.php?id=1100000000127081167"]C166[/URL] from P172+1

[URL="http://factordb.com/index.php?id=1100000000127485518"]P172[/URL] is the largest factor of [URL="http://factordb.com/index.php?id=1100000000438408722"]687015720002749009^11-1[/URL]
687015720002749009 is the largest factor of [URL="http://factordb.com/index.php?query=%28829007553280001^3-1%29%2F829007553280000"]829007553280001^3-1[/URL]
829007553280001 is the larger factor of [URL="http://factordb.com/index.php?id=1100000000126316847"]22406023^5-1[/URL]
22406023 is [URL="http://factordb.com/index.php?query=%284733^3-1%29%2F4732"](4733^3-1)/4732[/URL]

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

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

I'll take a run at the C164.

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[/CODE]

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

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

[URL="http://factordb.com/index.php?id=1100000000127141653"]P201[/URL] is the largest factor of [URL="http://factordb.com/index.php?id=1100000000438464167"]P51^5-1[/URL]
[URL="http://factordb.com/index.php?id=1100000000127044390"]P51[/URL] is the largest factor of [URL="http://factordb.com/index.php?query=%2825702205581365923346602787457585129653367632740563^3-1%29%2F25702205581365923346602787457585129653367632740562"]P50^3-1[/URL]
[URL="http://factordb.com/index.php?id=1100000000127754723"]P50[/URL] is the largest factor of [URL="http://factordb.com/index.php?query=%2813127711096135369231293810925810719^3-1%29%2F13127711096135369231293810925810718"]P35^3-1[/URL]
[URL="http://factordb.com/index.php?id=1100000000127608769"]P35[/URL] is the largest factor of [URL="http://factordb.com/index.php?query=%28872153100939711875724676704162421^3-1%29%2F872153100939711875724676704162420"]P33^3-1[/URL]
[URL="http://factordb.com/index.php?id=1100000000127175625"]P33[/URL] is the largest factor of [URL="http://factordb.com/index.php?query=%28282510594090638575830851732813^3-1%29%2F282510594090638575830851732812"]P30^3-1[/URL]
[URL="http://factordb.com/index.php?id=1100000000126618959"]P30[/URL] is the largest factor of [URL="http://factordb.com/index.php?id=1100000000815934564"]129574807^7-1[/URL]
129574807 is the largest factor of [URL="http://factordb.com/index.php?query=%2899995282631947^3-1%29%2F99995282631946"]99995282631947^3-1[/URL]
99995282631947 is the larger factor of [URL="http://factordb.com/index.php?id=1000000000043614041"]19^17-1[/URL]