GNFS targets which need more ECM

[XYYXF]

Now it's time to find a good poly for C178_131_81 to ensure that it's not an SNFS target :)

[wombatman]

I've started working on C174_136_69 at B1=110e6.

[swellman]

Originally Posted by XYYXF

Now it's time to find a good poly for C178_131_81 to ensure that it's not an SNFS target :)

Should 10k curves @B1=26e7 be run first? Same thing with C178_133_71? Maybe yoyo will negate the need for poly searching. One can hope.

[XYYXF]

The chance to find a factor is small. But who knows, indeed...

[fivemack]

I intend to run 20384 or so curves at B1=3e8 on C184_146_89

[fivemack]

Originally Posted by swellman

Should 10k curves @B1=26e7 be run first? Same thing with C178_133_71? Maybe yoyo will negate the need for poly searching. One can hope.

C178_133_71 will take less than three CPU-years to sieve.

A quick Bayesian analysis using a uniform prior and the approximations, good for N>=45, of

P(success at N digits for one 11e7 curve) = 16139*exp(-0.356N)
P(success at N digits for one 26e7 curve) = 9669*exp(-0.331N)

says that the probability of success for 10k curves at 26e7 after 18k curves at 11e7 is 7.5%, so it's worth spending 2000 hours but no more.

(in fact, this argument leads to one that it is only worth spending *any* curves at 26e7 after 18k curves at 11e7 if the GNFS takes longer than running 90,000 curves at 26e7, i.e. 45k hours or about 180 digits)

(likewise that it's only worth running any curves at 11e7 after 8000@43e6 if the GNFS takes longer than running 50,000 curves at 11e7, i.e. 12k hours or 172 digits)

I'm well aware that RDS has been talking about Bayesian analyses for years, but I was stalled because I thought it was necessary to use exact success probabilities: but the exponentials fit so well that I am reasonably happy with this vastly easier approach.

[swellman]

Originally Posted by XYYXF

Now it's time to find a good poly for C178_131_81 to ensure that it's not an SNFS target :)

Noticed your request for GNFS polys over in the msieve forum. I've got the optimal SNFS poly and will run a comparison test sieve once msieve generates a poly.

[wombatman]

I've started working on C174_136_75 at B1=110e6. The Stage 1 curves from C174_136_69 have been sent to Sean to carry out Stage 2.

[fivemack]

Originally Posted by fivemack

I intend to run 20384 or so curves at B1=3e8 on C184_146_89

Fairly quickly found a P52, I've mentioned it on the ECM thread.

Looking at C182_136_109 next; if I believe my new implementation of how-much-ECM then it needs about 5000 curves at B1=3e8, which will take about a week, before being ready for polynomial selection. I am running these.

[swellman]

At the risk of smothering the GNFS efforts currently underway, I am proposing seven more candidates for the OP.

C195_148_83
C196_143_111
C196_146_83
C197_149_70
C198_143_115
C198_143_98
C200_139_113

All appear to be GNFS per test sieving and the methodology discussed previously.

These are not the only GNFS candidates I've identified, but I used an arbitrary cutoff of C200. There are 20 more composites so far that are very slow in SNFS and would seem better suited to GNFS. Size range is C201 to a breathtaking C230. 😳 I am not sure if there are clear lines of demarcation between hard to sieve, really hard and forget it but my list definitely strays into "here be dragons" territory.

[swellman]

Here is the remainder of my list. Not sure which (if any) are practical GNFS targets.

C201_137_134
C202_147_116
C203_145_119
C203_146_107
C203_147_104
C203_137_127
C203_142_87
C204_147_118
C206_139_123
C207_143_127
C208_145_99
C211_137_135
C213_147_128
C213_141_113
C214_143_135
C214_143_119
C218_142_133
C222_149_141
C228_145_141
C230_149_136