[QUOTE=Batalov;396284]Interesting![/QUOTE]Well spotted!

That typpo must have been there for years without anyone drawing it to my attention. I'll fix it.

Thanks.

[QUOTE=xilman;396308]Well spotted!

That typpo :smile: must have been there for years without anyone drawing it to my attention. I'll fix it.

Thanks.[/QUOTE]

:smile:

[QUOTE=Batalov;396281]My resources are as limited as the next guy's. :rolleyes: ...logarithmically speaking. That is to say, we factor a few more, and all we will get as a result will be an extension from Paul. The number will never be under 100!
[/QUOTE]

Paul has said he would extend when the number drops below 50, so it will get below 100. But you are correct to within a small constant term. :smile:

[QUOTE=Batalov;396281]
I did try to squeeze it into the "Need For Speed" competition. These are easily automated, conveyor belt-style. There are no tricky polynomials and/or GNFS' left. Only plain sextics.[/QUOTE]

I was wondering about this. Some test sieving I did with numbers of difficulty 223 suggested that a quintic was still better, at least with the parameters I was using. Have your tests strongly contradicted this with numbers of this size?

Also, I'll point out that akruppa's 'phi' program (as modified by others) generates polynomials for these numbers very well, including those which are "tricky". See [URL="http://mersenneforum.org/showthread.php?t=8739"]http://mersenneforum.org/showthread.php?t=8739[/URL]. The exception is those numbers with Aurifeuillian factorizations, but there are no such composites in the current range (or any other trickery I guess, thanks to your recent efforts).

Oh, and there are still two GNFS numbers. They're reserved to bsquared, but he has renounced them. He just can't cancel the reservation because he doesn't have the codes. I have generated a decent polynomial for the smaller of the two and will start sieving it when I've cleared some other work.

[QUOTE=R.D. Silverman;396275]I do what I can with the hardware I have available. One 5-yr old I7 home PC,
an I7 laptop, and 9 i5 based PC's available nights and weekends. --> i.e. not much.

Our server has been down for almost a week, so my current sieve job has been mostly stalled.

Of course help would be nice......[/QUOTE]

Fivemack said that he released the two numbers that had been accidently reserved for over 4 months.

However, in the process it appears that all composites under 160 digits have been deleted........

[QUOTE=R.D. Silverman;396951]Fivemack said that he released the two numbers that had been accidently reserved for over 4 months.

However, in the process it appears that all composites under 160 digits have been deleted........[/QUOTE]

Those two which were reserved were the only composites under 160 digits (7+3,296 having been already completed on 2015-03-01). Did fivemack perhaps complete their factorizations? They haven't shown up in factordb. I am currently doing polynomial selection for 9-2,251, but I will stop if I get confirmation that it's already been done.

I have a snapshot from those days. Let's see.
The numbers that disappeared are:
[CODE]7^296+3^296 153.6 250.1 - [URL="http://factordb.com/index.php?query=7%5E296%2B3%5E296"]done[/URL]
9^233+5^233 154.3 222.3 - not done in factorDB, and restored now
9^251-2^251 155.9 239.5 - not done in factorDB, and restored now
[STRIKE]7^263+3^263 171.0 222.3 - not done in factorDB[/STRIKE]
9^233+8^233 182.3 222.3 - [URL="http://factordb.com/index.php?query=9%5E233%2B8%5E233"]done[/URL]
9^233-8^233 192.3 222.3 - done
[STRIKE]7^263-3^263 214.6 222.3 - not done in factorDB[/STRIKE]
7^268+2^268 223.2 226.5 - done[/CODE]

[QUOTE=jyb;396355]...I was wondering about this. Some test sieving I did with numbers of difficulty 223 suggested that a quintic was still better, at least with the parameters I was using. Have your tests strongly contradicted this with numbers of this size?

Also, I'll point out that akruppa's 'phi' program (as modified by others) generates polynomials for these numbers very well, including those which are "tricky". [/QUOTE]
Ah, missed that part. I can sort of agree for the size just teetering at 223. I tried 9^233 - 5^233:
[CODE]#============================
# 9^233 - 5^233 snfs quintic poly
# skew 0.42, size 2.792e-15, alpha 0.711, combined = 1.961e-12 rroots = 1
#============================
n: 63418225481676000933402477821262151544891063218633660456992164788123242948432290326657382152137758816800429527674573881065971729588513211218491413046158884196550029559794087838020682289955118126178080261544861
type: snfs
skew: 0.4217
lss: 1 # ?
c5: 75
c0: -1
Y1: 710542735760100185871124267578125
Y0: -235655016338368235499067731945871638181119123
#============================
# 9^233 - 5^233 snfs sextic poly
# skew 1.10, size 5.024e-11, alpha 1.204, combined = 2.045e-12 rroots = 2, slightly better
#============================
n: 63418225481676000933402477821262151544891063218633660456992164788123242948432290326657382152137758816800429527674573881065971729588513211218491413046158884196550029559794087838020682289955118126178080261544861
type: snfs
skew: 1.1029
lss: 1
c6: 5
c0: -9
Y1: 1818989403545856475830078125
Y0: -16423203268260658146231467800709255289
[/CODE]
Didn't test-sieve this one. Sextic seems slightly better by E score, but it sieves equally well on both sides.
Quintic will have not equally better sieving, therefore one of the sides might be better than either side of the sextic.

But as you go up to 230-240s, it is too lazy to change horses midstream, so I built deg 6 into the perl script.

I will always cheer a person who does test sieving.
(And much less so someone who would say, "Ugh, I prefer to just fire up a one-liner in yafu. Why is [B]yafu[/B] not working!?" [/a slight sting totally intentional; if the arrow reached its target, I will only be pleased] :razz: )

Jason used to remind us frequently that E-score for GNFS sextics are not comparable to quintics. Is this true for SNFS polys as well?

This may or not be outdated; more generally, score is only good for eliminating far outliers (by e.g. >10% worse score). But it is very fast to compute.

These two polys actually sieve quite similar, with quintic mandatorily on -r side; sextic can be sieved on either side. I sieved very little; not enough to say conclusively, but it is almost exactly the same. There's also the 3x^5-125 poly; it's score is even higher than that of the sextics, but it too seems to sieve the same.

Anyway, this is a gedanken experiment for the smallest of the available composites (and for it, it is almost a wash between deg 5 and 6), and the trend going up is clear shift from 5 to 6, the higher the more.

It will all change for the few chosen simple projects that will only appear when the extension happens. It reminds of the last time Sam extended, I was able to single out and quickly factor a rare one, 7,861M (861 is a multiple of 21). But until then, they will all be quite a fit for a conveyor approach. The first 10% can be done with either degree.

[QUOTE=Batalov;396961]I have a snapshot from those days. Let's see.
The numbers that disappeared are:
[CODE]7^296+3^296 153.6 250.1 - [URL="http://factordb.com/index.php?query=7%5E296%2B3%5E296"]done[/URL]
9^233+5^233 154.3 222.3 - not done in factorDB
9^251-2^251 155.9 239.5 - not done in factorDB
7^263+3^263 171.0 222.3 - not done in factorDB
9^233+8^233 182.3 222.3 - [URL="http://factordb.com/index.php?query=9%5E233%2B8%5E233"]done[/URL]
9^233-8^233 192.3 222.3 - done
7^263-3^263 214.6 222.3 - not done in factorDB
7^268+2^268 223.2 226.5 - done[/CODE][/QUOTE]

7+3,263 and 7-3,263 were both gone from the reservation page at least two days ago, before this latest change. I believe Bob had them reserved, so I assume he finished them. He doesn't add his factors to factorDB, so that's consistent. So it's just 9-2,251, which was reserved to Ben, and 9+5,233, which was reserved to Tom.

From my database logs
 

[code]
submitted factor 255315395057727481050868531668810148009004867835570694031213 for 34824779803150243287226243651067114500556526400796556418181958832511106130052342226810866774008234486878874065840442708932715061912373464305357775927262571060534294230265187306178000582904798945525999314553678080059 (7^263-3^263) at 20150216114742
submitted factor 253333366089098007403559542626254658064762532109852936867506388973 for 936493054720188445572413288455732478152493804855611817908724175155694909343775988210036740619556606480089216556945858206914064307540594299762634403651407160319004641532367 (7^263+3^263) at 20150223114716
[/code]

I had accidentally deleted 9+5,233 and 9-2,251 and have now put them back; aren't editor backups a wonderful thing?