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-   -   Poly select and CADO sieving for 2,1165+ C217 (https://www.mersenneforum.org/showthread.php?t=25031)

swellman 2020-01-01 15:35

I’ve started another CADO poly search on a second machine, with deg 5, nq = 3125, admax 2e5, incr 420, P = 14000000 and adrange = 1680. I also used ropteffort = 35 though it’s not clear if this parameter is required for deg 5.

Reserving up to admax = 3e6.

VBCurtis 2020-01-01 16:40

ropteffort is definitely useful for any search.

I'd use nq=15625 for deg 5, but chances are quite high that your search of small ad-values will have enormous skews anyway. So, leave it alone, see what pops out.

We might choose nq=7776 for deg 6 searches; that is; 45000 might be bigger than optimal. CADO documentation suggests a power of the degree for this, but that's not strictly necessary- perhaps something like 10000 for deg 5 is better than 15625. I've never tried.

Gimarel 2020-01-01 19:36

I've come to the conclusion that for useful deg 5 polys admin has to be >1e9 otherwise the skew will be to high.

swellman 2020-01-02 02:58

My first deg 5 effort with CADO to admax = 2e5, the result being a very high skew (and apparently incapable of improvement or scoring by cownoise) poly:

[CODE]
n: 3213773553731676734673029767649076184026081109505643819433123522398392216242493939130914684819990019996494667995485530318906995221039607546449005638410444687839629323036119079997039490112821634482150496640217083568211
skew: 793565000.033
c0: 296183829866616673978610883054549331035904575033571950
c1: -1803889324581136986860772969432750937688290385
c2: -2871473145762276337090828771070946326
c3: 1383027719019022289629291033
c4: -3893225332311264192
c5: 972866160
Y0: -2331785922123026514071918561866671528246462
Y1: 505059498353022512351192971
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.640e-09
# f(x) = 972866160*x^5-3893225332311264192*x^4+1383027719019022289629291033*x^3-2871473145762276337090828771070946326*x^2-1803889324581136986860772969432750937688290385*x+296183829866616673978610883054549331035904575033571950
# g(x) = 505059498353022512351192971*x-2331785922123026514071918561866671528246462
[/CODE]

It is as VBCurtis and Gimarel predicted - searching on low values of a5 produces untenable polynomials. I’m bailing on my reserved range of admax = 3e6. Instead reserving admin = 1e9 for a range of 1e6. Will start searching with a smaller chunk of 100,000 just to see if CADO produces useful quintics.

And I will try bumping nq to 15625.

VBCurtis 2020-01-02 05:32

For deg 5 searching, I suggest you take a page from Gimarel's msieve searches and set incr to 120120 or 210210.

1001 = 7*11*13, so 210210 = 210 * 1001 = 2*3*5*7*7*11*13, while 120120 = 120*1001 = 2*2*2*3*5*7*11*13. I've played with 120120 myself.

I suppose 30030 might be fruitful, too.

Good luck!

swellman 2020-01-03 02:18

Deg 5 CADO search with admin = 1e9 results in a much better skew poly, though still not a great score:

[CODE]
n: 3213773553731676734673029767649076184026081109505643819433123522398392216242493939130914684819990019996494667995485530318906995221039607546449005638410444687839629323036119079997039490112821634482150496640217083568211
skew: 93538652.862
c0: 164523557893662943796717352790852500285901385104107
c1: -4792313235809904351042387494952954383763528
c2: -25123717386359997987823357136788862
c3: -49557042588250550452052948
c4: -11885981563875775869
c5: 9000675180
Y0: -317246328253894345004777241765941376352878
Y1: 181842605602377583548024937
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.887e-09
# f(x) = 9000675180*x^5-11885981563875775869*x^4-49557042588250550452052948*x^3-25123717386359997987823357136788862*x^2-4792313235809904351042387494952954383763528*x+164523557893662943796717352790852500285901385104107
# g(x) = 181842605602377583548024937*x-317246328253894345004777241765941376352878
[/CODE]

Cownoise says skew of 139010939.44436 gives a score of 2.233e-16. I’m relieved, at least things seem to be getting better. Searching the remaining 900,000 in my search range with incr = 30030.

swellman 2020-01-04 01:10

30030 got me through a range of 900,000 overnight, with poor results. But I’m getting more comfortable with CADO. Now working range 970M < a5 < 1B using the same incr of 30030.

VBCurtis 2020-01-05 08:08

Here's the result of my next deg 6 run:
[code]skew: 1080763.305
c0: -201869394004181205724423495608425095348224384
c1: 1533975234876098133833772337881747505224
c2: 4276663040354231769078308262478714
c3: -30519115901769437344788339659
c4: -6106082259814635100149
c5: 8268339420665676
c6: 1132306560
Y0: -79750366340269635074646060047152969
Y1: 163481813872529787753319279
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=2.147e+16) = 1.066e-08
[/code]
cownoise: skew 1030433.87131 score 5.06955831e-16
This was about 10M thread-seconds of work. admin 1e7 admax 3e7 incr 4620.
Taking a break from this poly search for a bit.

swellman 2020-01-09 03:09

Deg 6 search with admax = 3e6 gave a reasonable result:

[CODE]
n: 3213773553731676734673029767649076184026081109505643819433123522398392216242493939130914684819990019996494667995485530318906995221039607546449005638410444687839629323036119079997039490112821634482150496640217083568211
skew: 641389.376
c0: -120561174635091771898975998857907044093318250
c1: 880187848484739419183546057061251000005
c2: 4764916896756892833867595202349562
c3: -24246448571150763259239758749
c4: -16360844327421682351876
c5: 15319532132265900
c6: -1097560800
Y0: -103653625868807926755041004802191418
Y1: 62548308560499268785701639
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.975e-09
# f(x) = -1097560800*x^6+15319532132265900*x^5-16360844327421682351876*x^4-24246448571150763259239758749*x^3+4764916896756892833867595202349562*x^2+880187848484739419183546057061251000005*x-120561174635091771898975998857907044093318250
# g(x) = 62548308560499268785701639*x-103653625868807926755041004802191418
[/CODE]

Cownoise says best skew of 814245.20 gives an e-score = 4.813e-16.

Next I’ll go at admin = 5e6, admax = 10e6, incr = 2310, adrange = 4620, all else as above.

swellman 2020-01-09 12:22

I’ve now got msieve-GPU searching for a deg 5 poly over the range 40M < c5 < 45M.

swellman 2020-01-10 11:35

My CADO deg 5 search has finished 970e6 < a5 < 1e9:

[CODE]
n: 3213773553731676734673029767649076184026081109505643819433123522398392216242493939130914684819990019996494667995485530318906995221039607546449005638410444687839629323036119079997039490112821634482150496640217083568211
skew: 81925937.712
c0: 20979117737896229889501593134036124581546875899439
c1: 702888888638716632053630701142158258021494
c2: 4805942957212842715569169595729246
c3: -1015952315801263566432172936
c4: -1641253174806907117
c5: 970539570
Y0: -319154102222244908033626629552413265381850
Y1: 56066781401775656648141249
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 2.372e-09
# f(x) = 970539570*x^5-1641253174806907117*x^4-1015952315801263566432172936*x^3+4805942957212842715569169595729246*x^2+702888888638716632053630701142158258021494*x+20979117737896229889501593134036124581546875899439
# g(x) = 56066781401775656648141249*x-319154102222244908033626629552413265381850
[/CODE]

Cownoise says skew of 206843455.873 gives an e-score of 3.441e-16.

Continuing search with same parameters over range 1e9 < a5 < 1.05e9.


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