C207_127_103 and C206_129_95 are ready for NFS. Sieve using 14e.


[code]
n: 381704906927879421312056510857538053155858776390310032847439225786233948892834352085403252680665987643131289809797419808316399164669416257559643814360462067141085658599143558692095693670328817277329724173799
# 127^103+103^127, difficulty: 257.64, anorm: 2.29e+038, rnorm: 1.83e+048
# scaled difficulty: 259.29, suggest sieving rational side
# size = 5.559e-013, alpha = 0.000, combined = 7.870e-014, rroots = 0
type: snfs
size: 257
skew: 1.0355
c6: 103
c0: 127
Y1: -581652040856250348581103942808504447
Y0: 1860294571709496226110032706809177658295303
rlim: 240000000
alim: 240000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]


Test sieving with Q in blocks of 5000
[code]
Q=20M total yield: 8232, q=20005003 (0.76654 sec/rel)
Q=100M total yield: 6732, q=100005001 (1.00778 sec/rel)
Q=200M total yield: 5528, q=200005007 (1.40776 sec/rel)
Q=300M total yield: 5141, q=300005039 (1.57456 sec/rel)
[/code]
suggesting a sieving range for Q of 20-480M


[code]
n: 82739763050618261459944062822029481086261568048108928042758674940753725990266316561602510605437377120986715580704445181098385778578492897916317459273643266219727394445877980087458027748876345097839851375273
# 129^95+95^129, difficulty: 255.13, anorm: 2.10e+040, rnorm: -1.59e+048
# scaled difficulty: 256.44, suggest sieving rational side
# size = 4.515e-013, alpha = 0.000, combined = 6.806e-014, rroots = 0
type: snfs
size: 255
skew: 21.9092
c6: 1
c0: 110601375
Y1: -340561626288115122639539918422698974609375
Y0: 5880785850256519209198206471505921
rlim: 240000000
alim: 240000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]


Test sieving with Q in blocks of 5000
[code]
Q=20M total yield: 8734, q=20005003 (0.72242 sec/rel)
Q=100M total yield: 7096, q=100005001 (0.96160 sec/rel)
Q=200M total yield: 6103, q=200005007 (1.28523 sec/rel)
Q=300M total yield: 5248, q=300005039 (1.54877 sec/rel)
[/code]
suggesting a sieving range for Q of 20-460M

HP2(4496) index 310
 

The C207 has been fully ECM'd and (thanks to the users of this forum) has been extensively searched for an appropriate polynomial.
There were two polynomials that test-sieved fairly closely (within ~3-5%) when tested with YAFU. I ran my own test-sieving on each for a range of parameters (rational and algebraic sides, 3LPs vs 2LPs, etc) and minimized the time per relation.
All test sieving was done with the 16e GGNFS siever. I'm fairly certain this will need to be in the 16e queue, and I think it will require some heavyweight computing power for the linear algebra, which I am not able to provide.
It would be greatly appreciated if this number could be queued. Full details plus polynomial follows:

C207:
[CODE]183724913753361567376492453926230323715345031792001208551707422272237266349933302881515963689094609592709968359761386456940894165548045328984901031969851838708505435691913321760214712695688550560374318369687[/CODE]

Polynomial with best parameters:
[CODE]n: 183724913753361567376492453926230323715345031792001208551707422272237266349933302881515963689094609592709968359761386456940894165548045328984901031969851838708505435691913321760214712695688550560374318369687
# norm 2.865842e-020 alpha -7.774942 e 1.627e-015 rroots 3
skew: 340123234.89
c0: 571991564598637896614710101239020638310733930025
c1: 167700052788587220002691890175305892882498
c2: 6476627046873628489030255421467789
c3: -13678387964207629928614248
c4: 17897969236909044
c5: 22320144
Y0: 6068679638793281991245086507839408878726
Y1: -39500688790939641031
type: gnfs

rlim: 800000000
alim: 800000000
lpbr: 32
lpba: 33
mfbr: 64
mfba: 96
rlambda: 2.6
alambda: 4.6[/CODE]

Timings (on a machine with half the cores in use) on block of 1000Q at 25M:
[CODE]22A: total yield: 248, q=25001029 (6.40776 sec/rel)
22R: total yield: 309, q=25001029 (6.44973 sec/rel)
32A: total yield: 508, q=25001029 (3.22992 sec/rel)
32A_LPBA33: total yield: 660, q=25001029 (2.48489 sec/rel)
32A_LPBA33_alambda4.6: total yield: 881, q=25001029 (2.14951 sec/rel)[/CODE]

Test-sieving (blocks of 1000Q):
[CODE]25M: total yield: 881, q=25001029 (2.14951 sec/rel)
50M: total yield: 1388, q=50001037 (2.65706 sec/rel)
100M: total yield: 1215, q=100001029 (2.56781 sec/rel)
200M: total yield: 1621, q=200001001 (2.86097 sec/rel)
300M: total yield: 1126, q=300001001 (3.06091 sec/rel)
400M: total yield: 1061, q=400001009 (3.33016 sec/rel)
500M: total yield: 1413, q=500001001 (3.48125 sec/rel)
600M: total yield: 1121, q=600001021 (3.78163 sec/rel)
700M: total yield: 1049, q=700001011 (3.87128 sec/rel)
800M: total yield: 1086, q=800001071 (4.23842 sec/rel)
[/CODE]

I don't know how many relations are expected to be needed, but I test-sieved from 25M up to 800M so that there's plenty of space to choose from. No idea why the yield goes up and down, but they're generally greater than 1 at 50M+.
I hope this is all sufficient for consideration. If there's anything I missed and should include, please let me know.
Thanks again to everyone who helped with both the polynomial search and advised on how best to go about testing parameters and test-sieving.

C207
 

@wombatman
Thank you for pulling all the test-sieving through! The polyselect was another example of a productive collaboration of Msieve & CADO. We should learn to always use them together, both are available, and projects are not getting any easier either.

C205_125_117 and C208_138_73 are ready for NFS. Sieve using 14e.

[code]
n: 1281391649236418351602951600256058919882810571399099834538395547428107884746687254512839657624121302691713820093300981087247076423566422509243255544515194093681083657095913190158948865741118224336595703241
# 125^117+117^125, difficulty: 260.59, anorm: 2.42e+038, rnorm: 1.21e+049
# scaled difficulty: 262.37, suggest sieving rational side
# size = 4.926e-013, alpha = 0.000, combined = 7.048e-014, rroots = 0
type: snfs
size: 260
skew: 4.9452
c6: 1
c0: 14625
Y1: -34694469519536141888238489627838134765625
Y0: 27033551021470087806679878288841875415489317
rlim: 260000000
alim: 260000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]

Test sieving with Q in blocks of 5000
[code]
Q=20M total yield: 8416, q=20005003 (0.78020 sec/rel)
Q=100M total yield: 7246, q=100005001 (0.97638 sec/rel)
Q=200M total yield: 6057, q=200005007 (1.33968 sec/rel)
Q=300M total yield: 5407, q=300005039 (1.60261 sec/rel)
[/code]
suggesting a sieving range for Q of 20-450M


[code]
n: 9682172549759977817280440817745192373346520333807918948384967474684409321103942149950106448794418488886498766692493973661509359455402281867346856560850545412691940736896899559425920586209802807009228826852567
# 138^73+73^138, difficulty: 257.14, anorm: 2.35e+037, rnorm: 4.77e+048
# scaled difficulty: 259.02, suggest sieving rational side
# size = 1.035e-012, alpha = 0.000, combined = 1.202e-013, rroots = 0
type: snfs
size: 257
skew: 2.2732
c6: 1
c0: 138
Y1: -47703367363695867545849856
Y0: 7184983626352716099297100617536359330111417
rlim: 240000000
alim: 240000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]

Test sieving with Q in blocks of 5000
[code]
Q=20M total yield: 11104, q=20005003 (0.48071 sec/rel)
Q=100M total yield: 9535, q=100005001 (0.60287 sec/rel)
Q=200M total yield: 8031, q=200005007 (0.82748 sec/rel)
Q=300M total yield: 7105, q=300005039 (0.97495 sec/rel)
[/code]

suggesting a sieving range for Q of 20-320M

Please queue C165 from 11040:i10029. Here is the fastest poly:

[CODE]
n: 548053161872286094263546390942532925280484495878287628018996658359830769025595729605632079717852442811109714651767256348336257841788345910368127498252314702339291049
# norm 4.589867e-16 alpha -6.706725 e 6.261e-13 rroots 5
skew: 9216896.39
c0: 8592717878299972283339126425141474811280
c1: 3041053898941390683885715314090252
c2: -740005961644725299986648110
c3: -208386829472386131734
c4: 12368070595697
c5: 229680
Y0: -75082701001833231044422797434639
Y1: 228408202789936501
type: gnfs
rlim: 134217727
alim: 134217727
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7
[/CODE]

Siever 14e, range 20M-120M (or 40M-140M) aiming for 200M+ relations.

C211_125_112 and C212_142_108 are ready for NFS. Sieve using 14e.


Note the first poly (C211_125_112) is best sieved on the -a side.


[code]
n: 1689507061605102889217543282905214634102582281131872983829885401870656891759881658183519703945629754132695708201544163632070863778419050545756623099343361881219961368278598736405423549981323295341551169130715323
# 125^112+112^125, difficulty: 258.50, anorm: 1.06e+037, rnorm: 5.15e+048
# scaled difficulty: 260.45, suggest sieving [b]algebraic side[/b]
# size = 9.957e-013, alpha = 1.534, combined = 1.168e-013, rroots = 0
type: snfs
size: 258
skew: 1.0978
c6: 4
c0: 7
Y1: -1387778780781445675529539585113525390625
Y0: 5401924132233963086793068268357579079417856
rlim: 240000000
alim: 240000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]


Test sieving with Q in blocks of 5000
[code]
Q=20M total yield: 11928, q=20005003 (0.52655 sec/rel)
Q=100M total yield: 8366, q=100005001 (0.74236 sec/rel)
Q=200M total yield: 8283, q=200005007 (1.08382 sec/rel)
Q=300M total yield: 6086, q=300005039 (1.26756 sec/rel)
[/code]

suggesting a sieving range for Q of 20-340M




[code]
n: 91126004014867590868461238416818426882727371388191556422498253862882787328598694224042703997985409713456644204584975765412626909572032335628860161594110434879526087880364839445510693095057648147229404318461288893
# 142^108+108^142, difficulty: 259.35, anorm: 8.00e+036, rnorm: 6.40e+048
# scaled difficulty: 261.33, suggest sieving rational side
# size = 1.028e-012, alpha = 0.000, combined = 1.191e-013, rroots = 0
type: snfs
size: 259
skew: 1.5874
c6: 1
c0: 16
Y1: -2102085018129621311776010144838961
Y0: 8063228273061253034007789191829366377545728
rlim: 240000000
alim: 240000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]


Test sieving with Q in blocks of 5000
[code]
Q=20M total yield: 10829, q=20005003 (0.47526 sec/rel)
Q=100M total yield: 9337, q=100005001 (0.59239 sec/rel)
Q=200M total yield: 7754, q=200005007 (0.82499 sec/rel)
Q=300M total yield: 7173, q=300005039 (0.93322 sec/rel)
[/code]

suggesting a sieving range for Q of 20-330M

I did attempt to sieve this second composite using c6=4, c0=1 but it would not sieve. Not sure if this is due to my setup, a siever bug or number theory in general.

13*2^798-1:
[code]# 13*2^798-1 difficulty: 241
n: 346247349907241163585308458757929567124659986167606695746616522331616952376380451008019260360292079973456363032432287677367375873009775610170148915959622326863279523899867843130802995834514334508157
m: 10889035741470030830827987437816582766592
type: snfs
skew: 0.70
c6: 13
c0: -1
rlim: 110000000
alim: 110000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.7
alambda: 2.7[/code]
ECM'ed to half a t55.
Q of 20M to 110M should be sufficient for ~350M raw relations.
I'd like to do the post-processing when it's ready.

OPN (C197) from the t600 file which survived a full t55.
[CODE]n: 76168789033078306528545510523783851836825949741968982499279727789871412694249124010078841499570187735718916285158940989141405074631832098698287693088761942446767032814304058444846489745122492050123
# 128341^47-1, difficulty: 245.20, skewness: 7.10, alpha: 0.00
# cost: 5.74422e+18, est. time: 2735.34 GHz days (not accurate yet!)
skew: 7.102
c6: 1
c0: -128341
Y1: -1
Y0: 73607717520239639878892572595537274407521
m: 73607717520239639878892572595537274407521
type: snfs
rlim: 134000000
alim: 134000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.6
alambda: 2.6[/CODE]
Test sieving 5K blocks.
[CODE] Q Yield
20M 10076
60M 7768
100M 7364
140M 6359[/CODE]

Queued C197_128341_47
Queued 13_2_798m
Queued C211_125_112
Queued C212_142_108

25125200742702138527^13-1 Revisited
 

After reviewing this [URL=http://www.mersenneforum.org/showpost.php?p=457984&postcount=1027]post[/URL] it appears we may be able to squeeze the number in as a 30 LPB job.
[CODE]n: 3582123724009125350979135532253668176917146315309069102903598732280603715909936623363796377970580002623282837233544467878001808051279400221966150804199215087404769081158554191159143409953966039
# 25125200742702138527^13-1, difficulty: 232.80, skewness: 1.00, alpha: 3.10
# cost: 2.17123e+18, est. time: 1033.92 GHz days (not accurate yet!)
skew: 1.000
c6: 1
c5: 1
c4: -5
c3: -4
c2: 6
c1: 3
c0: -1
Y1: -25125200742702138527
Y0: 631275712361080093443627372579097729730
m: 2942309812454780857174959580625797121082650591780520548459155615893205344204950445727368887008237009235463040328040082883725470745346026159304591613666306253853561846670793772820592220799691604
type: snfs
rlim: 67000000
alim: 67000000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6[/CODE]

Test sieving 5K blocks.
[CODE] Q Yield
20M 9742
60M 7226
100M 6251[/CODE]

Much better poly for C165 from 11040:i10029 (thx to Max).

[CODE]n: 548053161872286094263546390942532925280484495878287628018996658359830769025595729605632079717852442811109714651767256348336257841788345910368127498252314702339291049
Y0: -66293314740471378847093879949751
Y1: 1631428933119792335581
c0: -6502334456108684229848773957534620127960
c1: 4137968742928655885127027704264398
c2: 1330621088475088099747541529
c3: -199123773602778674989
c4: -30080739151610
c5: 856800
skew: 7541903.96641
# lognorm 52.93, E 44.95, alpha -7.98 (proj -2.42), 5 real roots
# MurphyE = 7.53624407e-13
type: gnfs
rlim: 134217727
alim: 134217727
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7[/CODE]