[QUOTE=Raman;138062]So, can you please explain to me up how you derived the 4th degree
polynomial from the 8th degree one for [tex]10,375[/tex] [tex]x^8x^7+x^5x^4+x^3x+1[/tex] [tex]x10^{25}[/tex][/quote] Substitute x = y + 1/y in the octic and see what you get ... [QUOTE=Raman;138062] I am starting to sieve for 10,375 now. 10,312+ is in Linear Algebra and will finish up within about 12 hours or so (Matrix has less than 20 million rows!) :exclaim: [SIZE=4]EMERGENCY[/SIZE] Also that I can't enter the value of [B]m[/B] in the GGNFS poly file too, because of the fact that [tex]\division_{10^{25}}^{(10^{50}+1)}[/tex] is again not an integer at all[/QUOTE]Solve the equation 10^25x = 1 (mod 10^50) in integers. The solution is the integer you want. Paul 
[QUOTE=xilman;138066]
Solve the equation 10^25x = 1 (mod 10^50) in integers. The solution is the integer you want. Paul[/QUOTE] Although it's certainly a good exercise, actually entering m in the GGNFS poly file causes it to use the rational poly xm. Enter the rational poly coefficients using Y1 and Y0, and the programs will calculate m. Greg 
[quote=xilman;138066]
Solve the equation 10[sup]25[/sup]x = 1 (mod 10[sup]50[/sup]) in integers. The solution is the integer you want. [/quote] Be careful! There exist no solution to this equation. Since 10[sup]25[/sup] is even, a multiple of it is always even, and on the right hand side, 1 (mod 10[sup]50[/sup]) is always odd. A solution is impossible to exist! [quote=xilman;138066] Substitute x = y + 1/y in the octic and see what you get ... [/quote] No hopes for degree 4. Substituting x = y + (1/y) in x[sup]8[/sup], so it gives up [tex]\sum_{z=0}^8 ^8C_z y^z (1/y)^{8z}[/tex] which is clearly being at degree 8. Other terms will have their appropriate degrees. So, when substituted, the whole algebraic polynomial will be of degree 8 only. And the linear polynomial becomes more cumbersome, in this form, with 10[sup]25[/sup](y+(1/y))  (10[sup]50[/sup]+1) 
Hi Raman.
The calculation of M should be modulo the number you're trying to factor  ie 10^25 N = (10^50+1) mod cofactor. But as xilman pointed out you just fill in the numerator and denominator in the Y0 and Y1 fields. The idea of substituting y+1/y is to take advantage of the symmetry of the octic; you write {octic} = x^4 * quartic(x+1/x) for some suitablychosen quartic, and the 10^50+1 and 10^25 are from (x + 1/x) written as (x^2+1)/x. 
[QUOTE=fivemack;138325]Hi Raman.
The calculation of M should be modulo the number you're trying to factor  ie 10^25 N = (10^50+1) mod cofactor. But as xilman pointed out you just fill in the numerator and denominator in the Y0 and Y1 fields. The idea of substituting y+1/y is to take advantage of the symmetry of the octic; you write {octic} = x^4 * quartic(x+1/x) for some suitablychosen quartic, and the 10^50+1 and 10^25 are from (x + 1/x) written as (x^2+1)/x.[/QUOTE] The reason this works is that *reversing* the coefficients of any polynomial results in a homomorphism of its splitting field, sending a root r of the polynomial to 1/r. Thus, if the coefficients of the polynomial are the same when reversed, we can replace the polynomial with one whose roots are r + 1/r and get an isomorphic field. 
[QUOTE=garo;48284][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
7 271 C214 : 1570202...53660188716054727305891 ... 7 301 C189 : 7473377...279834566763898163532521 ... 7 393 C217 : 580546345...10110568816475625168427 [/CODE][/QUOTE] These three cofactors are no longer in the ECMNET input file, and the indices 271, 301 and 393 are not in the 7/08 appendix C. That leaves 18, with the NFSNET number 7,319 sieved. with the matrix running; and 7,313 a C/D number, also sieved, with matrix running. Bruce 
count/recount
[QUOTE=bdodson;142925] ... That leaves 18, with the NFSNET number 7,319
sieved. with the matrix running; and 7,313 a C/D number, also sieved, with matrix running. Bruce[/QUOTE] OK, the database is now closer to being current than the table in the first post. There should be 15, with [code] 7 277 C201 done 7 311 C225 first 7 313 C248 done 7 323 C241 second, &etc. [/code] If I'm reading the thread activity correctly, out of 18 tables (with four base2's and two each for 3, 5, 6, 7, 10, 11 and 12, so 4+2*7 = 18) this one is the one that's gone the longest without a new factor report? No reserved numbers, either; with 311 on the more wanted list. Bruce Off Topic PS: from the old pages on Sam's site, the cover letter for page 80 (from 1998) lists a bunch of the tables as having been extended [QUOTE] to insure that every table has at least five holes [/QUOTE] which explains which tables would be extended, but the trigger seems to have been an update 2.C. There was also an update 2.E, followed the the 3rd edition of the tables, Sept 2001. I don't see any update 3.*'s; so suppose that it's unclear whether dropping one of the table below five entries would trigger an update and extension, or we might have some more time to clear an entire table (most likely 3 perhaps). 
In the DB, someone has entered the (previously unknown) factor of 7,391:
p57 = 478566296656273815311438559010751123205277732759848440243 with a p187 cofactor. However, it can be found nowhere else  at least the forum and Sam's page don't mention it, and Google doesn't return any results for it. I expect the finder will come forward soon, but anyway, that's one "impossible" out of the way. :smile: 
[quote=10metreh;199499]In the DB, someone has entered the (previously unknown) factor of 7,391:
p57 = 478566296656273815311438559010751123205277732759848440243 with a p187 cofactor. However, it can be found nowhere else  at least the forum and Sam's page don't mention it, and Google doesn't return any results for it. I expect the finder will come forward soon, but anyway, that's one "impossible" out of the way. :smile:[/quote] Have you checked up the ECMNET page of Mr. Paul Zimmermann? 
[QUOTE=Raman;199502]Have you checked up the ECMNET page of Mr. Paul Zimmermann?[/QUOTE]Indeed, Paul mailed it out to the usual suspects yesterday evening.
Paul (the other one) 
LA Failure?
Did the LA for 7,311 fail?

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