Brent tables reservations

[charybdis]

Originally Posted by kruoli

Where is my error thinking that both have >300 SNFS difficulty? Is this wrong because of algebraic factors?

Yes, both exponents are divisible by 3 so you can divide out the algebraic factors 13^94+1 and 13^96+1 respectively. So you have to multiply the size of the number by 2/3 to get the actual difficulty.

[sweety439]

Originally Posted by charybdis

Yes, both exponents are divisible by 3 so you can divide out the algebraic factors 13^94+1 and 13^96+1 respectively. So you have to multiply the size of the number by 2/3 to get the actual difficulty.

The nontrivial parts are Phi(564,13) and Phi(576,13), where Phi is the cyclotomic polynomial, thus the SNFS difficulty should be eulerphi(564)*log(13) = 204.9656 and eulerphi(576)*log(13) = 213.8771, right?

[charybdis]

Originally Posted by sweety439

The nontrivial parts are Phi(564,13) and Phi(576,13), where Phi is the cyclotomic polynomial, thus the SNFS difficulty should be eulerphi(564)*log(13) = 204.9656 and eulerphi(576)*log(13) = 213.8771, right?

Correct for the second one, but not the first.
288 = 2*3*47, so 13^288+1 has algebraic factors 13^94+1 and 13^6+1, which themselves share a common factor 13^2+1. We can't pull out both algebraic factors and end up with a usable SNFS polynomial; even with the degree-halving trick we would have a degree-46 polynomial.

[chris2be8]

13^282+1 is probably easier by GNFS, SNFS 210 is about as hard as GNFS 155, but 13^282+1's cofactor is 147 digits.

13^288+1 is about equal difficulty by SNFS and GNFS. SNFS 214 is about as hard as GNFS 152 which is how many digits the cofactor is.

Neither should take you too long on a decent PC.

[chris2be8]

Update, I've generated a .poly for 13^288+1 and msieve rates it's e-score as 4.429e-12 which is only slightly worse that the record for GNFS 152 (5.193e-12). So SNFS might be quicker since it saves time looking for a .poly.

If you want to use the SNFS .poly it is:

n: 71438373999729136352606292343760129183029739070786196603000989067197279062061478948276862644139546551399870347831118641859705696979258190407032284290689
type: snfs
# m=13^32
m: 442779263776840698304313192148785281
c6: 1
c3: -1
c0: 1
# msieve rating: skew 1.00, size 1.484e-10, alpha 1.996, combined = 4.429e-12 rroots = 0

[charybdis]

Originally Posted by chris2be8

Update, I've generated a .poly for 13^288+1 and msieve rates it's e-score as 4.429e-12 which is only slightly worse that the record for GNFS 152 (5.193e-12). So SNFS might be quicker since it saves time looking for a .poly.

Usual warning that you can't directly compare E-scores for polys with different degrees. Lower degrees overpeform their scores, higher degrees underperform.

[sweety439]

Originally Posted by chris2be8

SNFS 210 is about as hard as GNFS 155

What is the approximately equivalent for SNFS and GNFS? I guess that SNFS difficulty n is approximately equivalent to GNFS difficulty (2/3)*n, however, if my guess is true, then SNFS 210 is approximately equivalent to GNFS 140

[swellman]

Originally Posted by sweety439

What is the approximately equivalent for SNFS and GNFS? I guess that SNFS difficulty n is approximately equivalent to GNFS difficulty (2/3)*n, however, if my guess is true, then SNFS 210 is approximately equivalent to GNFS 140

The commonly used ratio of GNFS/SNFS is 0.68 to 0.69. This ratio doesn’t hold true here for the case of SNFS 210 ~ GNFS 155 but those values are on the low side.

The ratio holds much better at higher difficulty.

[sweety439]

Originally Posted by swellman

The commonly used ratio of GNFS/SNFS is 0.68 to 0.69. This ratio doesn’t hold true here for the case of SNFS 210 ~ GNFS 155 but those values are on the low side.

The ratio holds much better at higher difficulty.

So can you factor these two numbers (the composite cofactors of 13^282+1 and 13^288+1)? They are much smaller than your C193, also they have simple SNFS polynomials, while your C193 can only be used GNFS

[swellman]

Originally Posted by sweety439

So can you factor these two numbers (the composite cofactors of 13^282+1 and 13^288+1)? They are much smaller than your C193, also they have simple SNFS polynomials, while your C193 can only be used GNFS

I can help you work these numbers. Please PM me.