20220622, 13:03  #496 
Apr 2020
857 Posts 
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.

20220622, 14:17  #497  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:
Last fiddled with by sweety439 on 20220622 at 14:21 

20220622, 14:35  #498  
Apr 2020
857 Posts 
Quote:
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 degreehalving trick we would have a degree46 polynomial. 

20220622, 15:37  #499 
Sep 2009
2,389 Posts 
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. 
20220622, 16:21  #500 
Sep 2009
2,389 Posts 
Update, I've generated a .poly for 13^288+1 and msieve rates it's escore as 4.429e12 which is only slightly worse that the record for GNFS 152 (5.193e12). So SNFS might be quicker since it saves time looking for a .poly.
If you want to use the SNFS .poly it is: Code:
n: 71438373999729136352606292343760129183029739070786196603000989067197279062061478948276862644139546551399870347831118641859705696979258190407032284290689 type: snfs # m=13^32 m: 442779263776840698304313192148785281 c6: 1 c3: 1 c0: 1 # msieve rating: skew 1.00, size 1.484e10, alpha 1.996, combined = 4.429e12 rroots = 0 
20220622, 16:42  #501 
Apr 2020
857 Posts 
Usual warning that you can't directly compare Escores for polys with different degrees. Lower degrees overpeform their scores, higher degrees underperform.

20220628, 17:32  #502 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
110111111001_{2} Posts 
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

20220629, 00:17  #503  
Jun 2012
2×19×97 Posts 
Quote:
The ratio holds much better at higher difficulty. 

20220718, 05:59  #504  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 
Quote:


20220718, 11:10  #505  
Jun 2012
111001100110_{2} Posts 
Quote:


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