Hi Bob,
Quote:
Actually, the *really* interesting question is whether the number would be
faster with SNFS or GNFS. SNFS lets us take advantage of the algebraic
factor 2^152+1, but requires a quartic, which is suboptimal for numbers
this size.

Using the (only) trick I know I get a quadratic and a linear:
f(x) = x^2  x  1
g(x) = 2^152*x2^3041
x=(2^152+1/2^152)
Clever selection of polynomials is certainly not my forte and I've probably missed something.
Any tips?
Here is PARI code to show the process I used to reach the quadratic and linear:
Code:
x^608  x^456 + x^304  x^152 + 1
y=x^152
y^4  y^3 + y^2  y + 1
(y^4 + y^2)  (y^3 + y) + 1
(y^4 + y^2)  (y^3 + y) + 1
( (y^4 + y^2)  (y^3 + y) + 1 ) / y^2
( (y^2 + 1)  (y^1 + y^1) + y^2 )
y^2 + 1  y^1  y^1 + y^2
y^2 + y^2  (y^1 + y^1) + 1
z=y+y^1
y^2 + y^2  z + 1
z^2= (y^2 + y^2 + 2)
z^2  2  z + 1
z^2  z  1
n=(2^760+1)/(2^152+1)
f(x) = x^2  x  1
g(x) = 2^152*x2^3041
m=(2^152+1/2^152)
f(m)%n
g(m)%n
Don