Riesel conjecture base 540 algebraic factors

Started: Sept. 10, 2023
Last update: Nov. 15, 2024

Compiled by Gary Barnes
Riesel conjectures
Riesel conjectures powers of 2
Riesel conjecture reservations
Sierpinski conjectures
Sierpinski conjectures powers of 2
Sierpinski conjecture reservations

(Condition 1):
All k where k = m^2
and m = = 52 or 489 mod 541:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*540^q - 1) *
     (m*540^q + 1)
   odd n:
     factor of 541

(Condition 2):
All k where k = 15*m^2
and m = = 229 or 312 mod 541:
   even n:
     factor of 541
   for odd n let k = 15*m^2
   and let n=2*q-1; factors to:
     [m*6^n*15^q - 1] *
     [m*6^n*15^q + 1]

(Condition 3):
k = 61009:
   n = = 0, 2 mod 4:
     let n = 2*q; factors to:
     (247*540^q - 1) *
     (247*540^q + 1)
   n = = 1 mod 4:
     factor of 1009
   n = = 3 mod 4:
     factor of 17