Riesel conjecture base 243 algebraic factors

Started: Sept. 10, 2023
Last update: Sept. 10, 2023

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 = = 11 or 50 mod 61:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*243^q - 1) *
     (m*243^q + 1)
   odd n:
     factor of 61

(Condition 2):
All k where k = 3*m^2
and m = = 23 or 38 mod 61:
   even n:
     factor of 61
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*9^n*3^q - 1] *
     [m*9^n*3^q + 1]

(Condition 3):
All k = m^5 for all n; factors to:
(m*3^n - 1) *
(m^4*81^n + m^3*27^n + m^2*9^n + m*3^n + 1)