Riesel conjecture base 936 algebraic factors

Started: Sept. 10, 2023
Last update: Sept. 14, 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 = = 196 or 741 mod 937:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*936^q - 1) *
     (m*936^q + 1)
   odd n:
     factor of 937

(Condition 2):
k = 64:
   n = = 0, 2, 4 mod 6:
     let n = 2*q; factors to:
     (8*936^q - 1) *
     (8*936^q + 1)
   n = = 0, 3 mod 6:
     let n=3*q; factors to:
     (4*936^q - 1) *
     [16*936^(2*q) + 4*936^q + 1]
   n = = 1 mod 6:
     factor of 37
   n = = 5 mod 6:
     factor of 109

(Condition 3):
k = 13689:
   n = = 0, 2, 4 mod 6:
     let n = 2*q; factors to:
     (117*936^q - 1) *
     (117*936^q + 1)
   n = = 1, 4 mod 6:
     let n=3*q+1; factors to:
     (234*936^q - 1) *
     [54756*936^(2*q) + 234*936^q + 1]
   n = = 3 mod 6:
     factor of 37
   n = = 5 mod 6:
     factor of 109

(Condition 4):
k = 59904:
   n = = 0 mod 6:
     factor of 37
   n = = 1, 3, 5 mod 6:
     let n = 2*q-1; factors to:
     (8*936^q - 1) *
     (8*936^q + 1)
   n = = 2, 5 mod 6:
     let n=3*q-1; factors to:
     (4*936^q - 1) *
     [16*936^(2*q) + 4*936^q + 1]
   n = = 4 mod 6:
     factor of 109