View Single Post
Old 2021-01-09, 10:38   #115
sweety439
 
Nov 2016

282010 Posts
Default

It is conjectured that for all simple families x{y}z cannot be proved as only contain composites (for numbers > base) in one of these four ways:

** Periodic sequence p of prime divisors with p(n) | (xyyy...yyyz with n y's)
** Algebraic factors (e.g. difference-of-squares factorization, difference-of-cubes factorization, sum-of-cubes factorization, difference-of-5th-powers factorization, sum-of-5th-powers factorization, Aurifeuillian factorization of x^4+4*y^4, etc.) of x{y}z
** The combine of the above two ways (like the case of {B}9B in base 12)
** Reduced to (b^(r*n+s)+1)/gcd(b+1,2), and r*n+s can never be power of 2 (like the case of 8{0}1 in base 128)

Then x{y}z contain primes (for numbers > base).

Last fiddled with by sweety439 on 2021-04-05 at 16:12
sweety439 is offline   Reply With Quote