mersenneforum.org "Mixed Sierpinski conjecture base 5" proven!! (if probable primes allowed)
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 2020-12-21, 12:52 #1 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5×7×83 Posts "Mixed Sierpinski conjecture base 5" proven!! (if probable primes allowed) This conjecture is from http://www.kurims.kyoto-u.ac.jp/EMIS...rs/i61/i61.pdf, this article is about the mixed Sierpinski (base 2) theorem, which is that for every odd k<78557, there is a prime either of the form k*2^n+1 or of the form 2^n+k, we generalized this theorem (may be only conjectures to other bases) to other prime bases (since the dual form for composite bases is more complex when gcd(k,b) > 1 (see thread https://mersenneforum.org/showthread.php?t=21954), we only consider prime bases), we conjectured that for every k
 2020-12-21, 14:08 #2 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5·7·83 Posts Note that the weight of b^n+k is the same as that of k*b^n+1, if gcd(k,b)=1

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