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2018-12-14, 21:42   #9
sweety439

Nov 2016

3·5·132 Posts

Quote:
 Originally Posted by sweety439 See post https://mersenneforum.org/showpost.p...&postcount=281, the conjectured k's for R4 are 361, 919, 1114, ..., and the conjectured k's for R10 are 334, 1585, 1882, ... and we can prove them.
The 1st, 2nd and 3rd conjectures for R4 and R10 are all proven (the conjectures cover the original conjectures (https://mersenneforum.org/showthread.php?t=21839), the additional k's for R4 are only the square k's except 361 (we need n such that (m*2^q-1)/gcd(m*2^q-1,3) and (m*2^q+1)/gcd(m*2^q+1,3) are both primes (where q=n/2, and m=sqrt(k)) for all q <= 33 except q = 19 (since 19^2 = 361, and (361*4^n-1)/gcd(361-1,4-1) has covering set {3, 5, 7, 13})), and the additional k's for R10 are only k = 343 (we need n such that (7*10^q-1)/3 and (49*100^q+7*10^q+1)/3 are both primes), and we found the n for all of these k's.

Last fiddled with by sweety439 on 2018-12-14 at 21:42