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Old 2018-12-14, 21:48   #10
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Nov 2016

17·149 Posts

Originally Posted by sweety439 View Post
The 1st, 2nd and 3rd conjectures for R4 and R10 are all proven (the conjectures cover the original conjectures (, 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.
Upload the text file for additional k's for R4, if you need it.

For R10, the n for k = 343 is 1, since (7*10^1-1)/3 (= 23) and (49*100^1+7*10^1+1)/3 (= 1657) are both primes.
Attached Files
File Type: txt R4.txt (241 Bytes, 72 views)

Last fiddled with by sweety439 on 2018-12-14 at 22:01
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