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2018-12-14, 21:48   #10
sweety439

Nov 2016

17·149 Posts

Quote:
 Originally Posted by sweety439 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.
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
 R4.txt (241 Bytes, 72 views)

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