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^q1)/gcd(m*2^q1,3) 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^n1)/gcd(3611,41) 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^q1)/3 and (49*100^q+7*10^q+1)/3 are both primes), and we found the n for all of these k's.

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For R10, the n for k = 343 is 1, since (7*10^11)/3 (= 23) and (49*100^1+7*10^1+1)/3 (= 1657) are both primes.