For 1 < d < c < 79/71 and 1 < α < β < 6^{1-d/c}, sufficiently large N1, N2 with α ≤ N2/N1^{d/c} ≤ β admit six primes p_i satisfying the two Diophantine inequalities with errors N^{-(1/c)(79/71-c)} (log N)^{201} and analog for d.
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On a system of two Diophantine inequalities with six prime variables
For 1 < d < c < 79/71 and 1 < α < β < 6^{1-d/c}, sufficiently large N1, N2 with α ≤ N2/N1^{d/c} ≤ β admit six primes p_i satisfying the two Diophantine inequalities with errors N^{-(1/c)(79/71-c)} (log N)^{201} and analog for d.