A system of two Diophantine inequalities with primes

Key Points

• The main goal is to establish conditions under which a system of Diophantine inequalities has prime solutions.
• Fixed k ≥ 7, define v based on k and constants.
• Set parameters 1 < d < c < v and conditions on μ and ν.
• Utilize inequalities involving prime sums to establish bounds.
• Confirmed conditions yield prime solutions p1,…,pk.
• Demonstrated specific bounds on real numbers related to primes.
• Established logarithmic relationships in inequalities.