Goldbach Primes Associated with 2n

Muhammad Nawaz

Abstract


For 2n= p+q where p and q are primes, the pair (p, q) is called Goldbach pair (or Goldbach partition) and any constituent prime of a Goldbach pair for 2n will be called the Goldbach prime associated with 2n. the Goldbach primes associated with 2n are distributed evely on both sides of n. in the paper we show that the number of Goldbach primes associated with 2n is odd if and only if n is prime. We also prove that if p is a Goldbach prime associated with 2n then any prime q is Goldbach prime associated with 2n + (q-p).

Keywords


Prime; Goldbach pair; ceiling function

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