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**1 - 5**of**5**### ELEMENTARY PROBLEMS WHICH ARE EQUIVALENT TO THE GOLDBACH’S CONJECTURE

"... Abstract. We denote by {p1=2, p2=3, p3=5,..., pk,...} the sequence of increasing primes, and for each positive integer k≥1 let S(k):=min{2n>pk: 2n−p1, 2n−p2,..., 2n−pk all are composite numbers}. We prove that the following conjectures are equivalent to the Goldbach’s conjecture. Conjecture B. Fo ..."

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Abstract. We denote by {p1=2, p2=3, p3=5,..., pk,...} the sequence of increasing primes, and for each positive integer k≥1 let S(k):=min{2n>pk: 2n−p1, 2n−p2,..., 2n−pk all are composite numbers}. We prove that the following conjectures are equivalent to the Goldbach’s conjecture. Conjecture B. For every positive integer k, we have S(k) ≥ pk+1 + 3. Conjecture C. For every positive integer k, the number S(k) is the sum of two odd primes. 1.

### Sparse Periodic Goldbach Sets

"... In this paper, we consider sets of natural numbers P ⊆ N = {0, 1, 2, 3,...} which satisfy the property that every x in N is expressible as the arithmetic average of two (not necessarily distinct) elements from P. We call such sets “Goldbach sets”, and demonstrate the existence of periodic Goldbach s ..."

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In this paper, we consider sets of natural numbers P ⊆ N = {0, 1, 2, 3,...} which satisfy the property that every x in N is expressible as the arithmetic average of two (not necessarily distinct) elements from P. We call such sets “Goldbach sets”, and demonstrate the existence of periodic Goldbach sets with arbitrarily small positive density in the natural numbers. 1

### Computational Sieving Applied to some Classical Number-Theoretic

, 1998

"... Computational sieving applied to some classical number-theoretic problems H.J.J. te Riele Modelling, Analysis and Simulation (MAS) ..."

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Computational sieving applied to some classical number-theoretic problems H.J.J. te Riele Modelling, Analysis and Simulation (MAS)

### Weak Golbach’s Conjecture from Isomorphic and Equivalent Odd Prime Number Functions Research

"... Abstract: Mathematicians has been trying to prove the weak Goldbach’s conjecture by adding prime numbers, as stated in the conjecture. However, we believe that the solution does not need to be analytically solved. Instead of trying to add prime numbers to prove the conjecture, we developed a prime n ..."

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Abstract: Mathematicians has been trying to prove the weak Goldbach’s conjecture by adding prime numbers, as stated in the conjecture. However, we believe that the solution does not need to be analytically solved. Instead of trying to add prime numbers to prove the conjecture, we developed a prime number function Podd(x)p>2, including odd primes p> 2, isomorphic and equivalent to a function Nodd(x)n>1, including odd natural numbers greater than one, nodd> 1, in which, the sum of three of its elements result in odd numbers greater than 7, proving the conjecture. MSC: 11P32, 37M10