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**1 - 4**of**4**### 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)

### 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