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New experimental results concerning the Goldbach conjecture
 ALGORITHMIC NUMBER THEORY (THIRD INTERNATIONAL SYMPOSIUM, ANTSIII
, 1998
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Checking the Goldbach conjecture up to 4 × 1011
 MR 94a:11157, Zbl 783.11037
, 1993
"... Abstract. One of the most studied problems in additive number theory, Goldbach's conjecture, states that every even integer greater than or equal to 4 can be expressed as a sum of two primes. In this paper checking of this conjecture up to 4 • 10 " by the IBM 3083 mainframe with vector pro ..."
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Abstract. One of the most studied problems in additive number theory, Goldbach's conjecture, states that every even integer greater than or equal to 4 can be expressed as a sum of two primes. In this paper checking of this conjecture up to 4 • 10 " by the IBM 3083 mainframe with vector processor is reported. 1.
On Partitions of Goldbach’s Conjecture
"... An approximate formula for the partitions of Goldbach’s Conjecture is derived using Prime Number Theorem and a probabilistic approach. A strong form of Goldbach’s conjecture follows in the form of a lower bounding function for the partition function of Goldbach’s conjecture. Numerical computations s ..."
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An approximate formula for the partitions of Goldbach’s Conjecture is derived using Prime Number Theorem and a probabilistic approach. A strong form of Goldbach’s conjecture follows in the form of a lower bounding function for the partition function of Goldbach’s conjecture. Numerical computations suggest that the lower and upper bounding functions for the partition function satisfy a simple functional equation. Assuming that this invariant scaling property holds for all even integer n, the lower and upper bounds can be expressed as simple exponentials. 1 Goldbach’s Conjecture and Recent Progress Goldbach’s Conjecture states that every even integer> 2 can be expressed as a sum of two primes. The proof remains an unsolved problem since Goldbach first wrote the conjecture in a letter to Euler in 1792. However, significant progress has been made in recent years.
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
On Partitions of Goldbach’s Conjecture
, 2000
"... An approximate formula for the partitions of Goldbach’s Conjecture is derived using Prime Number Theorem and a probabilistic approach. A strong form of Goldbach’s conjecture follows in the form of a lower bounding function for the partitions of Goldbach’s conjecture. Numerical computations suggest t ..."
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An approximate formula for the partitions of Goldbach’s Conjecture is derived using Prime Number Theorem and a probabilistic approach. A strong form of Goldbach’s conjecture follows in the form of a lower bounding function for the partitions of Goldbach’s conjecture. Numerical computations suggest that the lower and upper bounding functions for the partitions satisfy a simple functional equation. Assuming that this invariant scaling property holds for all even integer n, the lower and upper bounds can be expressed as simple exponentials. 1 Goldbach’s Conjecture and Recent Progress Goldbach’s Conjecture states that every even integer> 2 can be expressed as a sum of two primes. The proof remains an unsolved problem since Goldbach first wrote the conjecture in a letter to Euler in 1792. However, significant progress has been made in recent years. On the front of verifying Goldbach’s Conjecture, no counterexample has