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New experimental results concerning the Goldbach conjecture
 ALGORITHMIC NUMBER THEORY (THIRD INTERNATIONAL SYMPOSIUM, ANTSIII
, 1998
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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.
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
Dealing with prime numbers I.: On the Goldbach
"... In this paper we present some observations about the wellknown Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also determine very thin and low diverging ranges in which the proba ..."
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In this paper we present some observations about the wellknown Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also determine very thin and low diverging ranges in which the probability of finding a prime is one.
1 Some issues on Goldbach Conjecture
"... This paper presents a deterministic process of finding all pairs (p, q) of odd numbers (composites and primes) of natural numbers ≥ 3 whose sum (p + q) is equal to a given even natural number 2n ≥ 6. Subsequently, based on the above procedure and also relying on the distribution of primes in the set ..."
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This paper presents a deterministic process of finding all pairs (p, q) of odd numbers (composites and primes) of natural numbers ≥ 3 whose sum (p + q) is equal to a given even natural number 2n ≥ 6. Subsequently, based on the above procedure and also relying on the distribution of primes in the set of natural numbers, we propose a closed analytical formula, which estimates the number of primes which satisfy Goldbach’s conjecture for positive integers ≥ 6. 1.