On Randomness of Goldbach Sequences
This work addresses the theoretical analysis of number sequences for applications in randomness testing, but it appears incremental as it builds on known concepts like Goldbach partitions.
The paper tackled the problem of analyzing the randomness of Goldbach sequences by examining autocorrelation functions and specific partitions called Goldbach ellipses, showing that these sequences exhibit excellent randomness properties.
We consider the use of Goldbach numbers as random sequences. The randomness is analyzed in terms of the autocorrelation function of the sequence of number of partitions. The distinct representations of an even number n as the sum of two primes is a local maximum for multiples of the product of the consecutive smallest primes less than the number. Specific partitions, which we call Goldbach ellipses, are examined. It is shown that such ellipse sequences also have excellent randomness property.