  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.

Cryptography and Security