(2). Brief History of Goldbach's Conjecture
Goldbach's Conjecture
In 1725 Goldbach became professor of mathematics
and historian at St. Peterburg. Then, in 1728, he went to Moscow
as tutor to Tsar Peter II. Goldbach's Conjecture states:
Every even positive integer greater than
3 is the sum of two (not necessarily distinct) primes.
This famous conjecture was made in 1742 and
for 255 years, no one has succeeded in proving or disproving the
validity of this conjecture. The term Goldbach's sequence was
not defined previously. It is defined here as the square of
two identical prime sequences. The sequence is not always filled because
unlike in Goldbach's Conjecture where one is free to choose any two primes
between 3 to infinity, here you are restricted to the choice within the finite
prime sequences chosen to generate the Goldbach's sequence.
There are large gaps in it. In other words, sporadically, Goldbach's
sequence is filled or unfilled depending on the lengths of the
prime sequences. There are actually two versions by Goldbach,
viz., the binary and tertiary Goldbach's conjectures, the former
being more well known than the latter. We will confine the search
to the first version. Right now, we do not know whether there
are many or few full Goldbach's sequences. Neither do we know
whether there is an incomplete Goldbach's sequence with the highest
percentage of missing terms for its length.
