THE EDGE CONJECTURE
There are a finite number of primes.
All the proofs that there are an infinite number of primes, are based
on the rather rash and unsupported assumption that numbers behave in
the same way for enormous numbers as they do for tangible everyday
numbers. This is clearly ridiculous as no one has seen, comprehended
and become familiar with a really huge number, in its wild
unabbreviated state, to be able to verify its behaviour under the
basic mathematical operations such as addition, division etc.
Newtonian mechanics appeared totally accurate and satisfactory and was
unchallenged for many years, but was eventually found to break down
for very large masses, distances and velocities. In a similar way, I
suggest that beyond a certain finite, but as yet unapproached, limit
arithmetic breaks down into quite different behaviour.
To a young child, whose arithmetical understanding and manipulation is
limited by her 10 fingers and thumbs, numbers beyond 10( the number
beyond which there are insufficient fingers to set up a one to one
correspondence with the numbers involved) are mysterious and have
unknown behaviour. This sense of excitement at the unknown properties
of large numbers is shown when children talk with wonder of "What is
one million plus two million?". It seems incredible to them
that two such huge numbers can be tamed by the same logic as 1+2=3.
I venture that, at the point beyond which no direct correspondence
can be found for a number, i.e. the number of elementary particles in
the universe, all arithmetic breaks down.
Numbers are too often treated coldly and impersonally, without regard
for their different characters. Who could possibly consider that 4,
with its familiar properties and real world affinities, has a similar
character to the rather anonymous, less frequently encountered 71?
Numbers so huge and powerful as to be unimaginable may well simply
shrug off arithmetical convention and behave as they choose, returning
unexpected results to simple operations. They may consider being prime
as being a number without ancestors and may choose to disassociate
themselves from such outlandishness and the accompanying social
stigma.
All newly discovered primes such as those found by GIMPS, merely raise
the lower limit at which this may happen. Beyond this limit, who knows
what strange behaviour may occur? All conventional proofs and logic
mean nothing. In such an environment an entity such as a superodd
factor which is a factor of all odd numbers, in the same way that 2 is
a factor of all even numbers, could feasibly exist.
The rest of you are free to continue your vain search for an ever
larger prime, beyond which you always know that there are more.
Personally, I will continue to contribute, but with the higher, more
concrete, goal of helping to find THE FINAL PRIME NUMBER.
#\o \
# ) |
#/o /
I have a brilliant proof of the above, but my email software does not
support margins.
-----------------------------------
Kevin Edge - [EMAIL PROTECTED]
-----------------------------------
The opinions herein are my own and,
unless explicitly stated,
may not represent those of MDIS.
================================
