The title of this post is not capricious in "all sorts of forms" There
are the two listed forms but there are many
other forms of primes such as k^2 +1 and k^2 -1 and then there are
forms such as k!+1 and k!-1.
So there are very many forms of primes, and if my memory is correct,
someone thought they proved
a certain form of primes is a finite set. I say they must review their
alleged proof because they
started with the assumption that Natural Numbers are finite integers
when in fact the true blue
Natural Numbers are the AP-adics or infinite integers.
A number such as this is a prime number 100000.......00000003 which is
an infinite integer whose
front-view is "1" and whose endview is "3". Another prime number
is ....1413121110987654321.
So in earlier times, mathematicians never realized that the set of
primes is so much larger than their
deluded picture of primes. They were playing cards with over half the
deck missing.
In a previous post I gave a proof of the infinitude of Twin Primes by
grafting 11 and 13 unto the backbone
of the above Champernownes number .....1413121110987654321. So I
constructed a infinite string of
Twin Primes.
Now, can I construct an infinite string of primes of form 2k+1? It is
a little more challenging than Twin
Primes construction.
It goes like this. I start with the prime number of .......
1111100001111000111001101. Now it is
similar to the pattern of Champernownes number only its digits are 1
and 0. It is prime because these
numbers are "Irrational Counting Numbers". Now I have to give a
precise definition of Irrational Natural
Numbers. We have definition of Composite Natural Number and Prime
Natural Number but now
we must provide definitions of Irrational Natural Numbers and Rational
Natural Numbers. I am not going
to do that here for this is already long enough.
Now this number .......1111100001111000111001101 in the form 2k+1
is .......2222200002222000222002203
which is also prime. Now the next prime I construct is to scoot down
leftwards and eliminate the first
"1" as this number .......111110000111100011100110 which is not prime
itself but when I do the
2k+1 it becomes .......222220000222200022200221 Now I infinitely scoot
down the line and produce a
new prime of form 2k+1. Thus the set of all primes of form 2k+1 is an
infinite set. Likewise for primes
of form 2k-1 and likewise for all other forms.
Even the form that some mathematicians of the past were thought to be
a finite set, because of their
alleged proof, is not questioned since they started their work with
the deluded belief that Natural Numbers
are finite integers.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
