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From: Archimedes Plutonium on 22 Feb 2010 03:22
My last post remarked about the definition of prime, and how it would
relate with a
Algebra Zone, a zone in which multiplication and division would be
broken down
after 10% of all the numbers. That we cannot rely on Algebra to tell
us if a
infinite integer is prime or composite with certainty, since Algebra
would only be
good for 10% of all the numbers that exist.

So we defined the boundary between Finite and Infinite as 10^500. So
is the
number 9*999..99 and 1*000..001 where the asterik means the 10^500
place value.
So are those two twin primes? Or is one of them prime? Or is neither
prime?

Now it may well be that there is never a well-defined definition of
infinite number
place value and that it is impossible to tell where the 1 digit in the
infinite
number 1*0000.....0000 is located. Or it may not.

But one question that certainly has a answer in mathematics is which
one of these
numbers in this sequence is a prime number?

97, 997, 9997, 99997, up to the upper bound of 10^500 ?

Another thing we know for sure is that all primes after 2 must end in
a 1,3,7, or 9
digit. So we have another sequence to question:

91, 991, 9991, 99991, up to the upper bound of 10^500

89, 989, 9989, 99989, up to the upper bound of 10^500

Now so far these lists are purely patterned lists such as the 9s block
repeating and we can have other blocks repeating such as 821, 821821,
821821821, up to the upper bound of 10^500

But here is a question at this moment of these patterned lists.

The question is what math formula fits for the 97 sequence for
primeness
with an upper bound of 10^500?

In this sequence
97, 997, 9997, 99997, up to 10^500 upper bound

How many of those numbers are prime numbers and is the formula that
characterizes the density of those primes from 97 to the upper bound
of 10^500
similar to the formula x/Ln(x) the difference being that this is a
patterned
sequence and not an all inclusive interval.

Then the question comes, whether the same formula for the 97 sequence
covers the 91 sequence or the 89 sequence?

Now the patterned sequence of the 101 can look like this:

101, 1001, 10001, 100001, up to 10^500

or look like this:

101, 101101, 101101101, up to 10^500

Now I expect that the 97 and 89 sequences to be almost identical as
far as
primeness density, but that 101 sequence to be a little bit off and
for the
sequence of 821 to be far more off with a upper bound placed at
10^500 simply because the primes in those sequences started with a
larger
number than that of 97 or 89 sequences.

What I am driving at, ultimately in this questioning, is that primes
do follow
a density pattern of x/Ln(x) and that 10^500 precision definition of
the boundary
between finite and infinite. That we should be able to say something
about the
patterned sequences of odd numbers and how many primes contained in
that
sequence. And whether a sequence such as the 97 and 89 have the same
number of primes from 0 to 10^500? I think they should have the same
number
of primes. This maybe a math proof already proven.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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