#161 comparing the world's tiniest Primes with the world's largest Primes; new textbook: "Mathematical-Physics (p-adic primer) for students of age 6 onwards"
Archimedes Plutonium
Archimedes Plutonium wrote last night:
>
> By the way these are the primes in the last 100 numbers before
> we reach the last and largest integer in the world 99999.....9999999
>
> .....999997
> ......999991
> .......9999989
> ......9999983
> .......99999979
>
> .....9999973
> ......99999971
> .......99999967
> ......999999961
> .......99999959
>
>
> .....9999953
> ......9999949
> .......9999947
> ......99999943
> .......99999941
>
> .....99999937
> ......99999929
> .......99999923
> ......999999913
> .......999999911
>
> ........9999999907
> .........9999999901
>
> So there are 22 Primes in the last interval of one hundred Integers
> and there are 24
> primes in the first one hundred Integers.
>
> Is there any explanation for the break in symmetry? Yes, because in
> the first
> one hundred there is the Triplet primes of 2,3,5 and if not for that,
> then the last
> 100 integers would have the same quantity of primes as the first 100
> integers.
Before I dive into math, I want to comment on the evolution of the
Internet in the past 14 years of my experience of writing science to the
sci newsgroups. I loved it when DejaNews was doing the sci newsgroups
for in 1 second I could reach the post I wanted to reach. With Google
doing the sci newsgroups and their latest format, it now takes me
sometimes 3 minutes to reach the post I want to reach. And I hear Google
had record profits for the fiscal quarter. So what I suspect is
happening is that as the commercialization creeps forward to where the
Internet is like the analog of TV, that science discussions become less
and less money making, they are in a sequence of increasing time wasted
to reach a post you want to reach as this sequence: 1 second in 1993 to
3 minutes by 2007 to what? 5 minutes by 2009??
It looks to me as though I need to rely more and more on my ISP reader
and less on Google. Maybe those that engineer the newsgroup reader at
Google, never factor in the idea-- how much time it takes for a reader
to get to a post that he/she wants to get to? Just yesterday I needed to
get to a post that was 151st and I had to wait for every 25 post
segments to unwind before I reached beyond the 150 segment.
It seems to me that Google engineers do not have the best priority in
their plans-- speed, speed and more speed. If it takes me 3 minutes to
get to what I want to read, then I look elsewhere.
MATH TALK:
Above I made the mistake of saying there are 24 primes in the first 100
Counting Numbers which should have read there are 25 primes. Now it is
very interesting to compare the list of the world's largest primes in
the the last 100 Counting Numbers with the smallest primes from 0 to
100. Here is that list:
.....999997 97
.....9999991
......9999989 89
.......99999983 83
.......99999979 79
......999999973 73
......999999971 71
......99999967 67
......999999961 61
.......9999999959 59
.......9999999953 53
.....9999999949
.....9999999947 47
......999999943 43
.......99999941 41
.......99999937 37
31
......999999929 29
......999999923 23
19
17
......99999913 13
......999999911 11
.......9999999907 7
.......9999999901 5
3
2
Now obviously the old math with its Prime Distribution Theorem that
prime density follows a logarithmic function that becomes sparse in
primes the further we go out towards infinity is false as that the above
attestifies that there are almost the same number of Primes in the last
100 Counting Numbers as there are primes in the first 100 Counting
Numbers, specifically 22 and 25. Now if we were to deny that 2 and 3 and
5 were prime numbers since they are strange because 2 is even and that
3 has no space between 2 and 3 as consecutive ordered primes for there
are no other consecutive ordered primes in all the Infinite Integers.
And 5 is oddball also since it is the only prime that ends in the 5
digit. So if we were to say "discount" the first three primes of the
smallest primes then their quantity per the density of 100 Counting
Numbers would equal the quantity of the largest primes. But we should
not consider them strange or oddball because this is the start of the
Counting Numbers and when you start something like this, you must expect
that the first, second third and fourth and fifth are more likely to
have to be prime numbers since this is a starting point of all the
Counting Numbers, for we should not expect 3 to be divisible by 2 and
if it were, the Counting Numbers would collapse for lack of energy or
motion to go forward.
But let us examine the above list for SYMMETRY Comparison. And if I
did my calculations correctly about whether a number such as
.....99999949 is really prime or not.
And what I notice is that there is a huge stack of primes in the 40s
range. Can there be some sort of explanation for that occurence? I would
have thought that the reasonable explanation is that since 2 is prime
that it causes a elevation of primes in the 40s range, but that
explanation does not suffice for the world's largest primes because it
is at the other end of the spectrum from 2 and so the 40s range would
not be elevated once we reach .....99999 series.
We notice another pattern, that each range usually has two primes in it
regardless of whether we have the 0 to 100 Counting Numbers or the
.....999999999 to ......99999900 Counting Numbers.
So that if a mathematician were to hold a bet and given any range in any
Series of Counting Numbers, that the best bet is that there are two
primes sitting in that range. So if asked how many primes from
......5656565656130 to ....565656140
the best bet is two primes.
Now there is one highly symmetrical pattern in that the 20s range
and the 50s range, 60s range, 70s range and 80s range match exactly
the primes. So that 50% of the smallest prime ranges matches the
largest prime ranges.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
Archimedes Plutonium
Archimedes Plutonium wrote:
So let me try to show what the most dense collection of Primes in
an interval of 100 Counting Numbers would look like. Such an interval
will contain alot of Triplet Primes which is similar to 3,5,7 in the
smallest Primes. I did this exercise some months and years back, so this
is nothing new to me. And I remember Dik Winter commenting on the word
"Triplet" and gave it a better name, but I do not recall his name for
them at this moment (hate it when I cannot remember something).
In this exercise I shall use as trunck or base Infinite Integer that of
................22212019181716151413121110987654321
I have a personal name for that trunk Infinite Integer and I call it the
Prime-buster because whatever odd-digit is at the end, that it is then
automatically prime except for "5". For as you can intuit, that since
every Counting Number is represented in the digit arrangement that
dividing into this Prime-buster will end up likely to leave a remainder
unless the ones-place-value digit is even or "5".
Now I look at the series of this number for its first 100 Counting
Numbers as this
........1312111098765432100 to that of ......1312111098765432101
So here are all the primes where the Trunk is this Prime-buster:
.......98765432101
.......98765432103
.......98765432107
.......98765432109
.......98765432111
.......98765432113
.......98765432117
.......98765432119
.......98765432121
.......98765432123
.......98765432127
.......98765432129
.......98765432131
.......98765432133
.......98765432137
.......98765432139
where the pattern repeats for 40s and 50s and 60s and 70s and 80s and 90s
Thus there are 40 primes within that 100 Counting Number interval
and that is the densest collection of primes in all the Counting Numbers
for a 100 interval. For a 10 interval the above density matches the
density of primes from 0 to 10 as 2, 3, 5, 7.
Now what I am trying to eagerly see is what kind of overall pattern
could these primes be in, so that the end of them is about equal in
density to the start of them, yet there are intervals in between where
they are immensely dense of a 40/100. And there are intervals such as
887,500 to 887,600 interval where there are few primes.
So what is the overall picture of this sort of density?
My answer would be that of the density of numbers on the surface of a
sphere. The lines of latitude compared to the lines of longitude. So
that all the longitude lines are the same just as all the 100 count
intervals are the same but the lines of latitude are immensely different
between the poles. So the density of primes follows latitude lines where
they seem to sparse out from the pole but as you approach closer and
closer to the equator line, they get dense. In a previous post I gave
the metaphor analogy of an onion where the layers of the onion represent
the Infinite Integer layers of ......0000s series and the .....11111s
series and ......222222s series.
So that Primes are layered within the Counting Numbers and as we count
from 1 all the way up to ....999999999 we traverse layers where we see
few primes then alot of primes then fewer again and then back to alot
etc etc.
P.S. at least with Decimal P-adics, I and everyone else can visualize
these things, but in the old math of P-adics where they were just
some fake imitation of Reals ....9999 = -1, well, noone could visualize
them and make any sort of sense out of them, and this is because they
were merely a new name for the Reals.
Archimedes Plutonium
Archimedes Plutonium wrote:
I made three errors in the above for which an earlier post
this evening concerning a question of division of 3 into
....88888888871 had me thinking about three numbers in this
list above.
I now realize I missed .....999999931 and ....99999919 and
.....999999917 as primes also.
So the above list should look like this:
.....999997 97
.....9999991
......9999989 89
.......99999983 83
.......99999979 79
......999999973 73
......999999971 71
......99999967 67
......999999961 61
.......9999999959 59
.......9999999953 53
.....9999999949
.....9999999947 47
......999999943 43
.......99999941 41
.......99999937 37
.......99999931 31
......999999929 29
......999999923 23
......99999919 19
......99999917 17
......99999913 13
......999999911 11
.......9999999907 7
.......9999999901 5
3
2
So about the only real question to ask is why the 999s series has a
prime at ....9999991 and ....999999949.
But the above list is very much more Symmetrical in that both lists
have 25 Primes.
Frank
re-arranged to spell "Mr Meticulous Pinhead".
"Archimedes Plutonium" <a_plu...@hotmail.com> wrote in message
news:471AE78F...@hotmail.com...
>
Archimedes Plutonium
Archimedes Plutonium wrote:
Now I did a preliminary look at the density of Primes between 100 and
200 was 21 primes and between 200 and 300 was 16 primes and between
300 and 400 was 16 primes and between 400 and 500 was 17 primes and
between 500 and 600 was 14 primes and between 600 and 700 was 16
primes and between 700 and 800 was 14 primes and between 800 and 900
was 15 primes and between 900 and 1000 was 14 primes and between 1000
and 1100 was 16 primes.
Now I have not yet checked whether the Infinite Integers of the
9999series matches the exact number of quantity of primes in their
respective 100 Counting Number interval so that there are 21 primes
between ....99999999200 and .....999999100 and there are 16 primes
between ......999999300 and ......999999200 and so forth
But I suspect that they match completely as per quantity. So they are
symmetrically the same as far as quantity.
And why should they match? Because they are points of the sphere or
globe and the Primes are on lines of latitude whereas all the Counting
Numbers are on lines of longitude. So that the latitude lines near the
North Pole -- primes in the interval 0 to 100 have the same quantity
as primes in the South Pole latitude of ....999999100 to .....9999999