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• ... Welcome to the group. ... You choose to skip all numbers divisible by 2 and 3. The zigzag pattern is exactly all other numbers. The smallest such number
Message 1 of 19 , Aug 9, 2005
Jensen Lee wrote:

> I'm new to this group

Welcome to the group.

> I discovered a pattern in primes which i'm not sure if anyone has
> seen before, but it involves primes and prime*primes. It goes like
> this.
>
>
> 55 56 57 55 is p*p 5*11
> 52 53 54 53 is prime
> 49 50 51 49 is p*p 7*7
> 46 47 45 47 is prime
> 43 44 45 43 is prime
> 40 41 42 41 is prime
> 37 38 39 37 is prime
> 34 35 36 35 is p*p 7*5
> 31 32 33 31 is prime
> 28 29 30 29 is prime
> 25 26 27 25 is p*p 5*5
> 22 23 24 23 is prime
> 19 20 21 19 is prime
> 16 17 18 17 is prime
> 13 14 15 13 is prime
> 10 11 12 11 is prime
> 7 8 9 7 is prime
> 4 5 6 5 is prime
> 1 2 3 2 and 3 are prime, 1 is p*p
>
> if you highlight the prime and prime*prime numbers in the first and
> second columns you can get a simple zigzag pattern. For some reason
> this doesn't include 2 and 3 as these are special case numbers.

You choose to skip all numbers divisible by 2 and 3. The zigzag pattern is
exactly all other numbers. The smallest such number which is not a prime or
prime*prime (called semiprime) is clearly 5*5*5 = 125. Eventually almost all
numbers will have at least 3 prime factors - and at least n for any fixed n.

> if z is a p*p, then I have a few maths bits i came up with
>
> z = 6x +- 1

Nothing to do with semiprimes.
2 divides 6x, 6x+2, 6x+4. 3 divides 6x+3. Then all numbers not divisible by 2
or 3 is on the form 6x +-1.

> z = y + i*sqrt(y) (i = 0,2,4,6,8,...)

Nothing to do with semiprimes.
If y divides odd z then there is even i with:
z = y*(1+i) = y + i*y = y + i*sqrt(y^2).

> z = p1*p2

> I found that under 1000 there are 168 prime*prime
> and 169 primes. This seems to be some sort of balancing point.

There are 168 primes under 1000. 169 if you include 1, but 1 is usually not
considered prime by definition.
I don't know which numbers you counted to reach 168 prime*prime. There are 299
semiprimes below 1000. 204 of them are odd. 138 are both odd and not divisible
by 3.
Numbers with many factors start out rare. For all natural m,n with m<n, there
should be a balance point f(m,n) (or a set of points relatively close
together) where numbers with n factors become more common.

> Is this an old method coz I can't seem to find this in books.

Sorry, but it is mostly simple observations not interesting enough to put in
books. However, all numbers not divisible by 2 or 3 being on the form 6x +- 1
is often mentioned. Many amateur mathematicians think they are the first to
discover this or a simple variant of it.

--
Jens Kruse Andersen
• Hello, I do not know college level math (yet), but that does not stop me from studying and learning really cool things about primes. I am able to use
Message 2 of 19 , Jan 28, 2013
Hello,

I do not know college level math (yet), but that does not stop me from studying and learning really cool things about primes. I am able to use paper,pen, and archimedian tesselated graph paper, to make diagrams dealing with primes.

I do not use GIMPS. I try to find primes on my own. My highest prime I have found and tested positive, is 4027 digits.
I hope to break that personal record, once a possible prime I am testing finishes.
It is a 2p-1 Mersenne type prime. P being a prime that is 6 digits and starts with 9. I am sure it is well known here, the world record Mersenne prime, p is 6 digits and starts with 4.
I am guessing, if my number is positive, it would be about 26 million digits.

I tested my number with Mathematica 9 primality testing. It ran the number for 20 days before my computer crashed. That was using a platter HDD. Now I am running 3 OCZ Vertex 2 SSDs in raid 0, for extra speed,and upgraded from Windows 7 32 bit to 64 bit.

I have been rerunning the test for 3 days now on my main PC, but have also been running it on my laptop since January 19th, in case of another crash.
I have recently found the primality theorum, (2p+1)/3.
I started that on Mathematica 9 last night and tonight it is still running.

I work on primes with all of my spare time, apart from work. My 2 room-mates think I am nuts, but I am having fun and found I really enjoy math.
I joined this group hoping to meet like minded people, and maybe get advice. I do not yet know how to use Mathematica's abilities.

I have made a graph by hand, that shows values of p-squared, with symetrical high sine waves, and mirrored asymetrical low sine waves in between.I can explain that more, if anyone is interested.

Thanks,
Dwayne
• You might find interesting stuff to read on mersenneforum.org (not limited to Mersenne primes), which is a forum easier to navigate through than this group (I
Message 3 of 19 , Jan 28, 2013
You might find interesting stuff to read on mersenneforum.org
(not limited to Mersenne primes),
which is a forum easier to navigate through than this group (I think).

Also, a better place for informal discussions,
getting help from friendly users,
and a little more on the "fun" side.

Maximilian

>
> I work on primes with all of my spare time, apart from work. My 2
> room-mates think I am nuts, but I am having fun and found I really enjoy
> math.
> I joined this group hoping to meet like minded people, and maybe get
> advice. I do not yet know how to use Mathematica's abilities.
> (...)
> Thanks,
> Dwayne
>

[Non-text portions of this message have been removed]
• ... Indeed. Be aware, though, that the forum owner and supermods (I m one) have a rather idiosyncratic sense of humour and that some of the forum behaviour
Message 4 of 19 , Jan 29, 2013
On Mon, 2013-01-28 at 22:36 -0400, Maximilian Hasler wrote:
>
> You might find interesting stuff to read on mersenneforum.org
> (not limited to Mersenne primes),
> which is a forum easier to navigate through than this group (I think).
>
> Also, a better place for informal discussions,
> getting help from friendly users,
> and a little more on the "fun" side.
>
> Maximilian

Indeed. Be aware, though, that the forum owner and supermods (I'm one)
have a rather idiosyncratic sense of humour and that some of the forum
behaviour isn't always what you might have expected. That said, it is a
very friendly and helpful site, by and large. I've learned a lot there
and have taught a lot there too.

Neither is it limited to primes, mersenne or otherwise. As well as the