- There are a lot of consecutive lines without any primes, or primes*primes.

For example :

3000000000000000000000000000028 3000000000000000000000000000029

3000000000000000000000000000030

3000000000000000000000000000031 3000000000000000000000000000032

3000000000000000000000000000033

3000000000000000000000000000034 3000000000000000000000000000035

3000000000000000000000000000036

3000000000000000000000000000037 3000000000000000000000000000038

3000000000000000000000000000039

3000000000000000000000000000040 3000000000000000000000000000041

3000000000000000000000000000042

3000000000000000000000000000043 3000000000000000000000000000044

3000000000000000000000000000045

3000000000000000000000000000046 3000000000000000000000000000047

3000000000000000000000000000048

3000000000000000000000000000049 3000000000000000000000000000050

3000000000000000000000000000051

3000000000000000000000000000052 3000000000000000000000000000053

3000000000000000000000000000054

3000000000000000000000000000055 3000000000000000000000000000056

3000000000000000000000000000057

3000000000000000000000000000058 3000000000000000000000000000059

3000000000000000000000000000060

----- Original Message -----

From: "Jensen Lee" <jensenlee@...>

.

>

> 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 <-- 51 is also p*p

> 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 <-- 34 is also p*p

> 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

>

> ..... - 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

You choose to skip all numbers divisible by 2 and 3. The zigzag pattern is

> 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.

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

Nothing to do with semiprimes.

>

> z = 6x +- 1

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

That was your assumption.

> I found that under 1000 there are 168 prime*prime

There are 168 primes under 1000. 169 if you include 1, but 1 is usually not

> and 169 primes. This seems to be some sort of balancing point.

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 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 think).

Also, a better place for informal discussions,

getting help from friendly users,

and a little more on the "fun" side.

Maximilian

>

[Non-text portions of this message have been removed]

> 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

>

- On Mon, 2013-01-28 at 22:36 -0400, Maximilian Hasler wrote:
>

Indeed. Be aware, though, that the forum owner and supermods (I'm one)

> 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

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

obvious factorization threads, there are also discussions about science,

technology, mathematics, politics, finance, health and several versions

of general purpose silliness.

OK, ad-break over. We now return you to your scheduled programming.

Paul