My New Twin Prime Numbers

Stangerzv · 2013-04-16 22:14:39

Consider this equation

Where all Pi are the consecutive primes, Pt is the Prime-th Power, n is the n-th of the Prime number, P1=2, and Ps is the resulting Prime.

Example for smallest solution for each Prime-th Power.

For P=2,

For P=3,

-Thanks to bobbym:)

For P=5,

-Thanks to phrontister

For P=7,

-Thanks to bobbym

For P=11,

For P=13, -Thanks to phrontister

Last edited by Stangerzv (2023-01-31 01:02:05)

bobbym · 2013-04-19 04:18:45

For P=3

2^3 + 3^3 + 2 = 37

Stangerzv · 2013-04-19 04:34:11

Dear bobbym

P=3 has no twin prime solution because

and 33=3x11 which is not a prime

Last edited by Stangerzv (2013-04-19 04:34:49)

bobbym · 2013-04-19 04:35:46

Hi;

Oh, it has to both of them? I did not understand the question, sorry for the false positive.

Stangerzv · 2013-04-19 04:38:46

Yes bobbym..both have to be primes.

bobbym · 2013-04-19 04:44:35

For P = 3, how is this?

2^3 + 3^3 + 5^3 ± 3 = {157, 163}

Stangerzv · 2013-04-19 04:49:22

Thanks bobbym for the result for P=3

bobbym · 2013-04-19 04:54:58

Next one is at:

Stangerzv · 2013-04-19 05:06:38

I think there are few more solutions for P=3, have you tried P=7 and I think there would be no solution at lower amount or no solution at all.

bobbym · 2013-04-19 05:09:24

There are 5 solutions for P = 3 using the first 1000 primes.

I will check for P = 7:

No solutions up to n = 2000.

Stangerzv · 2013-04-19 05:18:28

I do believe that if there is a solution it should occur at lower primes, as the prime number getting larger, it would be hard or impossible to find.

Last edited by Stangerzv (2013-04-19 05:19:11)

bobbym · 2013-04-19 05:20:32

Yes, the primes get rarer as the numbers get larger.

I have searched all the way up to the 2000th prime for P = 7 and found none.

Stangerzv · 2013-04-19 13:49:39

Hi bobbym

What program do you use to calculate them? On the other hands, can you get any solution for P>11? I think there could be no more solution, if there is one, it would be very large.

bobbym · 2013-04-19 14:14:42

Hi;

I am using mathematica right now for this:

For P=11

Stangerzv · 2013-04-19 18:00:48

I see, for P=11, I got the result already but not 13 and above.

bobbym · 2013-04-19 20:31:57

Hi;

For P = 13 , I could not find any and I went up to the 4000th prime.

bobbym · 2013-04-21 23:56:50

Hi;

For P = 17:

Stangerzv · 2013-04-22 02:42:35

Hi bobbym

Thanks..It is really kool to know there is a solution for P=17.

bobbym · 2013-04-22 04:46:56

Hi;

For P = 7:

Stangerzv · 2013-04-22 11:12:33

Hi bobbym

It seems there must be a solution for P=13 otherwise it would look strange. Otherwise there would be a gap for sure. By the way, thanks for calculate the primes. If you could tell me how to do it with the mathematica, maybe I would do some calculation myself for bigger P and finding the solution for P=13.

bobbym · 2013-04-22 12:01:36

Hi;

I am looking for one but so far there is none among the first 20000 primes.

The code I have developed is highly inefficient, it only has the virtue of being quick to discover. I would need to clean it up some because right now it takes a lot of human intervention.

Also, I have an idea to speed it up greatly.

Stangerzv · 2013-04-22 13:27:39

Basically, If there is no solution for P=13, it would be mind boggling to proof it so but if there is a solution, it would be very big. I am currently working on my equations and primes numbers, there are many more equations but I need someone to help me with the coding. There is someone suggesting me to use grid computing and the problem is that, I am not a programmer and I have left programming more than 10 years ago. Maybe I could apply for a research grant to study these prime numbers and work with collaborators.

Last edited by Stangerzv (2013-04-22 13:29:16)

bobbym · 2013-04-22 16:56:47

Grid computing? Where are you going to get all the computers from?

The P = 13 will fall as soon as I bring more computers into the problem.

Stangerzv · 2013-04-22 17:53:07

A university here did invite me to use their first grid computing to run my prime number equations.

bobbym · 2013-04-22 20:07:03

Hi;

Why didn't you accept?

Math Is Fun Forum

#1 2013-04-16 22:14:39

My New Twin Prime Numbers

#2 2013-04-19 04:18:45

Re: My New Twin Prime Numbers

#3 2013-04-19 04:34:11

Re: My New Twin Prime Numbers

#4 2013-04-19 04:35:46

Re: My New Twin Prime Numbers

#5 2013-04-19 04:38:46

Re: My New Twin Prime Numbers

#6 2013-04-19 04:44:35

Re: My New Twin Prime Numbers

#7 2013-04-19 04:49:22

Re: My New Twin Prime Numbers

#8 2013-04-19 04:54:58

Re: My New Twin Prime Numbers

#9 2013-04-19 05:06:38

Re: My New Twin Prime Numbers

#10 2013-04-19 05:09:24

Re: My New Twin Prime Numbers

#11 2013-04-19 05:18:28

Re: My New Twin Prime Numbers

#12 2013-04-19 05:20:32

Re: My New Twin Prime Numbers

#13 2013-04-19 13:49:39

Re: My New Twin Prime Numbers

#14 2013-04-19 14:14:42

Re: My New Twin Prime Numbers

#15 2013-04-19 18:00:48

Re: My New Twin Prime Numbers

#16 2013-04-19 20:31:57

Re: My New Twin Prime Numbers

#17 2013-04-21 23:56:50

Re: My New Twin Prime Numbers

#18 2013-04-22 02:42:35

Re: My New Twin Prime Numbers

#19 2013-04-22 04:46:56

Re: My New Twin Prime Numbers

#20 2013-04-22 11:12:33

Re: My New Twin Prime Numbers

#21 2013-04-22 12:01:36

Re: My New Twin Prime Numbers

#22 2013-04-22 13:27:39

Re: My New Twin Prime Numbers

#23 2013-04-22 16:56:47

Re: My New Twin Prime Numbers

#24 2013-04-22 17:53:07

Re: My New Twin Prime Numbers

#25 2013-04-22 20:07:03

Re: My New Twin Prime Numbers

Board footer