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#176 Re: This is Cool » My New Twin Prime Numbers » 2013-05-25 20:31:27

One thing that I notice about these prime pairs is that, all of their digital root for n>1 would be in pair of 2^y (y=1..3) and 1 or 7, example, (2,1), (2,7),(4,1), (4,7),(8,1), (8,7) and special case (7,7) when n is a square number (i.e n=9). This indicates that the prime distribution is not random but organized. Unless someone could find the counter examples. Perhaps for n=9, adding this into digital root system won't change anything as 9 has zero value in the decimal system and this is why the prime pairs would have the same digital roots. This applies for all n which has digital root of 9.

#177 Re: This is Cool » My New Twin Prime Numbers » 2013-05-10 19:01:47

Hi phrontister

Thanks for finding the solutions. I am setting up a website for finding my prime numbers. Maybe in the future I could offer some prize money for the larger prime (>100,000 digits) smile

#178 Re: This is Cool » My New Twin Prime Numbers » 2013-05-09 22:16:24

I am revising the equation and making it harder to get new resulting prime. I named it Perfect Twin Prime Numbers. The revised equation is given as follows:

Where all Ps are prime numbers.

Example:

#179 Re: This is Cool » My New Twin Prime Numbers » 2013-04-27 21:50:10

Hi bobbym

Equation in this thread..so far phrontister got 715 digit prime and how about 100,000 digits prime? How long would it take? And would it fry the CPU?

#180 Re: This is Cool » My New Twin Prime Numbers » 2013-04-27 18:55:03

Hi bobbym

Anyway, how long do you think it would take to get 1st 100,000 digits for this prime equation? I hope it won't take too much computing time.

#181 Re: This is Cool » My New Twin Prime Numbers » 2013-04-27 11:30:06

Hi bobbym

Amongst of those famous mathematicians there were amateurs like Pierre Fermat (a lawyer), Mersenne (a priest), etc. Here list of them http://en.wikipedia.org/wiki/List_of_am … ematicians
There is a mafia culture in the mathematical fields and those people tends to garbage other people ideas because they are jealous.

#182 Re: This is Cool » My New Twin Prime Numbers » 2013-04-26 22:55:08

Would they be able to get the 13th root of non-perfect 13th power? Or they simply knows how to calculate integers? Our brains are capable of doing many things wonderful and complex but why bother if you can use calculator or computer:)

#183 Re: This is Cool » My New Twin Prime Numbers » 2013-04-25 19:30:30

If there is no computer maybe it would take hundreds of years to verify this for sure. But now it takes less than a day:)

#184 Re: This is Cool » My New Twin Prime Numbers » 2013-04-25 15:21:16

hi bobbym

Yeah I notice it too..can you get n to be even for Ps? It is like finding odd perfect numbers, so far all perfect numbers are even.

#185 Re: This is Cool » My New Twin Prime Numbers » 2013-04-23 11:23:11

Hi phrontister

Thanks for the solutions, 2^2+-1=3,5 it is part of the solutions, in which I overlooked it, it seems the equation can generate larger primes and it is becoming more interesting.

bobbym, I am drafting a research grant for my prime equations, that is why I put on hold for the grid computing. It would be kool to have a facility that could run very big calculations at a faster rate. I have more prime equations, I am trying to get a research grant to study them and maybe trying to find the largest primes as alternative to Mersenne in the future. This is one of the prime equations that could give big Prime at a smaller prime number input, the derivation of the equation is simple.

(10002^214+10003^214)/(10002^2+10003^2)=849 Digits Prime and (10002^562+10003^562)/(10002^2+10003^2)=2241 Digits Prime.

#186 Re: This is Cool » My New Twin Prime Numbers » 2013-04-22 17:53:07

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

#187 Re: This is Cool » My New Twin Prime Numbers » 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.

#188 Re: This is Cool » My New Twin Prime Numbers » 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.

#189 Re: This is Cool » My New Twin Prime Numbers » 2013-04-22 02:42:35

Hi bobbym

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

#190 Re: This is Cool » My New Twin Prime Numbers » 2013-04-19 18:00:48

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

#191 Re: This is Cool » My New Twin Prime Numbers » 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.

#192 Re: This is Cool » My New Twin Prime Numbers » 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.

#193 Re: This is Cool » My New Twin Prime Numbers » 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.

#194 Re: This is Cool » My New Twin Prime Numbers » 2013-04-19 04:49:22

Thanks bobbym for the result for P=3

#195 Re: This is Cool » My New Twin Prime Numbers » 2013-04-19 04:38:46

Yes bobbym..both have to be primes.

#196 Re: This is Cool » My New Twin Prime Numbers » 2013-04-19 04:34:11

Dear bobbym

P=3 has no twin prime solution because

and 33=3x11 which is not a prime

#197 This is Cool » Double Twin Primes: My New Primes, Even more harder to find. » 2013-04-18 17:12:27

Stangerzv
Replies: 0

Consider this equation

Smallest Solutions:

The occurrence of this prime number would be lesser than the previous one.

#198 Re: This is Cool » What is the largest Twin Primes of this form you can get? Ver 3 » 2013-04-17 15:09:15

I just knew there is no solution as the multiplication got bigger, if there is a solution for primes, they usually occur at the smaller amount. It is interesting to know that there is no solution for 3n+1 but proving it would be a headache..I guess. How do you know it? You guessed?

#199 This is Cool » My New Twin Prime Numbers » 2013-04-16 22:14:39

Stangerzv
Replies: 230

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

#200 Re: This is Cool » What is the largest Twin Primes of this form you can get? Ver 3 » 2013-04-16 13:30:20

I think I had to retract the conjecture as there are many counter-examples:


However, once P1 becomes larger, this type of prime would become hard to find or simply non-exist.

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