My New Twin Prime Numbers Absolute Twin Primes

Stangerzv · 2013-06-04 23:49:15

Consider this equation

Where n is an even number, Pi is the consecutive prime and Ps is the resulting prime.

Some of the primes

Let P1=2 and n=4

Ps={193, 227}

Let P1=2 and n=6

Ps={29989, 30071}

Let P1=3 and n=2

Ps={7, 23}

Let P1=3 and n=4

Ps={1129, 1181}

Let P1=5 and n=2

Ps={23, 47}

Let P1=5 and n=6

Ps={1616543, 1616687}

Last edited by Stangerzv (2013-06-04 23:50:25)

Stangerzv · 2013-06-05 02:07:17

I think I could rearrange the equation to avoid negative prime. Below is the modified version.

barbie19022002 · 2013-06-05 02:14:47

did you make this equation yourself..?

Stangerzv · 2013-06-05 02:37:00

Yep barbie19022002..I kinda like prime numbers and I do lots of thinking about them. Most of the prime numbers I listed here were not known to me before and this prime formula was developed this morning. I got to know about prime numbers through my formulation of sums of power for arithmetic progression. I got involved in prime numbers after trying to link my sums of power formulation with Riemann's zeta function. Sometimes, it is a frustration to know that someone else had found it but it is kool to find something without knowing it beforehand.

Last edited by Stangerzv (2013-06-05 03:07:39)

bobbym · 2013-06-05 02:52:09

Hi;

Seems that for P1 = 2 that they are very rare.

anonimnystefy · 2013-06-05 03:02:02

Here are some (unconfirmed):
P1 n
2, 4
2, 6
5, 4
5, 8

Stangerzv · 2013-06-05 03:04:27

hi bobbym

There are three things that the prime has to match, a product, a sum and +- and when n becoming larger it would be harder to find the prime. This is what I believe and maybe a computational result would give a slightly different picture.

bobbym · 2013-06-05 03:14:16

There are no solutions with P1=2 and n < =1000 other than n = 4 and n = 6. These are already 3300 digit numbers!

Stangerzv · 2013-06-05 03:15:28

New update

P1=13 and n=2

Ps={191, 251}

P1=43 and n=2

Ps={1931, 2111}

Last edited by Stangerzv (2013-06-05 03:25:13)

Stangerzv · 2013-06-05 03:20:43

Hi bobbym

I had a feeling it would be hard to find prime for n>6 for P1=2 and I quit looking for them and now knowing there is no prime for n up to 1000 it is just worthy not trying:)

bobbym · 2013-06-05 03:22:14

There are no solutions with P1=3 and n < = 1000 other than n = 2 and n = 4.

For P1=5 and n < = 1000 other than n = 2 and n = 6, I can find no others.

For P1=7 and n < = 1000, I can find no solutions.

For P1=11 and n < = 1000, I can find no solutions.

For P1=13 and n < = 1000 other than n = 2, I can find no others.

For P1=17 and n < = 1000, I can find no solutions.

For P1=19 and n < = 1000, I can find no solutions.

For P1=23 and n < = 1000, I can find no solutions.

For P1=29 and n < = 1000, I can find no solutions.

For P1=31 and n < = 1000, I can find no solutions.

For P1=37 and n < = 1000, I can find no solutions.

For P1=41 and n < = 1000, I can find no solutions.

For P1=43 and n < = 1000 other than n = 2, I can find no others.

For P1=47 and n < = 1000, I can find no solutions.

anonimnystefy · 2013-06-05 05:03:59

Let P1=2 and n=4
Ps={193, 227}

How are you getting this? It seems I have misread something...

phrontister · 2013-06-05 05:21:27

Hi stefy,

P1 is the first prime in the sequence, and n is the number of primes in the sequence.

P1=2, n=4
2+3+5+7=17
2*3*5*7=210
210-17=193
210+17=227
Ps={193,227}

P1=3,n=2
3+5=8
3*5=15
15-8=7
15+8=23
Ps={7,23}

Last edited by phrontister (2013-06-05 05:27:52)

anonimnystefy · 2013-06-05 05:28:09

Ah, got it. Didn't subtract 1 in the upper summation bound.

phrontister · 2013-06-05 06:37:17

Testing for n<=100, I found many solutions up to P1=50929, most of which are for n=2. There are some n=4, 6 and 8, and several loners: n=14, 22, 26 and 56.

anonimnystefy · 2013-06-05 06:49:41

Hi

For P1<=p_10000 there is nothing for 34<=n<=54 and 58<=n<=68.

Also did a search for (P1,n) pairs where P1 can go up to p_100000 and 34<=n<=68.

Last edited by anonimnystefy (2013-06-05 10:22:38)

phrontister · 2013-06-05 12:34:34

The result with the highest n I've got so far is P=61001, n=154.

Backwards check (in M), where e1 and e2 are the two absolute +/- Ps elements:

Input: a = FactorInteger[(e1 + e2)/2]; {First[First[a]], Length[a]}
Output: {61001,154}

My code looks a bit clunky with the repeat "First[First", but it works and I don't know how to improve it.

Prime factor range is 61001 to 62761, which comprises 154 primes. 61001 and 62761 are the 6146th and 6299th primes (respectively), but I don't know how that information can be used.

Last edited by phrontister (2013-06-06 04:42:51)

Stangerzv · 2013-06-06 16:57:23

It seems there are plenty of these primes with an exception that most of them occur at smaller value of n.

phrontister · 2013-06-07 05:33:29

Yes, it's rarefied air up there for higher numbers.

I tried for P1=7, got to n=7350 with no result, and pulled the plug.

Math Is Fun Forum

#1 2013-06-04 23:49:15

My New Twin Prime Numbers Absolute Twin Primes

#2 2013-06-05 02:07:17

Re: My New Twin Prime Numbers Absolute Twin Primes

#3 2013-06-05 02:14:47

Re: My New Twin Prime Numbers Absolute Twin Primes

#4 2013-06-05 02:37:00

Re: My New Twin Prime Numbers Absolute Twin Primes

#5 2013-06-05 02:52:09

Re: My New Twin Prime Numbers Absolute Twin Primes

#6 2013-06-05 03:02:02

Re: My New Twin Prime Numbers Absolute Twin Primes

#7 2013-06-05 03:04:27

Re: My New Twin Prime Numbers Absolute Twin Primes

#8 2013-06-05 03:14:16

Re: My New Twin Prime Numbers Absolute Twin Primes

#9 2013-06-05 03:15:28

Re: My New Twin Prime Numbers Absolute Twin Primes

#10 2013-06-05 03:20:43

Re: My New Twin Prime Numbers Absolute Twin Primes

#11 2013-06-05 03:22:14

Re: My New Twin Prime Numbers Absolute Twin Primes

#12 2013-06-05 05:03:59

Re: My New Twin Prime Numbers Absolute Twin Primes

#13 2013-06-05 05:21:27

Re: My New Twin Prime Numbers Absolute Twin Primes

#14 2013-06-05 05:28:09

Re: My New Twin Prime Numbers Absolute Twin Primes

#15 2013-06-05 06:37:17

Re: My New Twin Prime Numbers Absolute Twin Primes

#16 2013-06-05 06:49:41

Re: My New Twin Prime Numbers Absolute Twin Primes

#17 2013-06-05 12:34:34

Re: My New Twin Prime Numbers Absolute Twin Primes

#18 2013-06-06 16:57:23

Re: My New Twin Prime Numbers Absolute Twin Primes

#19 2013-06-07 05:33:29

Re: My New Twin Prime Numbers Absolute Twin Primes

Board footer