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#151 Re: This is Cool » New Prime Unless Someone Else found it:) » 2013-06-09 04:14:51

Stangerzv

Hi phrontister

I think mathematica's PrimeQ function is the same with alpertron.

#152 Re: This is Cool » New Prime Unless Someone Else found it:) » 2013-06-09 03:58:28

Stangerzv

After 20h 14 mins 37s

  {1110 569841 961736 521093 527020 321061 997637 323487 171183 916164 743035
890337 478305 626254 080227 459404 322209 157812 216425 509264 920965 225954
216452 814660 943212 732459 541390 782750 026232 133733 246934 155146 590841
811410 546270 679392 624264 117413 197437 484536 121492 118007 586229 922433
542359 267360 140967 814731 499057 585417 184901 893328 122999 044651 625494
638152 554456 608373 144186 988936 455348 214706 248421 696806 985296 814269
741497 769100 215242 886224 200235 468455 936000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000030 732000
000000 000000 000197 is prime }

#153 Re: This is Cool » New Prime Unless Someone Else found it:) » 2013-06-08 13:42:13

Stangerzv

Hi phrontister

There is a primality software (open source) used by gimps to find the largest mersenne's prime. There is USD150,000 award for those who could find the 100,000,000 millions digit prime by electronic frontier. Since you are good at programming why not you try this software. I am looking for to find non-mersenne's prime. So far all biggest primes are mersenne numbers.

You can read about the software here http://en.wikipedia.org/wiki/Prime95

#154 Re: This is Cool » New Prime Unless Someone Else found it:) » 2013-06-08 08:07:04

Stangerzv

Hi phrontister

I would try to run it on alpertron and maybe after 1-2 days I would get the answer.

#155 Re: This is Cool » New Prime Unless Someone Else found it:) » 2013-06-07 12:59:34

Stangerzv

Some values for larger n:

For n=100000000

Ps={1000000000000000300000003}, {10000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002300000023} for Pt<200

#156 This is Cool » New Prime Unless Someone Else found it:) » 2013-06-07 07:23:18

Stangerzv
Replies: 20

Consider this equation.

Where, n is an integer, Pt is a prime number and Ps is the resulting Prime.

For n=1

Ps=5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383 for Pt<200 A well known prime (http://oeis.org/A005385)


For n=2

A well known prime (http://oeis.org/A155841)

For n=3

Ps=17, 263 for Pt<200

For n=4

Ps=79, 1049, 17179869269, 30354201441027016733116592294117482916287606860189680019559568902170379456331383469 for Pt<200

For n=5

Ps=37, 78167, 11920928955078263, 186264514923095703299, 4656612873077392578311 for Pt<200

For n=6

Ps=789730223053602977, 293242067884135544935936513642647623193965101483 for Pt<200

For n=7

Ps=367 for Pt<200

For n=8

Ps=144115188075856043, 154742504910672534362390789, 12259964326927110866866776217202473468949912977468817957, 363419362147803445274 661903944002267176820680343659030140745099590319644056698961663095525356881782780381260803133088966767300814308669 for Pt<200

For n=9

Ps=101, 4783039, 2541865828459 for Pt<200

For n=10

Ps=1033, 100000000000000000000253, 100000000000000000000000000319, 100000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000001243 for Pt<200

#157 Re: This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-06 16:57:23

Stangerzv

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

#158 Re: This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-05 03:20:43

Stangerzv

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:)

#159 Re: This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-05 03:15:28

Stangerzv

New update

P1=13 and n=2

Ps={191, 251}

P1=43 and n=2

Ps={1931, 2111}

#160 Re: This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-05 03:04:27

Stangerzv

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.

#161 Re: This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-05 02:37:00

Stangerzv

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.

#162 Re: This is Cool » My New Twin Prime Numbers » 2013-06-05 02:30:12

Stangerzv

Hi phrontister, thanks for the input. It would be wonderful to have a supercomputer indeed. I used to work with OSCAR Cray-SGI supercomputer when I was in the UK last time. I wish I was doing mathematics those times and the calculation would be lightening speed fast for sure. It is a sure thing that next Ps would be a rare thing and finding the bigger one is something kool because the probability to get the twin prime at higher Px is very small. It would be more challenging than finding Mersenne's prime because these primes exist in pair and usually bigger primes more than few millions digits rarely occurred next to each other.

#163 Re: This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-05 02:07:17

Stangerzv

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

#164 This is Cool » My New Twin Prime Numbers Absolute Twin Primes » 2013-06-04 23:49:15

Stangerzv
Replies: 18

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}

#165 Re: This is Cool » My New Twin Prime Numbers » 2013-06-01 06:59:31

Stangerzv

Well, DR for even number not always an even but  also can be a prime or odd number. DR(12)=3. What did I mean is that, would sums of prime-power with digital root 3, 6 and 9 always resulting in a prime Ps when Px also a prime? This is because, I think there are not that many of sums of prime-power with digital root 3, 6 & 9 could exist at the same time with prime Px, if they do, would all of them resulted in prime Ps or not necessarily to be prime.

I am not a mathematician and my maths could be more to classical approach rather than contemporary one. If I were to find a proof of something, I rather find something which is understandable to all people including the laymen. The good about maths is that, it was/is also developed by amateurs through history and that is why, we shouldn't feel bad about not having proper education in the mathematics.

#166 Re: This is Cool » My New Twin Prime Numbers » 2013-05-31 21:12:16

Stangerzv

It is easier to put something than making sure it is true for all. I think it would take like forever to proof that, why these prime always working with 3, 6 & 9 through computation.

phrontister, how often DR 3, 6 & 9 of

with prime Px resulted in non-prime Ps?

#167 Re: This is Cool » My New Twin Prime Numbers » 2013-05-30 23:41:41

Stangerzv

So, it seems that the sums of prime-power would be a multiple of 3. Well, do you think is it possible for it to have other than multiple of 3? for Pt>3. Maybe I need to learn programming again and run it on my computer. Mine is just core i5. Maybe it is just enough for smaller numbers Anyway, phrontister, thanks for the input, it is really a big help.

#168 Re: This is Cool » My New Twin Prime Numbers » 2013-05-30 23:06:09

Stangerzv

Ok, 2 and 3 always behave that way. I missed Pt=3 but I think more than Pt=3 the DG=3 would diminish unless you can find a counter example.

#169 Re: This is Cool » My New Twin Prime Numbers » 2013-05-30 22:16:43

Stangerzv

So, it means the sums of prime power for prime would be a multiple of 3 then. But have you tried prime power bigger than 2? I think there is no digital root of 3 for power greater than 2.

#170 Re: This is Cool » My New Twin Prime Numbers » 2013-05-30 17:31:47

Stangerzv

Hi phrontister

I agree with you, what to make it conclusive is that when you can prove there is no pair of {1,7} and do you notice or not that

is always either 9 or 6 for perfect prime twin pair other than when Px=3. Basically the proof is not complete otherwise people could at least prove one of the conditions above is true. If we could prove that
would always be either 6 or 9, then we can get the conclusive proof.

It is becoming more interesting I guess.

#171 Re: This is Cool » My New Twin Prime Numbers » 2013-05-30 13:30:07

Stangerzv

Hi phrontister

I think I know how to find the proof. You see, other than Px=3 & Pt=3 we will always having multiple of 3 digital roots for

. So, now consider equations as follows:

------------(1)

and


------------(2)

(1)+(2), yields,

Since Digital Root of

is multiple of 3, so as with the digital roots of
.

Since none of the values of

is multiple of 3 we can prove that Px is not a multiple of 3. Lets consider this equation,

(1)-(2)

Taking digital root both sides yields

If RHS is a negative DG, add 9. Since DG of RHS is never a multiple of 3 through prove by exhaustion. Therefore, digital root of LHS must also not a multiple of 3.

#172 Re: This is Cool » My New Twin Prime Numbers » 2013-05-29 22:58:08

Stangerzv

Ok, so far we got most of them but do you notice or not that digital root pair (1,4) occurs only once at Px=3 & Pt=3. By adding this digital root we get 1+4=5, yet the rest of digital roots above when added would give you a multiple of 3 digital roots examples, 1+2=3, 1+5=2x3, 1+8=3x3, 2+4=2x3, 2+7=3x3, 4+5=3x3, 5+7=12=>3, 7+8=15=2x3 but 1+7=8. I think it would be odd to get perfect prime pairs with the digital root {1,7} or if it does exist, it would be a special one. On the other hands, maybe there is only one pair of digital root of {1,4}.

#173 Re: This is Cool » My New Twin Prime Numbers » 2013-05-29 18:27:38

Stangerzv

Thanks for your input.

#174 Re: This is Cool » My New Twin Prime Numbers » 2013-05-29 17:34:07

Stangerzv

Hi phrontister

Can you find the digital roots pair (1,5) & (1,7) for the twin primes?

#175 Re: This is Cool » My New Twin Prime Numbers » 2013-05-29 13:16:36

Stangerzv

Kool, it seems I had overlooked the primes and new pairs of digital roots, (5,7) and (4,8)

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