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Twin Primes and Extracting.

lvl107
20-Turquoise

Twin Primes and Extracting.

Hi,

I have a question and need help. Assuming that we have a set of Prime Numbers (from 5 to 37

in this case) Let's extract Twin Primes like as the Output below. (IN .MCD12)

P.PNGTwinPrimes.PNG

Thanks in advance.

Regards,

Loi.

1 ACCEPTED SOLUTION

Accepted Solutions
StuartBruff
23-Emerald II
(To:lvl107)

Loi Le wrote:

Thanks, Richard. Possibly I should have the update-question :

P.PNG Twin_Non-Twin.PNG

Just a top-of-the-head thing, but might be worth playing with. Makes use of the fact that 'triple primes' don't exist (unless you count 1,2,3), to avoid re-testing numbers.

Stuart

View solution in original post

64 REPLIES 64
MikeArmstrong
5-Regular Member
(To:lvl107)

Something like the attached?

Mike

Sorry, but that's not correct. Twin primes are pairs of primes that differ by 2, so (23,29) is not a valid pair.

lvl107
20-Turquoise
(To:RichardJ)

Thanks, Richard. Possibly I should have the update-question :

P.PNG Twin_Non-Twin.PNG

StuartBruff
23-Emerald II
(To:lvl107)

Loi Le wrote:

Thanks, Richard. Possibly I should have the update-question :

P.PNG Twin_Non-Twin.PNG

Just a top-of-the-head thing, but might be worth playing with. Makes use of the fact that 'triple primes' don't exist (unless you count 1,2,3), to avoid re-testing numbers.

Stuart

RichardJ
19-Tanzanite
(To:StuartBruff)

Makes use of the fact that 'triple primes' don't exist (unless you count 1,2,3), to avoid re-testing numbers.

Another 10^-9 C saving in global warming

StuartBruff
23-Emerald II
(To:RichardJ)

Richard Jackson wrote:

Makes use of the fact that 'triple primes' don't exist (unless you count 1,2,3), to avoid re-testing numbers.

Another 10^-9 C saving in global warming

A nanocoulomb? Sorry, guv, I never really got past pounds, shillings and pence. What's that in moles of electrons?

However, you neglected the effects of relativity on subjective time experience ... that' gotta be worth a couple of microseconds of anybody's time!

Stuart

lvl107
20-Turquoise
(To:StuartBruff)

Your answer is very completely to my question. Thanks a lot indeed.

Loi.

MikeArmstrong
5-Regular Member
(To:StuartBruff)

Nice function...... Impressed

Was going to propose an alternative, but I don't think I could.

Mike

Mike Armstrong wrote:

Nice function...... Impressed

Was going to propose an alternative, but I don't think I could.

Mike

Oy vey iz mir! Are my lessons forgotten so soon, already?

There's *always* an alternative to anything I suggest

There are a couple of tricks to finding alternatives.

One is to just look at it sniffily and pick holes in it. "Hah! It doesn't handle the (special case) pairs (2,3) & (3,5)!" (having, naturally, extended the prime sequence) and then noting that it doesn't pick up the true prime triplets (2,3,5) & (3,5,7), extend the idea into Prime Constellations - ie, some sequence of primes that spans the minimum distance according to some criteria, eg prime triplets can be of the form (p,p+2,p+6), (p,p+4,p+6), (p,p+6,p+12), etc. Having then sneered at my rather pathetic program, you can then produce the piece de resistance that knocks mine into a cocked hat.

An alternative viewpoint is to, as Jean would have said, draw inspiration from a worksheet by saying "Wow! I wonder if it's possible to extend that program to cover other cases!"; both views can lead to the same result. Depends whether competition is your forte or you have a temperament like a Labrador puppy newly promoted to 2nd Lt.

Or you could be like me, a cross between Scrooge and the Four Yorkshiremen. I were raised when you could count each clock cycle of t' CPU and every bit counted, but you try and tell the young people of today that ..... they won't believe you. So profligate waste, such as Richard's checking a number more than once, that may be acceptable if you've got gigs of RAM and Hz, just offends my sensibilities (well, that's a bit of an exaggeration, I've only got the one sensibility).

Which leads to another way of developing alternatives - take a trick out of Paul Dirac's book and look for the beauty or elegance in a method.

Stuart

MikeArmstrong
5-Regular Member
(To:StuartBruff)

Stuart,

After reading your post I thought "I'm not a Labrador puppy" and decided to write a function which would collect Triplet Primes, see below.

Clipboard01.jpg

Then, I decided to do a little research into types of Prime numbers and realised that there are multiple types.

  • Pairs
  • Triplets
  • Quadruplets
  • Quintuplets

Which massivly deflated me and made me realsie I might be more of a Poodle than a Labrador

Mike

Mike Armstrong wrote:

Stuart,

After reading your post I thought "I'm not a Labrador puppy" and decided to write a function which would collect Triplet Primes, see below.

Clipboard01.jpg

Then, I decided to do a little research into types of Prime numbers and realised that there are multiple types.

  • Pairs
  • Triplets
  • Quadruplets
  • Quintuplets

Which massivly deflated me and made me realsie I might be more of a Poodle than a Labrador

Mike

First, I should point (pun intended) that Poodles are No 2 in the dog intelligence stakes, whereas Labradors are No 7. So well done on your promotion! (I, being of Welsh extraction, am, of course, a Border Collie, although my wife puts me about twenty places lower than an Afghan Hound. 🙂 )

Second, the term Labrador Puppy is not at all derdogatory! They are enthusiastic, intelligent, full of boundless energy and totally optimistic, just like a Second Lieutenant ... well, apart from the intelligence bit - never give a 2nd Lt a map unless you want to get totally lost.

As to your problem, this is where Labrador Nature comes in handy, as you should view it as a Labrador would view a Brontosaurus(*) - a big collection of bones (unlike my Collie self, which does a quick 180 and applies full military power).

Stuart

(*) Yes, I know it's really an Apatosaurus, but I'm with Gould on this one.

Stuart Bruff wrote:

... First, I should point (pun intended) that Poodles are No 2 in the dog intelligence stakes, whereas Labradors are No 7. So well done on your promotion! (I, being of Welsh extraction, am, of course, a Border Collie, although my wife puts me about twenty places lower than an Afghan Hound. 🙂 )

... As to your problem, this is where Labrador Nature comes in handy, as you should view it as a Labrador would view a Brontosaurus(*) - a big collection of bones (unlike my Collie self, which does a quick 180 and applies full military power).

Actually, thinking about it for a few seconds, I guess this proves my wife's point, as a real Collie would simply give a flock of Brontosauri 'The Eye' and start herding them.

RichardJ
19-Tanzanite
(To:StuartBruff)

Second, the term Labrador Puppy is not at all derdogatory!

Especially if it's a very determined Labrador puppy

http://communities.ptc.com/servlet/JiveServlet/showImage/38-1286-8574/Dog2.gif

lvl107
20-Turquoise
(To:MikeArmstrong)

To Mike.

Prime Triplet.PNG

Loi.

MikeArmstrong
5-Regular Member
(To:lvl107)

Interesting.

Are you trying to program this case now?

Mike

RichardJ
19-Tanzanite
(To:StuartBruff)

noting that it doesn't pick up the true prime triplets (2,3,5) & (3,5,7),

You said the only prime triplet was 1,2,3. I took you at your word there, and never even thought about it. It just goes to show that one should always think about what they are reading!

What a wasted opportunity to come up with a smart-ass reply

Edit: Oh God! The nanny-ware kicked in! Perhaps I'm supposed to say smart-donkey reply?

StuartBruff
23-Emerald II
(To:RichardJ)

Richard Jackson wrote:

noting that it doesn't pick up the true prime triplets (2,3,5) & (3,5,7),

You said the only prime triplet was 1,2,3. I took you at your word there, and never even thought about it. It just goes to show that one should always think about what they are reading!

What a wasted opportunity to come up with a smart-*** reply

Edit: Oh God! The nanny-ware kicked in! Perhaps I'm supposed to say smart-donkey reply?

I did say 'true' triplets, all the rest of them have are separated by more than 2. There are also some variations that I regard as cheating. For example, there are triplets that are consecutive primes but there are also other triplets that match a given pattern, but aren't consecutive (ie, there's one or more other primes in the minimum subsequence containing the triplet.

What a wasted opportunity to come up with a smart-*** reply

Edit: Oh God! The nanny-ware kicked in! Perhaps I'm supposed to say smart-donkey reply?

I'm shocked, Jackson, that you could impugn donkeys in such a way. Is it not enough that we denigrate cats, by attributing feminine malice to them, that we must now resort to defaming equus africanus asinus?

A friend of mine insists on a Right to Reply

http://football-talk.co.uk/wp-content/uploads/2010/07/donkey.jpg

lvl107
20-Turquoise
(To:lvl107)

I have a related question with the above, and need help.I wish to learn. ( IN .MCD12 ). Assuming that we have a set of Prime Numbers (from 41 to 59). Let's extract Twin Primes and Cousin Primes, and Non-of-those like as the Output below. (or the Output is a similar one).

P.PNGTwin-Cousin-Primes.PNG

Thanks in advance.

Loi.

MikeArmstrong
5-Regular Member
(To:lvl107)

Something like the attached?

Mike

Message was edited by: Mike Armstrong - Worksheet updated due to error

lvl107
20-Turquoise
(To:MikeArmstrong)

Thank you very much, Mike.

The reason, I need help with this, is I hope to find a way to write a function for Triplet Prime completely. And I have an extension of set of P need help. I hope you understand me. (The attached below).

Regards,

Loi.

MikeArmstrong
5-Regular Member
(To:lvl107)

I have just noticed an error in my function. 37 shouldn't be getting called up in the 'None of those' categories. I will modify the function to suit.

Do you now want to include Triplet Primes?

I will update my original worksheet to try and keep this thread as clean as possible!!!

Mike

lvl107
20-Turquoise
(To:MikeArmstrong)

Yes, please. If the output of your function include Triplet Primes, that is good for me, if it does not include Triplet Primes, anyway my question is answered.
Regards,
Loi.

MikeArmstrong
5-Regular Member
(To:lvl107)

I will have a look tomorrow.

Mike

MikeArmstrong
5-Regular Member
(To:lvl107)

Have a look at the attached sheet. I think it works.

It doesn't exclude the special case of Triplet primes.

The function is bulky and horrible at the moment and I will have a look at tidying it up.

Cheers

Mike

lvl107
20-Turquoise
(To:MikeArmstrong)

Mike,
My related question above, and my plan for "Prime Triplet" were answered.(from you, Mike !) (I hope you to understand me. Sometimes I really don't know how to "set-up" my question clearly and made you confused many times. Sorry about that.)
Thank you for your time and help.

P(5,113).PNG

PrimeTriplet.PNG

Regards,

Loi.

MikeArmstrong
5-Regular Member
(To:lvl107)

Sometimes I really don't know how to "set-up" my question clearly and made you confused many times. Sorry about that.)

Don't worry, I confuse myself most of the time.

The function is over the top if you only want Prime Triplets, but if you continue to build the function, eventually it will be able to extract all Prime cases.

Mike

lvl107
20-Turquoise
(To:MikeArmstrong)

Mike, I have been helped from you with writting a function for Prime Triplets. And now I have a related query with the above, wish learning, and wish be helped with any suggestion. It's about: "Prime Triplets and Extracting Their Non-Overlap". Assume having a set of Prime Triplets from 5 to 317.

Triplet from 5 to 317.PNG

Extract_NonOverLapTriplet(T).PNG

Thanks in advance.

Regards,

Loi.

MikeArmstrong
5-Regular Member
(To:lvl107)

Loi,

I will be more than happy to take a look, but I travel to Germany today and will not be able to access the Internet until tomorrow evening.

Mike

lvl107
20-Turquoise
(To:lvl107)

Hi,

I have a related question with the above, I am very interested in, wish learning, and need help.

B.PNGUnNested_Match_NonMatch(B).PNG

Thank you in advance.

Regards,

Loi.

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