Talk:Prime quadruplet
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[edit] Consectutive Prime Quadruplets
Are there any consecutive prime quadruplets, where the first values of the two quadruplets are separated by 30? There are plenty that are separated by 90. If there were any separated by 30, that'd be a prime octuplet, right? And then if there were any prime octuplets separated by 210, that'd be a prime 16-tuplet I suppose. But do any of these higher-order groupings exist?
- Please sign talk pages with four tildes ~ ~ ~ ~ (without spaces). Two quadruplets separated by 30 is an admissable constellation. This can be tested here. It would not be an octuplet which means something else (8 primes as closely together as possible for primes above 8). There is a plausible conjecture that all admissable constellations have infinitely many occurrences. Up to 10^14 I computed 33480 pairs of two quadruplets 30 apart. The form is not named. Maybe it could be called "twin quadruplets". I found the first "quadruple quadruplet". I'm not adding any of these own results to the article. PrimeHunter 12:50, 13 September 2006 (UTC)
[edit] Practical use?
Do prime quadruplets have any known real-world application? Epastore 03:18, 15 January 2006 (UTC)
- Maybe they could be used for cryptography. Other than that they're probably just as useless as any other kind of prime number. PrimeFan 20:59, 17 January 2006 (UTC)
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- Heh. Then do they, perhaps, reflect some sort of fundamental principle of the universe? They seem like such odd things... that 2 then 15 then 2 wandering through the list of primes. Or is this just us trying to find order in chaos, and therefore finding what we are looking for? Epastore 04:18, 19 January 2006 (UTC)
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- You're getting too philosophical for my taste. I'll just say that whoever can prove that there are infinitely many prime quadruplets deserves a medal. PrimeFan 00:47, 21 January 2006 (UTC)
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[edit] Why is {3, 5, 7, 11} not considered as a prime quadruplet?
I believe that {3, 5, 7, 11} should be considered a prime quadruplet for the following reasons:
1. There are 2 close pairs of twin primes (namely {3, 5} and {5, 7}). 2. There are 2 overlapping pairs of prime triplets (namely {3, 5, 7} and {5, 7, 11}). 3. It is of the form {p, p+2, p+4, p+8}, and therefore, in my mind, should be an acceptable prime quadruplet since the first and last numbers of the prime quadruplet differ by 8.
Since it meets the criteria for a prime quadruplet, {3, 5, 7, 11} should be an acccepted prime quadruplet. —Preceding unsigned comment added by PhiEaglesfan712 (talk • contribs)
- Wikipedia content should be based on reliable sources. I have seen different definitions but I believe the most common definition is that a prime quadruplet is 4 primes in the closest admissible constellation for 4 numbers. See for example [1] for the meaning of admissible. It's trivial to show that the closest admissible constellation of 4 primes is (p, p+2, p+6, p+8). Some prime quadruplet definitions skip the admissible reason and go straight to defining a prime quadruplet as (p, p+2, p+6, p+8). Note that (p, p+2, p+4, p+8) is not admissible, because at least one of the numbers is always divisible by 3. Apart from being the most common definition, I also personally think it is the most practical definition, because it's part of a systematic definition of a prime k-tuplet as k primes in the closest admissible contellation. Then twin primes are prime 2-tuplets, prime triplets are prime 3-tuplets, prime quadruplets are prime 4-tuplets, prime quintuplets are prime 5-tuplets, and so on. This is also the system used at the record page [2]. PrimeHunter 21:22, 17 June 2007 (UTC)
