Is it possible...

[awkwardxsilence]

to narrow the prime gap to 47? And if so, how do I depict that in an image?

Backstory: I'm participating in GISHWHES (the Greatest International Scavenger Hunt the World Has Ever Seen). One of the items on the scavenger hunt is to narrow the prime gap to 47 and depict that in an image. Is it possible? I know that's probably a stupid question, but I figured it was worth a shot. It's worth lik 42 points

Any help would be appreciated!

 

[Deleted member 4993]

to narrow the prime gap to 47? And if so, how do I depict that in an image?

Backstory: I'm participating in GISHWHES (the Greatest International Scavenger Hunt the World Has Ever Seen). One of the items on the scavenger hunt is to narrow the prime gap to 47 and depict that in an image. Is it possible? I know that's probably a stupid question, but I figured it was worth a shot. It's worth lik 42 points

Any help would be appreciated!

Except for the first prime-gap (1), all the others are even numbers (difference between to odd numbers). So what does that tell you?

 

[awkwardxsilence]

Except for the first prime-gap (1), all the others are even numbers (difference between to odd numbers). So what does that tell you?

It tells me what I already knew. That I have no idea why this is an item on the scavenger list. Thanks for the sarcasm, it was a nice touch.

 

[stapel]

Thanks for the sarcasm, it was a nice touch.

Um... what?

 

[HallsofIvy]

You seem to be mistaking for "sarcasm" genuine puzzlement! What "prime gap" are you talking about? And what do you mean by "narrow the prime gap"?? Subhotosh Khan seems to be interpreting "prime gap" as "the gap between two consecutive prime numbers". His point was that, since the gap between any two consectutive prime numbers is an even number, it cannot be "47". And certainly the "narrowest" gap between two prime numbers is 2, between 5 and 7, 11 and 13, etc.

So, exactly what are you asking?

 

[awkwardxsilence]

You seem to be mistaking for "sarcasm" genuine puzzlement! What "prime gap" are you talking about? And what do you mean by "narrow the prime gap"??

Sorry. haha. It's 7:30am and I haven't slept yet

And honestly, the clue is "narrow the prime gap to 47" so your guess is as good as mine. But everyone seems to think it has to do with math, which is definitely not my specialty.

 

[HallsofIvy]

Brilliant, Denis! It must be brilliant because I have no idea what it means!

 

[Dale10101]

What a prime gap is.

From Wikipedia, the free encyclopedia


A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted g_n or g(p_n) is the difference between the (n + 1)-th and the n-th prime numbers, i.e.

We have g₁ = 1, g₂ = g₃ = 2, and g₄ = 4. The sequence (g_n) of prime gaps has been extensively studied.
The first 30 prime gaps are:
1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14  A001223.

 

[Dale10101]

fodder

Since the question concerns a scavenger hunt on the web it is probably is prompted by a recent discovery.

The Beauty of Bounded Gaps

A huge discovery about prime numbers—and what it means for the future of math.


http://www.slate.com/articles/healt...e_a_huge_discovery_about_prime_numbers.2.html

An article for the somewhat math literate non-mathematicians. It might help those who can seriously consider the inquirers question.

 

[Dale10101]

Maybe

Except for the first prime-gap (1), all the others are even numbers (difference between to odd numbers). So what does that tell you?

All prime numbers are odd else they would be divisible by two.

The difference between two odd numbers must be even since each odd number is an even number plus one, that is, subtracting those two even numbers yields an even number, subtracting the additional ones yields 0 for an overall even number. QED you cannot have a gap of 47, or any other odd number. (I think)

An image? Still cogitating.

Hmmm. So the question of about "prime numbers" is a blind, it is really a question about two odd numbers?

 

[Dale10101]

OK

Dale, since whoever made up that puzzle used 47, then it is EVIDENT that he/she chose the
2nd definition: "AND ALSO q-p-1 which is the number of composite numbers between them".

I see no point in debating this...
Why was the puzzle setter so "vague"? That's his/her business

Ah, the old insideres double definition trick. Good to know. Looking at your previous reference. Thanks

I am never for no point. I suppose the puzzle was intentionally vague so as to confuse the contestants in the great scavenger whatever?

Am fine, thank you . Good day.

For the non mathematically inclined inquirer. Image? Two stacks of bricks, each a prime number (an odd number, primes are always odd) tall, say, 3 and 5 tall, the difference is easily seen as even, two, never odd, 3,5, or 47 for any pair of primes, consecutive or not. Maybe they are looking for such an illustration of the even difference of oddities.

 

[awkwardxsilence]

Answer is 28229.
28229 + (47+1) = 28277

9 people labelled consecutively 1 to 9 standing in line at McDonald's:
there are 7 between the 1st and last, but 9-1 = 8......whatever!!

Eeeks! Thanks so much We'll be using the answer you gave us

 

[awkwardxsilence]

Ah, the old insideres double definition trick. Good to know. Looking at your previous reference. Thanks

I am never for no point. I suppose the puzzle was intentionally vague so as to confuse the contestants in the great scavenger whatever?

Am fine, thank you . Good day.

For the non mathematically inclined inquirer. Image? Two stacks of bricks, each a prime number (an odd number, primes are always odd) tall, say, 3 and 5 tall, the difference is easily seen as even, two, never odd, 3,5, or 47 for any pair of primes, consecutive or not. Maybe they are looking for such an illustration of the even difference of oddities.

We will definitely try it!

This scavenger hunt is legitimately hard. However, Jeff Bezos just bought me a book from Amazon.com. So maybe it's not so bad after all?

 

[lookagain]

All prime numbers are odd else they would be divisible by two. \(\displaystyle \ \ \ \ \ \)No! The smallest prime number is 2.


QED you cannot have a gap of 47,

or any other odd number. (I think) \(\displaystyle \ \ \ \ \ \ \)No, there is a gap of 1 between 2 and 3.

Image? Two stacks of bricks, each a prime number (an odd number, primes are always odd) tall, say, 3 and 5 tall, \(\displaystyle \ \ \ \) Again, that is wrong. Primes are not always odd.


tall, say, 3 and 5 tall, the difference is easily seen as even, two, never odd, 3,5, or 47 for any pair of primes, consecutive or not. \(\displaystyle \ \ \ \) Wrong, between the consecutive primes of 2 and 3, the difference is odd.

.

 

[Dale10101]

Thanks

or any other odd number. (I think) \(\displaystyle \ \ \ \ \ \ \)No, there is a gap of 1 between 2 and 3.

.

Thank you for the correction. It is the little things that hurt most.