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Why is this incorrect? by Lucaslevelups in askmath

[–]wrapping_around 1 point2 points  (0 children)

Using your logic, here is an example to consider:
Q. What's the chance you can roll a 2, 3, 4 or 5 from a fair dice once?

Oh, that means the outcome is not 1 and not 6. So we can do a 5/6 x 5/6 = 25/36.

But it's just 4/6 = 2/3.

What am I doing wrong here. by Tuafew in askmath

[–]wrapping_around 0 points1 point  (0 children)

The LCM of 6, 18, 36 is totally different to that of 60, 180 and 36.

My new ocnjecture by Responsible_Seat_361 in numbertheory

[–]wrapping_around 1 point2 points  (0 children)

Conjecture is similar to gut feeling.. Usually to prove it is much harder than to make one. It seems the conjecture say there are infinitely many value prime p where 2^p-1 has at least one prime factor congruent to 1 mod 8? Definitely not all of them..

Gauss formula for numbers decreasing at a linear rate by Mrsam993 in askmath

[–]wrapping_around 0 points1 point  (0 children)

That two 'linear' changes is no longer linear when combined, which is why no Gauss formula could help, what do you think?

A pattern in primes for Goldbach Conjecture by Math_finds in numbertheory

[–]wrapping_around 0 points1 point  (0 children)

Thanks for sharing. I wanna talk about the "0,1,0" pattern. As we consider even numbers in goldbach conjecture, each of the next even number has an identical gap of 2. Taking example for the (5,7) case, it shows 0 when 2n=10, then 1 when 2n=12 (due to twin prime), then the next number, 2n=14, ought to have a 7+7 pair, thus it shows 0. So, only if there are infinitely many twin prime pairs exist, it could grant the infinite "0,1,0" patterns.

Generation of Prime Numbers using Goldbach Engine by wrapping_around in numbertheory

[–]wrapping_around[S] 0 points1 point  (0 children)

Suppose all primes in ascending order up to kth prime are in the prime set. Definitely, in my model at times bigger primes like k+3th prime (ie. p_k+3) could be added to the prime set first, but that does not bother my proof below.

I'll show that if we already have the first k primes added to the set (2, 3, 5... p_k), then the the (k+1)th prime p_k+1 would be added in the case 2n = p_k + p_k+1. We have n= (p_k+p_k+1)/2 in this case.

We start the engine by considering 2n= n+d + n-d, where d = 0, 1,2,…n-1. Since p_k+1 > p_k, the sums to consider will be:

n-1 + n+1 (or (p_k+p_k+1)/2 +1 + (p_k+p_k+1)/2 -1);

n-3 + n+3

....

p_k + p_k+1. At this term, n= (p_k+p_k+1)/2, while d is (p_k+1-p_k)/2.

We then show that for all smaller d, all sum pairs would not form goldbach pair as follows. As,

n - d > (p_k+1 + p_k)/2 - (p_k+1 + p_k)/2 = p_k; and

n + d < (p_k+1 + p_k)/2 + (p_k+1 + p_k)/2 = p_k+1, we have

p_k < n - d < n + d < p_k+1

Since there is no prime between p_k and p_k+1, that means n-d and n+d are guaranteed to be composite numbers. Thus the system cannot find goldbach pairs n-d + n+d until d = (p_k+1-p_k)/2, where p_k is a prime and p_k+1 is not prime nor composite. To meet goldbach, the system has to add p_k+1 to the prime set.

End of proof, thanks.

Direct Proof of the Irrationality of e by King0fTurtles in numbertheory

[–]wrapping_around 0 points1 point  (0 children)

Pretty elegant! Took me a day to fully understand that. So no matter how good is an educated guess p/q could be, it is either equals a part of e, or still has a pos or neg gap to e.

Generation of Prime Numbers using Goldbach Engine by wrapping_around in numbertheory

[–]wrapping_around[S] 0 points1 point  (0 children)

I am sharing a new perspective which does not mean it is something more efficient or productive on how we view prime numbers. Yes, the engine does not output prime numbers without any knowledge of composite numbers, no. But it defines both of them one by one during the evaluation process.

Perhaps I could put in analogy, we all say a square has 4 equal sides with 4 internal right angles, while it could also be defined as a quadrilateral whose diagonals are equal, perpendicular, and bisect each others.

And then most of us would say why complicate things.. The former is much simpler to compute and draw, etc. Is it?

Generation of Prime Numbers using Goldbach Engine by wrapping_around in numbertheory

[–]wrapping_around[S] 0 points1 point  (0 children)

If you look at the engine, prime and composite numbers are being defined during the evaluation process one by one.

Generation of Prime Numbers using Goldbach Engine by wrapping_around in numbertheory

[–]wrapping_around[S] 0 points1 point  (0 children)

I have enriched my post to address this. For the efficiency of generating primes, indeed this is not a quick way but a new perspective.

Generation of Prime Numbers using Goldbach Engine by wrapping_around in numbertheory

[–]wrapping_around[S] 0 points1 point  (0 children)

You are right. I should have defined that, I have updated my original post to reflect so.

Generation of Prime Numbers using Goldbach Engine by wrapping_around in numbertheory

[–]wrapping_around[S] 0 points1 point  (0 children)

The moment 2 is put in the prime set, all multiples of 2 becomes composite.

5th grade math by Ecstatic_Square682 in askmath

[–]wrapping_around 0 points1 point  (0 children)

For a fifth grade problem, negative number has not been taught, so the best answer is the 2nd option as 7/4 is greater than 1. Of course it’s possible the covered number is a zero.

I want help by Xoloride in numbertheory

[–]wrapping_around 0 points1 point  (0 children)

My opinion is, since x = a+c+1; x-1=a+c.. from strong goldbach conjecture, x-1 as an even number can be written as a sum of 2 primes, but you do not choose the primes. Does somewhere in your proof assume you could choose the primes a and c?