Number pairs with a remarkable property.

[HSE]

Gunther,

He was born in a hard time. That wasn't easy.

Yes. Here don't was the worst, but not easy at all. My father around that time play football in his town and all colonies around. He always telled us the fear of little boys because members of peronism (current governement) drived in the town with megafones saying "haga patria, mate un judío" (a lot of people now denie that). These little boys always asked shaking what happen to the few "criollos" they trust. It's presumed their fathers don't wanted to alarm them, and don't were saying to much. 

Back in the subjec, I adapted the JJ number pairs code to ML64. Very curious some q have a lot of points and others only few or one!

HSE

[Gunther]

HSE,

Very curious some q have a lot of points and others only few or one!

Yes, indeed. But not so rare either. Please think only about the distribution of the prime numbers. They grow like wild weeds in the set of natural numbers. Even there
it's difficult to find the regularities.

[daydreamer]

HSE,

Very curious some q have a lot of points and others only few or one!

Yes, indeed. But not so rare either. Please think only about the distribution of the prime numbers. They grow like wild weeds in the set of natural numbers. Even there
it's difficult to find the regularities.

but the composites have regularities
when I researched different ways to find Primes, I discovered the old multiplication table from school when I was kid,up to 120+ presented as GIF shows all composites have regularities
so all the gaps between for example between 6*2 and 7*2 = 13 is prime numbers
so I based a prime number checking algo,by MUL x*y loop saving into multiply LUT the composites,zeros left after zeroing it=primes

[Gunther]

Daydreamer,

but the composites have regularities
when I researched different ways to find Primes, I discovered the old multiplication table from school when I was kid,up to 120+ presented as GIF shows all composites have regularities
so all the gaps between for example between 6*2 and 7*2 = 13 is prime numbers
so I based a prime number checking algo,by MUL x*y loop saving into multiply LUT the composites,zeros left after zeroing it=primes

well, what can I say? There is one even prime number: the 2. All other prime numbers are odd. There is still an infinite number of them. Each of these prime numbers lies between two even numbers.
But how does that help us? The distance between the prime numbers is not regular - as far as we know. Perhaps the nontrivial zeros of the Riemann zeta function  ζ (s) might help us with this
question, who knows? But so far, there has been no breakthrough in this direction.

[daydreamer]

Daydreamer,

but the composites have regularities
when I researched different ways to find Primes, I discovered the old multiplication table from school when I was kid,up to 120+ presented as GIF shows all composites have regularities
so all the gaps between for example between 6*2 and 7*2 = 13 is prime numbers
so I based a prime number checking algo,by MUL x*y loop saving into multiply LUT the composites,zeros left after zeroing it=primes

well, what can I say? There is one even prime number: the 2. All other prime numbers are odd. There is still an infinite number of them. Each of these prime numbers lies between two even numbers.
But how does that help us? The distance between the prime numbers is not regular - as far as we know. Perhaps the nontrivial zeros of the Riemann zeta function  ζ (s) might help us with this
question, who knows? But so far, there has been no breakthrough in this direction.

thanks,interesting link
maybe in another dimension,or a dimension which doesnt have our usual time+3dimensions primes have a pattern?
look like caustics outside a boat
I dont remember if that was riemann_zeta,but there is a probability function of high primes returns probability for it might be a prime
I have SIMD experiment on test primes somewhere on forum,just to test use DIVPS and MULPS instead the usual div loop
whats your approach on prime testing?

the function 1/x in school I thought it might be related to wormhole shape

[HSE]

Gunther,

An additional feature is that maximum number always is less (but close) to (q + 1) ^2.

Eventually alway is q *(q+1), but that must be checked.

Updated in Re: 666, mathematics and Satan

HSE

[Gunther]

Daydreamer,

thanks,interesting link

thank you. Hopefully it helped you.

maybe in another dimension,or a dimension which doesnt have our usual time+3dimensions primes have a pattern?

That's very speculative.

I dont remember if that was riemann_zeta,but there is a probability function of high primes returns probability for it might be a prime

Do you mean the Prime number theorem? That' s very closely related to the zeta function.

whats your approach on prime testing?

It depends on the upper limit. For small and medium values, I would use a sieve technique (Eratosthenes or Atkin). But at the moment this question doesn't appear for me,
because I am involved in certain astronomical calculations. Prime numbers don't play a role for that.

the function 1/x in school I thought it might be related to wormhole shape

Wormholes. I've only seen them in certain movies: Star Trek, Deep Space Nine, Stargate SG-1, Déjà Vu, Contact, Donnie Darko etc. Do you know even one experimental result
for the existence of these theoretical objects?

[Gunther]

HSE,

An additional feature is that maximum number always is less (but close) to (q + 1) ^2.

Eventually alway is q *(q+1), ...

this is a remarkable phenomenon.

... but that must be checked.

Checking isn't enough. It should be proofed. The question would be: Is that a worthwhile effort?