Incorrect guess based on limited data: Number of Primes 6k-1 > Number of Primes 6k+1

[retina]

Originally Posted by Dobri

Thus I do not understand why an anonymous mod had to change the thread icon from 'question' sign to 'minus' sign.

Conjecture is too strong of a term for what is really just a basic observation over small numbers, so perhaps that was the impetus for the change. Anyhow, I didn't change it, it is merely guess.

[Dobri]

Originally Posted by retina

Conjecture is too strong of a term for what is really just a basic observation over small numbers, so perhaps that was the impetus for the change. Anyhow, I didn't change it, it is merely guess.

Please kindly delete "Conjecture" from the title if this would remove also the 'minus' icon.

[charybdis]

Originally Posted by Dobri

This is my humble task, to find the first crossover point for the mod 6 prime number race. Let the number theorists ponder about the long-term trends after that indeed.

It's at 608981813017, immediately before the first crossover in the mod 3 race which occurs at the following prime.

[Dobri]

Originally Posted by charybdis

It's at 608981813017, immediately before the first crossover in the mod 3 race which occurs at the following prime.

It is not explicitly said that x in π(x) has to be a prime at a crossover point.

[retina]

Originally Posted by Dobri

Please kindly delete "Conjecture" from the title if this would remove also the 'minus' icon.

It isn't just the title, the entire post reinforces the claim.

[charybdis]

Originally Posted by Dobri

It is not explicitly said that x in π(x) has to be a prime at a crossover point.

Leaving aside that the OEIS sequence I linked has an error in the definition (the terms given are q*k+1, not k), how do you expect a crossover to occur at a number that isn't prime?

[Dobri]

Originally Posted by retina

It isn't just the title, the entire post reinforces the claim.

Apparently, I am unable to edit the initial post anymore after the elapsed time.

[Dobri]

Originally Posted by charybdis

Leaving aside that the OEIS sequence I linked has an error in the definition (the terms given are q*k+1, not k), how do you expect a crossover to occur at a number that isn't prime?

I meant that after the occurrence of a crossover, it still could be observed for some x afterwards as the prime count would remain intact.

[Dobri]

What is of importance is a relative term in mathematics. One could state that a shift by 1 is irrelevant. But a shift down by one for Mersenneries could mean getting a new prime instead of dealing just with powers of 2.

[VBCurtis]

Originally Posted by Dobri

What is of importance is a relative term in mathematics. One could state that a shift by 1 is irrelevant. But a shift down by one for Mersenneries could mean getting a new prime instead of dealing just with powers of 2.

Making this sort of "point" to defend your arguments is likely related to why the thread got the red mark of "no new math in this here conjecture."

[Dobri]

Well, at least there is no strict proof about what happens with the prime race at infinity and it seems that since 1978 there was no new attempt to find a second reversal point or even verify the validity of the first one.