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Old 2021-08-27, 00:52   #23
retina
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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.
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Old 2021-08-27, 00:56   #24
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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.
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Old 2021-08-27, 00:57   #25
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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.
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Old 2021-08-27, 01:47   #26
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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.
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Old 2021-08-27, 02:03   #27
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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.
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Old 2021-08-27, 02:13   #28
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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?
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Old 2021-08-27, 04:30   #29
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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.
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Old 2021-08-27, 04:35   #30
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Quote:
Originally Posted by charybdis View Post
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.
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Old 2021-08-27, 04:52   #31
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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.
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Old 2021-08-27, 05:17   #32
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Originally Posted by Dobri View Post
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."
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Old 2021-08-27, 05:26   #33
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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.
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