Swamp Thing
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If a question posted on Math Stack Exchange, for example, goes unanswered for a couple of days, is it OK to post it on one of the math forums here?
Can I repost unanswered Math Stack Exchange questions here?
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Swamp Thing
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Not coursework, but in my case an interesting numerical observation that this retired engineer and math hobbyist is curious about.
Swamp Thing
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Thanks, that looks like a general math question and not for schoolwork.Swamp Thing said:
Since you find the general math question interesting, I think you can post it here in the math forums with your own LaTeX problem statement and show your initial work on it. Hopefully if we can help you out, in the end you can post a link at SE to our solution at PF just to show them where to go next time...Swamp Thing said:
Swamp Thing
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OK, thanks -- I'll give it a couple of days more and then post here if still unanswered.
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Can't we answer it now? Pleaseberkeman said:Since you find the general math question interesting, I think you can post it here in the math forums with your own LaTeX problem statement and show your initial work on it. Hopefully if we can help you out, in the end you can post a link at SE to our solution at PF just to show them where to go next time...
?!?
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Actually, I'll answer it without waiting for @berkeman's permission, since there is no point for @Swamp Thing to start a thread that will be quickly locked/deleted.
It is pure numerology. Strip out all the fluff (namely the logarithms and the arbitrary 69324), and you are left with a broad and uninteresting statement. You have
$$
\frac{p_1}{p_2} \approx 2^{N/69324}
$$
Considering the extent of what the author thinks as acceptable values of ##N##, namely anything between 120050 and 599310, you can change the above equation to the inequality
$$
3 < \frac{p_1}{p_2} < 400
$$
So, given a prime ##p_2##, can you find another prime that is between 3 and 400 bigger? Yeah, I guess so
It is pure numerology. Strip out all the fluff (namely the logarithms and the arbitrary 69324), and you are left with a broad and uninteresting statement. You have
$$
\frac{p_1}{p_2} \approx 2^{N/69324}
$$
Considering the extent of what the author thinks as acceptable values of ##N##, namely anything between 120050 and 599310, you can change the above equation to the inequality
$$
3 < \frac{p_1}{p_2} < 400
$$
So, given a prime ##p_2##, can you find another prime that is between 3 and 400 bigger? Yeah, I guess so
Swamp Thing
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To simplify a bit, ## 2^{N/69324}## for that range of N generates lots of numbers between 3 and 400, with a spacing of about ##10^{-13}##. So you can easily hit any p1/p2 with an error of that order. So the sample numbers seem to be actually doing not so well, considering.