What is the minimum size of an interval to determine there must contain a prime number? And so on. | Mathematics | Page 1

foggy vigil Dec 13, 2023, 10:37 AM

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What is the minimum size of an interval to determine there must contain a prime number? And so on for more amount of primes?

primal turtle Dec 13, 2023, 10:41 AM

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well, the primes have no explicit pattern, and as you study higher numbers, the frequency of primes obv decrease

forest geyser Dec 13, 2023, 10:50 AM

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you sure?

primal turtle Dec 13, 2023, 10:54 AM

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YOU sure?

lyric thorn Dec 13, 2023, 12:45 PM

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Only thing I know of is that one thereom stating for integer n, there must be a prime in [n,2n]

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Bertrand’s postulate

stiff sail Dec 13, 2023, 3:10 PM

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there are arbitrarily large intervals with no primes, so infinity

foggy vigil Dec 13, 2023, 6:47 PM

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any examples? Like intervals with the span over 20 integers?

stiff sail Dec 13, 2023, 7:36 PM

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21! + 2…21! + 21

lyric thorn Dec 13, 2023, 8:59 PM

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You also could’ve done the product of all primes up to and including 21

stiff sail Dec 13, 2023, 10:35 PM

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more effort

#What is the minimum size of an interval to determine there must contain a prime number? And so on.