Apa itu Teorema Bilangan Prima?

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π(n): prime counting function versus n/ln(n) approximation

π(n) counts the primes up to n (blue staircase). The Prime Number Theorem says π(n) ~ n/ln(n) – the ratio → 1 as n → ∞. The logarithmic integral Li(n) is even closer.

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How thin do primes become?

Table showing density of primes at various scales

Bis n	Primzahlen π(n)	Dichte ≈ 1/ln(n)
1 000	168	1 von 7
1 000 000	78 498	1 von 14
10⁹	50 847 534	1 von 21
10¹²	37 607 912 018	1 von 28

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Topic roundups

#memoryAll memory gamesHold a sequence, grid, or list in working memory and reproduce it under pressure.#numbersAll numbers gamesArithmetic, ratios, units, and number sense in short timed rounds.#sequenceAll sequence gamesReproduce or extend an ordered string of items in the right order.