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| − | Find the largest prime below $10^9$ | + | Find the largest prime below $10^9$ and which number is it in the list of primes?Which one is next? Compare to the prime-counting function $\pi(x)$ that counts how many primes are there below $x$ and which Gauss approximated to $x/\ln(x)$. |
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| − | Answer: This is $999\,999\,937$, the $50\,847\,534$th prime number, for which the prime-counting function $\pi(x)$ compares to Gauss' approximation $\pi(x)\approx x/\ln x=48\,254\,942$ to withing 5% accuracy. | + | Answer: This is $999\,999\,937$, the $50\,847\,534$th prime number, for which the prime-counting function $\pi(x)$ compares to Gauss' approximation $\pi(x)\approx x/\ln x=48\,254\,942$ to withing 5% accuracy. The next prime is $1\,000\,000\,007$. |
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Find the largest prime below $10^9$ and which number is it in the list of primes?Which one is next? Compare to the prime-counting function $\pi(x)$ that counts how many primes are there below $x$ and which Gauss approximated to $x/\ln(x)$.
Answer: This is $999\,999\,937$, the $50\,847\,534$th prime number, for which the prime-counting function $\pi(x)$ compares to Gauss' approximation $\pi(x)\approx x/\ln x=48\,254\,942$ to withing 5% accuracy. The next prime is $1\,000\,000\,007$.
well, more things today?