Testwiki:Reference desk/Archives/Mathematics/2018 December 28

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December 28

Primes less than a given limit

Is there a website or program that I can download that will give the number of primes less than a given limit, the various limits are $<10^{14}$. Bubba73 ^{You talkin' to me?} 05:40, 28 December 2018 (UTC)

Prime-counting_function. Bo Jacoby (talk) 05:46, 28 December 2018 (UTC).

I know of that article, but I'm looking for an implentation of one of those algorithms. Bubba73 ^{You talkin' to me?} 06:38, 28 December 2018 (UTC)

Perhaps [1] will help. Replace the 1000000 with the number(s) you're interested in. --RDBury (talk) 12:46, 28 December 2018 (UTC)

That doesn't give the exact value for as large as I need it. Bubba73 ^{You talkin' to me?} 19:53, 28 December 2018 (UTC)

Prime-counting function#External links gives [2] and [3]. PrimeHunter (talk) 20:05, 28 December 2018 (UTC)

Thanks, but the first one gives exact values only up to $3\cdot 10^{13}$ and I need up to about $7\cdot 10^{13}$. The second one has a lot of good stuff, but not quite what I'm looking far. I need 62 specific values of $\pi (n)$ to confirm or refute a minor conjecture. I've started a simple sieve to give me the data I need - in the meantime I'm working on my main program. Bubba73 ^{You talkin' to me?} 22:53, 28 December 2018 (UTC)