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Ruud H.G. van Tol on Fri, 02 Feb 2024 04:23:07 +0100
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Re: primepi([from,until])
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: primepi([from,until])
- From: "Ruud H.G. van Tol" <rvtol@isolution.nl>
- Date: Fri, 2 Feb 2024 04:22:58 +0100
- Delivery-date: Fri, 02 Feb 2024 04:23:07 +0100
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- In-reply-to: <Zbv7st/VF+x7AaIH@seventeen>
- References: <eea41fa1-7ed8-442c-a395-17a3cc7dcb47@isolution.nl> <Zbv7st/VF+x7AaIH@seventeen>
On 2024-02-01 21:14, Bill Allombert wrote:
On Thu, Feb 01, 2024 at 09:08:00PM +0100, Ruud H.G. van Tol wrote:
I'm adding
a(n) = #primes( [ n^2/4, (n+1)^2/4 ] );
to https://oeis.org/A220492
and was wondering if primepi() should grow a primepi([x1, x2]) variant,
to return the number of primes p, x1 <= p <= x2.
just do primepi(floor(x2))- primepi(ceil(x1)-1) or something ?
a(n) = #primes( [ n^2/4, (n+1)^2/4 ] )
? a( prime(2^16) );
cpu time = 3 ms, real time = 3 ms.
a1(n) = primepi((n+1)^2/4) - primepi(n^2/4)
? a1( prime(2^16) );
cpu time = 1min, 12,013 ms, real time = 1min, 12,437 ms.
So for this case, the primepi-delta-version is much slower.
-- Ruud