The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000720

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A000720

pi(n), the number of primes <= n. Sometimes called PrimePi(n) to distinguish it from the number 3.14159...
(history; published version)

#394 by R. J. Mathar at Sat Aug 03 12:28:31 EDT 2024

STATUS

editing

approved

#393 by R. J. Mathar at Sat Aug 03 12:28:21 EDT 2024

LINKS

Bent E. Petersen, <a href="https://www.math.ucdavis.edu/~tracy/courses/math205A/PNT_Petersen.pdf">Prime Number Theorem</a>, Seminar Lecture Note, 1996; <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.502.4684&rep=rep1&type=pdf/118ddc1708154d5a7d5aaf28b9527c33f0ee5b69">version 2002-05-14</a>.

STATUS

approved

editing

#392 by Stefano Spezia at Sun May 19 11:56:06 EDT 2024

MATHEMATICA

PrimePiOptimized[n_] := Count[Range[2, n], _?PrimeQ] (* Navvye Anand, May 19 2024 *)

KEYWORD

nonn,core,easy,nice,changed

STATUS

proposed

approved

#391 by Michel Marcus at Sun May 19 07:24:23 EDT 2024

STATUS

editing

proposed

Discussion

Sun May 19

08:56

Amiram Eldar: I am getting 0.015625 for Timing[Array[PrimePi[#] &, 3000];] and 2.234375 for PrimePiOptimized[n_] := Count[Range[2, n], _?PrimeQ]; Timing[Array[PrimePiOptimized, 3000];], i.e., your code is 100 times slower.

09:01

Navvye Anand: That's weird, for me it's showing the opposite, as shown in https://ibb.co/JHT4XXJ. Could you try AbsoluteTiming?

09:08

Amiram Eldar: Try 10000: With PrimePi you don't wait. Then try with PrimePiOptimized and see for yourself.

11:55

Stefano Spezia: Trying 100000 your code is about 300 slower. I will revert your change

#390 by Michel Marcus at Sun May 19 07:23:19 EDT 2024

MATHEMATICA

PrimePiOptimized[n_] := Count[Range[2, n], _?PrimeQ] (* Navvye Anand, May 19, 2024 *)

STATUS

proposed

editing

Discussion

Sun May 19

07:24

Michel Marcus: no comma in the date ; next time please use (* ~~~~ *) to sign , as explained in the stylesheet

#389 by Navvye Anand at Sun May 19 07:21:25 EDT 2024

STATUS

editing

proposed

#388 by Navvye Anand at Sun May 19 07:18:41 EDT 2024

MATHEMATICA

PrimePiOptimized[n_] := Count[Range[2, n], _?PrimeQ] (* Navvye Anand, May 19, 2024 *)

STATUS

approved

editing

Discussion

Sun May 19

07:21

Navvye Anand: Faster way of counting the number of primes less than or equal to n. https://ibb.co/JHT4XXJ.

#387 by Andrey Zabolotskiy at Fri Mar 22 07:32:49 EDT 2024

STATUS

editing

approved

#386 by Andrey Zabolotskiy at Fri Mar 22 07:32:46 EDT 2024

FORMULA

Let pf(n) denote the set of prime factors of an integer n. Then a(n) = card(pf(n!/floor(n/2)!)). - Peter Luschny, Mar 13 2011

STATUS

approved

editing

#385 by Peter Luschny at Tue Sep 05 04:25:49 EDT 2023

STATUS

editing

approved