Problem 52567. Easy Sequences 7: Easy as Composite Pi
The prime Pi function is defined as the number of prime numbers from 1 to a certain given limit. In MATLAB, it is easy to create a prime Pi procedure, because there are built-in functions such as "primes" and "isprime". To calculate the prime Pi up to 100, we may just proceed as follows:
>> numel(primes(100))
>> ans =
25
>> nnz(isprime(1:100))
>> ans =
25
Can we make a function for "composite Pi", which is the number of composite numbers from 1 to a given limit, inclusive? Let's find out...
NOTE: The number '1' is considered as neither prime nor composite.
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3 Comments
Lincoln Poon
on 25 Oct 2022
I mean...doing this above 1e10 won't be easy anyway, no matter prime or composite.
GeeTwo
on 26 Oct 2022
Lincoln Poon,
Yes, they're really the same problem, as (designating the composite counting function as κ(n)), κ(n) + ?(n) + 1 = n. There are techniques to do the count without creating an array for x>√n, and even for x>∛n.
Rafael S.T. Vieira
on 15 Nov 2022
If anyone does find a way to solve this precisely without some hack, please, publish a scientific paper, and do not post your code here. This problem is not made from an easy sequence at all.
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