How to create the most compact mapping n → isprime(n) up to a limit N?

Question

Naturally, for bool isprime(number) there would be a data structure I could query.
I define the best algorithm, to be the algorithm that pr

Answer 1

I have got a prime function which works until (2^61)-1 Here:

from math import sqrt
def isprime(num): num > 1 and return all(num % x for x in range(2, int(sqrt(num)+1)))

Explanation:

The all() function can be redefined to this:

def all(variables):
    for element in variables:
        if not element: return False
    return True

The all() function just goes through a series of bools / numbers and returns False if it sees 0 or False.

The sqrt() function is just doing the square root of a number.

For example:

>>> from math import sqrt
>>> sqrt(9)
>>> 3
>>> sqrt(100)
>>> 10

The num % x part returns the remainder of num / x.

Finally, range(2, int(sqrt(num))) means that it will create a list that starts at 2 and ends at int(sqrt(num)+1)

For more information about range, have a look at this website!

The num > 1 part is just checking if the variable num is larger than 1, becuase 1 and 0 are not considered prime numbers.

I hope this helped :)