Project Euler - problem 10

"Find the sum of all the primes below two million"

Prime number generation has been at the forefront of mathematics since ancient times, and they are one of the most critical parts of the modern Internet landscape: from cryptography to Bitcoin.

To say that prime numbers are essential is not an understatement.

To work with prime numbers we have to clear some basics:

• Prime numbers cannot be divided by any other number other than itself (and one, of course)
• Numbers zero, one and all negatives are not primes - don't insist!
• Prime number generation is a very intensive process
• Get acquainted with prime numbers by learning about the [sieve of Eratosthenes] https://planetmath.org/sieveoferatosthenes

To build a prime number generator, we have to examine two pieces: (1) the "prime number generator" and (2) the accumulator loop

In Python 3, part (1) looks like this

... def isPrime(num): isPrime = True numSqr = math.floor(math.sqrt(num)) + 1 ## negatives, 0 and 1 are not prime numbers if (num < 2): isPrime = False else : if (num == 2): isPrime = True else: ## test each divisor: ## smaller than sqrt of the candidate number, plus one for ix in range (2, numSqr): if (num % ix == 0): isPrime = False break ...

Part (2) can look like a loop through a range of numbers, with an accumulator that sums the prime numbers produced.

Enjoy!