# Riddle 10: Summation of primes

### [The Task](https://projecteuler.net/problem=10)

> The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

> Find the sum of all the primes below two million.

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This task is so easy that it is almost not worth its own post. The reason is because it is identical to Task 7, ["10001st prime"](https://picolisp-explored.com/riddle-7-10001st-prime) except that we need to add one single line.

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### The solution

What we need to do is:
1. Generate a list of all prime numbers below 2.000.000,
2. Sum up all list items.

For 1., we can re-use the code from Task 7 without modification. The only challenge is that instead of 10.000 prime numbers, we need to calculate around **150.000** prime numbers. Then we sum all list items up with ``apply``:

```undefined
(load "./Task_7_10001_Prime_final.l")
(prinl (apply + (sieve 2000000)))
```

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Let's compare the computation time for Task 7 and Task 10.

```
: (bench (apply + (sieve 110000)))
0.114 sec
-> 544815056
: (bench (apply + (sieve 2000000)))
5.135 sec
-> 142913828922
```

The computation time has increased from 0.1 s to 5.1 s, but is still much faster than the 60 seconds that the task description allows.

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You can find the "code" for the finished task [here](https://gitlab.com/picolisp-blog/single-plage-scripts/-/blob/main/euler/Task_10_Summation_of_primes.l).


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### Sources

- https://projecteuler.net/problem=10