This is problem 10 on Project Euler:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
This is another problem where I cannot see any other solution than the brute-force approach of simply adding primes until we find a prime greater than two million.
This is the Delphi code:
1procedure TfrmMain.Problem10;
2var
3 x : integer;
4 primeSum : int64;
5begin
6 GetPrimeList(2000000);
7 primeSum := 0;
8 for x := 0 to lstPrimes.Count - 1 do
9 inc(primeSum, GetPrime(x));
10 ShowMessage(IntToStr(primeSum));
11end;Line 6 populates our list of prime numbers with all primes up to 2 000 000. Line 7 initialises the result (primeSum) to zero. We then go through the list adding each entry to the result.
On my PC this code takes 62 milliseconds to execute.
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With 1 excluded, the smallest prime is therefore 2. However, since 2 is the only even prime (which, ironically, in some sense makes it the “oddest” prime), it is also somewhat special, and the set of all primes excluding 2 is therefore called the ” odd primes .” Note also that while 2 is considered a prime today, at one time it was not (Tietze 1965, p. 18; Tropfke 1921, p. 96).