SieveOfEratosthenes | Topcoder Archive

Problem Statement

The Sieve of Erathosthenes is an ancient method used to find all prime numbers between 2 and a given upper bound maxNum, inclusive. It works like this:

make a list of all numbers between 2 and maxNum, inclusive
for x = 2 to maxNum
   if x is not scratched
      for y = 2 to maxNum/x
         if x*y is not scratched, scratch x*y
      end for
   end if
end for

In this fashion, every composite number in the range will get scratched while every prime number will remain unscratched. Return the last number which gets scratched when the Sieve of Eratosthenes is run with the given maxNum.

Definition

Class:: SieveOfEratosthenes
Method:: lastScratch
Parameters:: int
Returns:: int
Method signature:: int lastScratch(int maxNum)
(be sure your method is public)

Constraints

maxNum will be between 4 and 2000000000 (2*109), inclusive.

Examples

```
18
```
```
Returns: 15
```
When x=2, the numbers 4, 6, 8, 10, 12, 14, 16, and 18 are scratched. When x=3, only 9 and 15 are scratched (other multiples like 6 and 12 were already scratched in a previous step). For x=5,7,11,13 and 17, there are no new scratches. Therefore, the answer is 15.
```
5
```
```
Returns: 4
```
2, 3 and 5 are all primes, so the only scratched number is 4.
```
100
```
```
Returns: 91
```
```
400
```
```
Returns: 361
```

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