## PROBLEM LINKS

## Author:SRIKANT BADRI

## DIFFICULTY:

SIMPLE

## PREREQUISITES:

## PROBLEM:

To find all prime numbers upto 10^7

## EXPLANATION:

To gain 100 points one must know an efficient algorithm to evaluate prime numbers upto 10^7 in 1 sec. One such algorithm is Sieve Of Eratosthenes.

The approach used by this algorithm is:

Step 1:Create a bool arrray having size 10000000.

Step 2:Initialize every value of that array with true & initialize index 0,1 as false since they are not primes.

(You can use memset function in C,C++ for this)

Step 3: Pick a number from bool array which is not false.

Step 4: Make all multiples of that number in the array as false.

Step 5: Repeat step 3 & 4 until all the elements (<=10000000) having true value have not been considered.

Step 6: All the elements having true values are primes.

The code for above algorithm is:

```
bool Primes[10000003];
long long int i,j;
memset(Primes,true,sizeof(Primes));
Primes[0]=false;
Primes[1]=false;
for(i=2;i<=10000000;i++)
{
if(Primes[i])
{
for(j=i*2;j<=10000000;j+=i)
{
Primes[j]=false;
}
}
}
```