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  3. Number Theory
  4. Twins
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Twins

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  • 2k23_cscys231043
     + 0 comments
    def sieve_of_eratosthenes(max_num):
    is_prime = [True] * (max_num + 1)
    p = 2
    while (p * p <= max_num):
        if (is_prime[p] == True):
            for i in range(p * p, max_num + 1, p):
                is_prime[i] = False
        p += 1
    prime_numbers = [p for p in range(2, max_num + 1) if is_prime[p]]
    return prime_numbers

def count_twin_primes(L, R):
    primes = sieve_of_eratosthenes(R)
    primes_in_range = [p for p in primes if p >= L]
    twin_prime_count = 0
    for i in range(len(primes_in_range) - 1):
        if primes_in_range[i + 1] - primes_in_range[i] == 2:
            twin_prime_count += 1
            
    return twin_prime_count

L, R = map(int, input().split())
result = count_twin_primes(L, R)
print(result)

  • japowa3965
     + 0 comments

    #include

    #include

    #include

    #include

    #include

    using namespace std;

    int primeTable[100001];

    vector primeList;

    void sieve(){

    fill(primeTable,primeTable+100000,0);

    primeTable[1]=1;

    for(int i=2;i<=100000;i++){

    if(primeTable[i]==0){

    primeList.push_back(i);

    for(int j=i*2;j<=100000;j+=i) primeTable[j]=1;

    }

    }

    }

    bool isPrime[1000001];

    void fill_up(int n,int m){

    //cout<

    if(n==1) isPrime[0]=true;

    for(int i=0;i

    int start=n/primeList[i];

    if(n%primeList[i]!=0) start++;

    int end=m/primeList[i];

    for(int j=max(2,start);j<=end;j++){

    isPrime[j*primeList[i]-n]=true;

    }

    }

    }

    int main() {

    /* Enter your code here. Read input from STDIN. Print output to STDOUT */

    int n,m;

    cin>>n>>m;

    sieve();

    fill_up(n,m);

    int ans=0;

    for(int i=0;i+2<=m-n;i++){

    if(isPrime[i]==false && isPrime[i+2]==false) ans++;

    }

    cout< return 0; }

  • japowa3965
     + 0 comments

    include

    include

    include

    include

    include

    using namespace std;

    int primeTable[100001]; vector primeList; void sieve(){ fill(primeTable,primeTable+100000,0); primeTable[1]=1; for(int i=2;i<=100000;i++){ if(primeTable[i]==0){ primeList.push_back(i); for(int j=i*2;j<=100000;j+=i) primeTable[j]=1; } } }

    bool isPrime[1000001]; void fill_up(int n,int m){ //cout<

    int main() { /* Enter your code here. Read input from STDIN. Print output to STDOUT */ int n,m; cin>>n>>m; sieve(); fill_up(n,m); int ans=0; for(int i=0;i+2<=m-n;i++){ if(isPrime[i]==false && isPrime[i+2]==false) ans++; } cout<

  • japowa3965
     + 0 comments

    include

    include

    include

    include

    include

    using namespace std;

    int primeTable[100001]; vector primeList; void sieve(){ fill(primeTable,primeTable+100000,0); primeTable[1]=1; for(int i=2;i<=100000;i++){ if(primeTable[i]==0){ primeList.push_back(i); for(int j=i*2;j<=100000;j+=i) primeTable[j]=1; } } }

    bool isPrime[1000001]; void fill_up(int n,int m){ //cout<

    int main() { /* Enter your code here. Read input from STDIN. Print output to STDOUT */ int n,m; cin>>n>>m; sieve(); fill_up(n,m); int ans=0; for(int i=0;i+2<=m-n;i++){ if(isPrime[i]==false && isPrime[i+2]==false) ans++; } cout<

  • harpercrane3
     + 0 comments

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