Find the prime numbers which can written as sum of most consecutive primes

Given an array of limits. For every limit, find the prime number which can be written as the sum of the most consecutive primes smaller than or equal to limit.
The maximum possible value of a limit is 10^4.

Example: 

Input  : arr[] = {10, 30}
Output : 5, 17
Explanation : There are two limit values 10 and 30.
Below limit 10, 5 is sum of two consecutive primes,
2 and 3. 5 is the prime number which is sum of largest 
chain of consecutive below limit 10.

Below limit 30, 17 is sum of four consecutive primes.
2 + 3 + 5 + 7 = 17

Below are steps. 

1. Find all prime numbers below a maximum limit (10^6) using Sieve of Sundaram and store them in primes[].
2. Construct a prefix sum array prime_sum[] for all prime numbers in primes[] 
   prime_sum[i+1] = prime_sum[i] + primes[i]. 
   Difference between two values in prime_sum[i] and prime_sum[j] represents sum of consecutive primes from index i to index j.
3. Traverse two loops , outer loop from i (0 to limit) and inner loop from j (0 to i)
4. For every i, inner loop traverse (0 to i), we check if current sum of consecutive primes (consSum = prime_sum[i] – prime_sum[j]) is prime number or not (we search consSum in prime[] using Binary search).
5. If consSum is prime number then we update the result if the current length is more than length of current result.

Below is implementation of above steps.

C++

\
// C++ program to find Longest Sum of consecutive
// primes
#include<bits/stdc++.h>
using namespace std;
const int MAX  = 10000;

// utility function for sieve of sundaram
void sieveSundaram(vector <int> &primes)
{
    // In general Sieve of Sundaram, produces primes smaller
    // than (2*x + 2) for a number given number x. Since
    // we want primes smaller than MAX, we reduce MAX to half
    // This array is used to separate numbers of the form
    // i+j+2ij from others where 1 <= i <= j
    bool marked[MAX/2 + 1] = {0};

    // Main logic of Sundaram. Mark all numbers which
    // do not generate prime number by doing 2*i+1
    for (int i=1; i<=(sqrt(MAX)-1)/2; i++)
        for (int j=(i*(i+1))<<1; j<=MAX/2; j=j+2*i+1)
            marked[j] = true;

    // Since 2 is a prime number
    primes.push_back(2);

    // Print other primes. Remaining primes are of the
    // form 2*i + 1 such that marked[i] is false.
    for (int i=1; i<=MAX/2; i++)
        if (marked[i] == false)
            primes.push_back(2*i + 1);
}

// function find the prime number which can be written
// as the sum of the most consecutive primes
int LSCPUtil(int limit, vector<int> &prime, long long int sum_prime[])
{
    // To store maximum length of consecutive primes that can
    // sum to a limit
    int max_length = -1;

    // The prime number (or result) that can be represented as
    // sum of maximum number of primes.
    int prime_number = -1;

    // Consider all lengths of consecutive primes below limit.
    for (int i=0; prime[i]<=limit; i++)
    {
        for (int j=0; j<i; j++)
        {
            // if we cross the limit, then break the loop
            if (sum_prime[i] - sum_prime[j] > limit)
                break;

            // sum_prime[i]-sum_prime[j] is prime number or not
            long long int consSum  = sum_prime[i] - sum_prime[j];

            // Check if sum of current length of consecutives is
            // prime or not.
            if (binary_search(prime.begin(), prime.end(), consSum))
            {
                // update the length and prime number
                if (max_length < i-j+1)
                {
                    max_length = i-j+1;
                    prime_number = consSum;
                }
            }
        }
    }

    return prime_number;
}

// Returns the prime number that can written as sum
// of longest chain of consecutive primes.
void LSCP(int arr[], int n)
{
    // Store prime number in vector
    vector<int> primes;
    sieveSundaram(primes);

    long long int sum_prime[primes.size() + 1];

    // Calculate sum of prime numbers and store them
    // in sum_prime array. sum_prime[i] stores sum of
    // prime numbers from primes[0] to primes[i-1]
    sum_prime[0] = 0;
    for (int i = 1 ; i <= primes.size(); i++)
        sum_prime[i] = primes[i-1] + sum_prime[i-1];

    // Process all queries one by one
    for (int i=0; i<n; i++)
      cout << LSCPUtil(arr[i], primes, sum_prime) << " ";
}

// Driver program
int main()
{
    int arr[] = {10, 30, 40, 50, 1000};
    int n = sizeof(arr)/sizeof(arr[0]);
    LSCP(arr, n);
    return 0;
}

Java

// Java program to find longest sum
// of consecutive primes
import java.util.*;

class GFG{

static int MAX = 10000;

// Store prime number in vector
static ArrayList<Object> primes = new ArrayList<Object>();

// Utility function for sieve of sundaram
static void sieveSundaram()
{

    // In general Sieve of Sundaram,
    // produces primes smaller than
    // (2*x + 2) for a number given
    // number x. Since we want primes
    // smaller than MAX, we reduce MAX
    // to half. This array is used to
    // separate numbers of the form
    // i+j+2ij from others where 1 <= i <= j
    boolean []marked = new boolean[MAX / 2 + 1];
    Arrays.fill(marked, false);

    // Main logic of Sundaram. Mark
    // all numbers which do not
    // generate prime number by
    // doing 2*i+1
    for(int i = 1;
            i <= (Math.sqrt(MAX) - 1) / 2; i++)
        for(int j = (i * (i + 1)) << 1;
                j <= MAX / 2;
                j = j + 2 * i + 1)
            marked[j] = true;

    // Since 2 is a prime number
    primes.add(2);

    // Print other primes. Remaining
    // primes are of the form 2*i + 1
    // such that marked[i] is false.
    for(int i = 1; i <= MAX / 2; i++)
        if (marked[i] == false)
            primes.add(2 * i + 1);
}

// Function find the prime number
// which can be written as the
// sum of the most consecutive primes
static int LSCPUtil(int limit, long []sum_prime)
{

    // To store maximum length of
    // consecutive primes that can
    // sum to a limit
    int max_length = -1;

    // The prime number (or result)
    // that can be represented as
    // sum of maximum number of primes.
    int prime_number = -1;

    // Consider all lengths of
    // consecutive primes below limit.
    for(int i = 0; (int)primes.get(i) <= limit; i++)
    {
        for(int j = 0; j < i; j++)
        {

            // If we cross the limit, then
            // break the loop
            if (sum_prime[i] - sum_prime[j] >
                limit)
                break;

            // sum_prime[i]-sum_prime[j] is
            // prime number or not
            long consSum  = sum_prime[i] -
                            sum_prime[j];

            Object[] prime = primes.toArray();

            // Check if sum of current length
            // of consecutives is prime or not.
            if (Arrays.binarySearch(
                prime, (int)consSum) >= 0)
            {

                // Update the length and prime number
                if (max_length < i - j + 1)
                {
                    max_length = i - j + 1;
                    prime_number = (int)consSum;
                }
            }
        }
    }
    return prime_number;
}

// Returns the prime number that
// can written as sum of longest
// chain of consecutive primes.
static void LSCP(int []arr, int n)
{
    sieveSundaram();

    long []sum_prime = new long[primes.size() + 1];

    // Calculate sum of prime numbers
    // and store them in sum_prime
    // array. sum_prime[i] stores sum
    // of prime numbers from
    // primes[0] to primes[i-1]
    sum_prime[0] = 0;
    for(int i = 1; i <= primes.size(); i++)
        sum_prime[i] = (int)primes.get(i - 1) +
                             sum_prime[i - 1];

    // Process all queries one by one
    for(int i = 0; i < n; i++)
      System.out.print(LSCPUtil(
          arr[i], sum_prime) + " ");
}

// Driver code
public static void main(String []arg)
{
    int []arr = { 10, 30, 40, 50, 1000 };
    int n = arr.length;

    LSCP(arr, n);
}
}

// This code is contributed by pratham76

Python3

# Python3 program to find Longest Sum of consecutive
# primes
MAX  = 10000;

# utility function for sieve of sundaram
def sieveSundaram(primes):

    # In general Sieve of Sundaram, produces primes smaller
    # than (2*x + 2) for a number given number x. Since
    # we want primes smaller than MAX, we reduce MAX to half
    # This array is used to separate numbers of the form
    # i+j+2ij from others where 1 <= i <= j
    marked = [0 for _ in range(1 + MAX // 2)]

    # Main logic of Sundaram. Mark all numbers which
    # do not generate prime number by doing 2*i+1
    for i in range(1, 1 + (int(MAX ** 0.5) - 1) // 2):
        for j in range((i*(i+1))<<1, 1 + MAX//2, 2*i+1):
            marked[j] = True

    # Since 2 is a prime number
    primes.append(2);

    # Print other primes. Remaining primes are of the
    # form 2*i + 1 such that marked[i] is false.
    for i in range(1, 1 + MAX // 2):
        if (marked[i] == False):
            primes.append(2*i + 1);

    return primes


# function find the prime number which can be written
# as the sum of the most consecutive primes
def LSCPUtil(limit, prime, sum_prime):

    # To store maximum length of consecutive primes that can
    # sum to a limit
    max_length = -1;

    # The prime number (or result) that can be represented as
    # sum of maximum number of primes.
    prime_number = -1;

    # Consider all lengths of consecutive primes below limit.
    i = 0
    while (prime[i] <= limit):
        for j in range(i):

            # if we cross the limit, then break the loop
            if (sum_prime[i] - sum_prime[j] > limit):
                break;

            # sum_prime[i]-sum_prime[j] is prime number or not
            consSum  = sum_prime[i] - sum_prime[j];

            # Check if sum of current length of consecutives is
            # prime or not.
            if consSum in prime:
                # update the length and prime number
                if (max_length < i-j+1):
                    max_length = i-j+1;
                    prime_number = consSum
        i += 1

    return prime_number;


# Returns the prime number that can written as sum
# of longest chain of consecutive primes.
def LSCP(arr, n):

    # Store prime number in vector
    primes = [];
    primes = sieveSundaram(primes);

    sum_prime = [None for _ in range(1 + len(primes))]

    # Calculate sum of prime numbers and store them
    # in sum_prime array. sum_prime[i] stores sum of
    # prime numbers from primes[0] to primes[i-1]
    sum_prime[0] = 0;
    for i in range(1, 1 + len(primes)):
        sum_prime[i] = primes[i-1] + sum_prime[i-1];

    # Process all queries one by one
    for i in range(n):
      print(LSCPUtil(arr[i], primes, sum_prime), end = " ");

# Driver program
arr = [ 10, 30, 40, 50, 1000 ];
n = len(arr)
LSCP(arr, n);

# This code is contributed by phasing17

C#

// C# program to find longest sum
// of consecutive primes
using System;
using System.Collections;

class GFG{

static int MAX = 10000;

// Store prime number in vector
static ArrayList primes = new ArrayList();

// Utility function for sieve of sundaram
static void sieveSundaram()
{

    // In general Sieve of Sundaram,
    // produces primes smaller than
    // (2*x + 2) for a number given
    // number x. Since we want primes
    // smaller than MAX, we reduce MAX
    // to half. This array is used to
    // separate numbers of the form
    // i+j+2ij from others where 1 <= i <= j
    bool []marked = new bool[MAX / 2 + 1];
    Array.Fill(marked, false);

    // Main logic of Sundaram. Mark
    // all numbers which do not
    // generate prime number by
    // doing 2*i+1
    for(int i = 1;
            i <= (Math.Sqrt(MAX) - 1) / 2; i++)
        for(int j = (i * (i + 1)) << 1;
                j <= MAX / 2;
                j = j + 2 * i + 1)
            marked[j] = true;

    // Since 2 is a prime number
    primes.Add(2);

    // Print other primes. Remaining
    // primes are of the form
    // 2*i + 1 such that marked[i] is false.
    for(int i = 1; i <= MAX / 2; i++)
        if (marked[i] == false)
            primes.Add(2 * i + 1);
}

// Function find the prime number
// which can be written as the
// sum of the most consecutive primes
static int LSCPUtil(int limit, long []sum_prime)
{

    // To store maximum length of
    // consecutive primes that can
    // sum to a limit
    int max_length = -1;

    // The prime number (or result)
    // that can be represented as
    // sum of maximum number of primes.
    int prime_number = -1;

    // Consider all lengths of
    // consecutive primes below limit.
    for(int i = 0; (int)primes[i] <= limit; i++)
    {
        for(int j = 0; j < i; j++)
        {

            // If we cross the limit, then
            // break the loop
            if (sum_prime[i] - sum_prime[j] >
                limit)
                break;

            // sum_prime[i]-sum_prime[j] is
            // prime number or not
            long consSum  = sum_prime[i] -
                            sum_prime[j];

            int[] prime = (int[])primes.ToArray(typeof(int));

            // Check if sum of current length
            // of consecutives is prime or not.
            if (Array.BinarySearch(prime,
                (int)consSum) >= 0)
            {

                // Update the length and prime number
                if (max_length < i - j + 1)
                {
                    max_length = i - j + 1;
                    prime_number = (int)consSum;
                }
            }
        }
    }
    return prime_number;
}

// Returns the prime number that
// can written as sum of longest
// chain of consecutive primes.
static void LSCP(int []arr, int n)
{
    sieveSundaram();

    long []sum_prime = new long[primes.Count + 1];

    // Calculate sum of prime numbers
    // and store them in sum_prime
    // array. sum_prime[i] stores sum
    // of prime numbers from
    // primes[0] to primes[i-1]
    sum_prime[0] = 0;
    for(int i = 1; i <= primes.Count; i++)
        sum_prime[i] = (int)primes[i - 1] +
                         sum_prime[i - 1];

    // Process all queries one by one
    for(int i = 0; i < n; i++)
      Console.Write(LSCPUtil(
          arr[i], sum_prime) + " ");
}

// Driver code
public static void Main(string []arg)
{
    int []arr = { 10, 30, 40, 50, 1000 };
    int n = arr.Length;

    LSCP(arr, n);
}
}

// This code is contributed by rutvik_56

Javascript

// JavaScript program to find Longest Sum of consecutive
// primes
let MAX  = 10000;

// utility function for sieve of sundaram
function sieveSundaram(primes)
{
    // In general Sieve of Sundaram, produces primes smaller
    // than (2*x + 2) for a number given number x. Since
    // we want primes smaller than MAX, we reduce MAX to half
    // This array is used to separate numbers of the form
    // i+j+2ij from others where 1 <= i <= j
    let marked = new Array(Math.floor(MAX / 2) + 1).fill(0);

    // Main logic of Sundaram. Mark all numbers which
    // do not generate prime number by doing 2*i+1
    for (var i=1; i<=(Math.sqrt(MAX)-1)/2; i++)
        for (var j=(i*(i+1))<<1; j<=MAX/2; j=j+2*i+1)
            marked[j] = true;

    // Since 2 is a prime number
    primes.push(2);

    // Print other primes. Remaining primes are of the
    // form 2*i + 1 such that marked[i] is false.
    for (var i=1; i<=MAX/2; i++)
        if (marked[i] == false)
            primes.push(2*i + 1);
}

// function find the prime number which can be written
// as the sum of the most consecutive primes
function LSCPUtil(limit, prime, sum_prime)
{
    // To store maximum length of consecutive primes that can
    // sum to a limit
    let max_length = -1;

    // The prime number (or result) that can be represented as
    // sum of maximum number of primes.
    let prime_number = -1;

    // Consider all lengths of consecutive primes below limit.
    for (var i=0; prime[i]<=limit; i++)
    {
        for (var j=0; j<i; j++)
        {
            // if we cross the limit, then break the loop
            if (sum_prime[i] - sum_prime[j] > limit)
                break;

            // sum_prime[i]-sum_prime[j] is prime number or not
            let consSum  = sum_prime[i] - sum_prime[j];

            // Check if sum of current length of consecutives is
            // prime or not.
            if (prime.indexOf(consSum) != -1)
            {
                // update the length and prime number
                if (max_length < i-j+1)
                {
                    max_length = i-j+1;
                    prime_number = consSum;
                }
            }
        }
    }

    return prime_number;
}

// Returns the prime number that can written as sum
// of longest chain of consecutive primes.
function LSCP(arr, n)
{
    // Store prime number in vector
    let primes = [];
    sieveSundaram(primes);

    let sum_prime = new Array(primes.length + 1);

    // Calculate sum of prime numbers and store them
    // in sum_prime array. sum_prime[i] stores sum of
    // prime numbers from primes[0] to primes[i-1]
    sum_prime[0] = 0;
    for (var i = 1 ; i <= primes.length; i++)
        sum_prime[i] = primes[i-1] + sum_prime[i-1];

    // Process all queries one by one
    for (var i=0; i<n; i++)
      process.stdout.write(LSCPUtil(arr[i], primes, sum_prime) + " ");
}

// Driver program
let arr = [ 10, 30, 40, 50, 1000 ];
let n = arr.length;
LSCP(arr, n);

// This code is contributed by phasing17

Output: 

5 17 17 41 953

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