The first line gives the number of queries T, and each of the next T lines gives an even number n.
For each query print, on its own line, the number of ways to write n as a sum of two primes n = p + q with p ≤ q.
Swapping p and q is the same way (10 = 3 + 7 = 7 + 3 counts once).
p = q is allowed (6 = 3 + 3).
1 is not a prime.
4 4 6 10 100
1 1 2 6
When you run, these lines are fed to input()/stdin in order (the program doesn't stop to ask).
$ Ready
Open this on a computer to write and run code. On mobile you can read the problem and the solutions.
With 1,000 queries, testing each number by trial division is slow.
Find the primes up to 9,000 once with the sieve of Eratosthenes, then for each query try every p up to n/2 and look up whether n - p is prime in the table.
Building the sieve differs by language: Python [True] * (n + 1), JavaScript/TypeScript new Array(n + 1).fill(true), Java/C# new boolean[n + 1]/new bool[n + 1] (they start all false, so use them as a 'composite' table and skip filling), C static bool (only global/static arrays start at zero; a local array inside a function holds garbage), C++ std::vector<bool>(n + 1, true), Craykon NewList(n + 1, true).
Craykon lists hold at most 10,000 items, which is why n stops at 9,000.
Three common traps: not marking 0 and 1 as non-prime (counting 4 = 1 + 3), writing p < q and missing 6 = 3 + 3, and running p all the way to n so 3 + 7 and 7 + 3 are counted twice.
import sys LIMIT = 9000 # 에라토스테네스의 체: is_prime[k]는 k가 소수인지is_prime = [True] * (LIMIT + 1)is_prime[0] = is_prime[1] = Falsei = 2while i * i <= LIMIT: if is_prime[i]: for j in range(i * i, LIMIT + 1, i): is_prime[j] = False i += 1primes = [k for k in range(2, LIMIT + 1) if is_prime[k]] data = sys.stdin.read().split()t = int(data[0])out = []for n in map(int, data[1:1 + t]): count = 0 for p in primes: if p > n - p: # p <= q 인 것만 센다 break if is_prime[n - p]: count += 1 out.append(count)print("\n".join(map(str, out)))const LIMIT = 9000; // 에라토스테네스의 체: isPrime[k]는 k가 소수인지const isPrime = new Array(LIMIT + 1).fill(true);isPrime[0] = isPrime[1] = false;for (let i = 2; i * i <= LIMIT; i++) { if (!isPrime[i]) continue; for (let j = i * i; j <= LIMIT; j += i) isPrime[j] = false;}const primes = [];for (let k = 2; k <= LIMIT; k++) if (isPrime[k]) primes.push(k); const [t, ...ns] = require("fs").readFileSync(0, "utf8").trim().split(/\s+/).map(Number);const out = ns.slice(0, t).map((n) => { let count = 0; for (const p of primes) { if (p > n - p) break; // p <= q 인 것만 센다 if (isPrime[n - p]) count++; } return count;});console.log(out.join("\n"));import { readFileSync } from "node:fs"; const LIMIT = 9000; // 에라토스테네스의 체: isPrime[k]는 k가 소수인지const isPrime: boolean[] = new Array(LIMIT + 1).fill(true);isPrime[0] = isPrime[1] = false;for (let i = 2; i * i <= LIMIT; i++) { if (!isPrime[i]) continue; for (let j = i * i; j <= LIMIT; j += i) isPrime[j] = false;}const primes: number[] = [];for (let k = 2; k <= LIMIT; k++) if (isPrime[k]) primes.push(k); const [t, ...ns]: number[] = readFileSync(0, "utf8").trim().split(/\s+/).map(Number);const out: number[] = ns.slice(0, t).map((n) => { let count = 0; for (const p of primes) { if (p > n - p) break; // p <= q 인 것만 센다 if (isPrime[n - p]) count++; } return count;});console.log(out.join("\n"));import java.io.BufferedReader;import java.io.InputStreamReader;import java.io.IOException;import java.util.ArrayList;import java.util.List; public class Main { public static void main(String[] args) throws IOException { final int LIMIT = 9000; boolean[] composite = new boolean[LIMIT + 1]; // 모두 false로 시작한다 composite[0] = composite[1] = true; for (int i = 2; i * i <= LIMIT; i++) { if (composite[i]) continue; for (int j = i * i; j <= LIMIT; j += i) composite[j] = true; } List<Integer> primes = new ArrayList<>(); for (int k = 2; k <= LIMIT; k++) if (!composite[k]) primes.add(k); BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); int t = Integer.parseInt(in.readLine().trim()); StringBuilder out = new StringBuilder(); for (int q = 0; q < t; q++) { int n = Integer.parseInt(in.readLine().trim()); int count = 0; for (int p : primes) { if (p > n - p) break; // p <= q 인 것만 센다 if (!composite[n - p]) count++; } out.append(count).append('\n'); } System.out.print(out); }}using System;using System.Collections.Generic;using System.Text; class Program{ static void Main() { const int LIMIT = 9000; bool[] composite = new bool[LIMIT + 1]; // 모두 false로 시작한다 composite[0] = composite[1] = true; for (int i = 2; i * i <= LIMIT; i++) { if (composite[i]) continue; for (int j = i * i; j <= LIMIT; j += i) composite[j] = true; } var primes = new List<int>(); for (int k = 2; k <= LIMIT; k++) if (!composite[k]) primes.Add(k); int t = int.Parse(Console.ReadLine().Trim()); var sb = new StringBuilder(); for (int q = 0; q < t; q++) { int n = int.Parse(Console.ReadLine().Trim()); int count = 0; foreach (int p in primes) { if (p > n - p) break; // p <= q 인 것만 센다 if (!composite[n - p]) count++; } sb.Append(count).Append('\n'); } Console.Write(sb); }}#include <iostream>#include <vector> int main() { const int LIMIT = 9000; std::vector<bool> isPrime(LIMIT + 1, true); isPrime[0] = isPrime[1] = false; for (int i = 2; i * i <= LIMIT; i++) { if (!isPrime[i]) continue; for (int j = i * i; j <= LIMIT; j += i) isPrime[j] = false; } std::vector<int> primes; for (int k = 2; k <= LIMIT; k++) if (isPrime[k]) primes.push_back(k); int t, n; std::cin >> t; while (t-- > 0) { std::cin >> n; int count = 0; for (int p : primes) { if (p > n - p) break; // p <= q 인 것만 센다 if (isPrime[n - p]) count++; } std::cout << count << "\n"; }}#include <stdbool.h>#include <stdio.h> #define LIMIT 9000 static bool composite[LIMIT + 1]; /* static이라 모두 false로 시작한다 */static int primes[LIMIT]; int main(void) { int count_primes = 0; composite[0] = composite[1] = true; for (int i = 2; i * i <= LIMIT; i++) { if (composite[i]) continue; for (int j = i * i; j <= LIMIT; j += i) composite[j] = true; } for (int k = 2; k <= LIMIT; k++) if (!composite[k]) primes[count_primes++] = k; int t, n; scanf("%d", &t); while (t-- > 0) { scanf("%d", &n); int count = 0; for (int i = 0; i < count_primes && primes[i] <= n - primes[i]; i++) if (!composite[n - primes[i]]) count++; printf("%d\n", count); } return 0;}LIMIT = 9000; // 에라토스테네스의 체: isPrime[k]는 k가 소수인지isPrime = NewList(LIMIT + 1, true);isPrime[0] = false;isPrime[1] = false;for (i = 2; i * i <= LIMIT; i++){ if (isPrime[i]) { for (j = i * i; j <= LIMIT; j += i) { isPrime[j] = false; } }}primes = [];for (k = 2; k <= LIMIT; k++){ if (isPrime[k]) { primes.Add(k); }} t = Console.ReadLine().ToNumber();for (q = 0; q < t; q++){ n = Console.ReadLine().ToNumber(); count = 0; foreach (p in primes) { // p <= q 인 것만 센다 if (p > n - p) { break; } if (isPrime[n - p]) { count += 1; } } Console.WriteLine(count);}