#include<bits/stdc++.h>
using namespace std;

vector<int> get_smallest_prime(int n_max) {
    vector<int> sp(n_max + 1);
    sp[1] = 1;
    for(int i = 2; i <= n_max; i++) {
        for(int j = i; j <= n_max; j += i) {
            if(!sp[j])
                sp[j] = i;
        }
    }
    return sp;
}

int main() {

    vector<int> sp = get_smallest_prime(4e5);
    vector<int> primes;
    for(int i = 2; i <= 390000; i++) {
        if(sp[i] == i) {
            primes.push_back(i);
        }
    }

    int tc;
    cin >> tc;
    while(tc--) {
        int n, m, k;
        cin >> n >> m >> k;
        const int inf = 1e9;
        vector<vector<int>> dis(4e5, vector<int>(2, inf));
        queue<pair<int, int>> q;
        for(int s = max(2, n - m); s <= n + m; s++) {
            if(s == n) {
                continue;
            }
            if(dis[sp[s]][1] == inf) {
                dis[sp[s]][1] = 1;
                q.push({s, 1});
            }
        }
        while(!q.empty()) {
            pair<int, int> top = q.front();
            q.pop();
            int x = top.first, parity = top.second;
            for(int s = max(2, x - m); s <= x + m; s++) {
                if(s == x) {
                    continue;
                }
                if(dis[sp[s]][parity ^ 1] > dis[x][parity] + 1) {
                    dis[sp[s]][parity ^ 1] = dis[x][parity] + 1;
                    q.push({s, parity ^ 1});
                }
            }
        }
        int best = 0;
        for(int i = (int)primes.size(); i >= 0; i--) {
            bool has_cycle = false;
            if(i + 1 < primes.size() && primes[i + 1] - primes[i] <= m) {
                has_cycle = true;
            }
            if(i > 0 && primes[i] - primes[i - 1] <= m) {
                has_cycle = true;
            }

            for(int p = 0; p < 2; p++) {
                if(dis[primes[i]][p] == k) {
                    // cout << "pr: " << primes[i] << " p: " << p << " d: " << dis[primes[i]][p] << endl;
                    best = max(best, primes[i]);
                }
                else if(has_cycle && dis[primes[i]][p] < k && (k - dis[primes[i]][p]) % 2 == 0) {
                    // cout << "pr: " << primes[i] << " p: " << p << " d: " << dis[primes[i]][p] << endl;
                    best = max(best, primes[i]);
                }
            }
        }

        cout << best << endl;
    }
}