#include <unordered_map>
#include <random>
#include <iostream>
#include <iomanip>
using namespace std;

const int maxN = 1e4+5;
int minp[maxN];
long long rweight[maxN];
vector<pair<long long, double>> elements;

long long calc_weight(int v) {
    if (v == 1) return 0;
    return rweight[minp[v]] + calc_weight(v / minp[v]);
}

int main() {
    mt19937 rng;
    for (int i = 2; i < maxN; i++) {
        if (!minp[i]) {
            rweight[i] = uniform_int_distribution<long long>(0, 1e16-1)(rng);
            minp[i] = i;
            if (i * (long long) i < maxN)
            for (int j = i*i; j < maxN; j+=i) if (!minp[j]) minp[j] = i;
        }
    }
    for (int i = 3; i < maxN-5; i++) {
        if (minp[i] == i) {
            elements.push_back({calc_weight(i+4) - calc_weight(i+2), log(double(i))});
        }
    }
    long long goal = calc_weight(43) - calc_weight(41);
    double opt = 1e18;
    unordered_map<long long, double> pair_sums;
    long long sz = elements.size()*((long long)elements.size()-1)/2;
    pair_sums.reserve(sz);
    for (int i = 0; i < elements.size(); i++) {
        cout << "Inserting " << i << " / " << elements.size() << " found " << opt << " size " << pair_sums.size() << endl;
        long long size = elements[i].first;
        double cost = elements[i].second;
        if (size == goal) opt = min(opt, cost);
        for (int j = 0; j < i; j++) {
            size += elements[j].first;
            cost += elements[j].second;
            if (size == goal) opt = min(opt, cost);
            double& cur = pair_sums[size];
            if (cur == 0 || cur > cost) cur = cost;
            size -= elements[j].first;
            cost -= elements[j].second;
        }
    }

    for (int i = 0; i < elements.size(); i++) {
        cout << "Doing " << i << " / " << elements.size() << " found " << fixed << setprecision(20) << opt << endl;
        long long size = elements[i].first;
        double cost = elements[i].second;
        if (pair_sums.count(goal - size)) opt = min(opt, cost + pair_sums[goal - size]);
        for (int j = 0; j < i; j++) {
            size += elements[j].first;
            cost += elements[j].second;
            if (pair_sums.count(goal - size)) opt = min(opt, cost + pair_sums[goal - size]);
            for (int k = 0; k < j; k++) {
                size += elements[k].first;
                cost += elements[k].second;
                if (pair_sums.count(goal - size)) opt = min(opt, cost + pair_sums[goal - size]);
                size -= elements[k].first;
                cost -= elements[k].second;
            }
            size -= elements[j].first;
            cost -= elements[j].second;
        }
    }
    cout << fixed << setprecision(20) << opt << '\n';
}