diff --git a/cpp/nth-prime/nth_prime.cpp b/cpp/nth-prime/nth_prime.cpp
index 762db61..f4089e6 100644
--- a/cpp/nth-prime/nth_prime.cpp
+++ b/cpp/nth-prime/nth_prime.cpp
@@ -15,31 +15,36 @@ number_t nth(size_t n, size_t sieve_size)
     if (n < 1)
         throw domain_error("invalid prime number index");
 
-    vector<number_t> primes = {2, 3, 5, 7, 11, 13};
+    if (n == 1)
+        return 2;
 
-    if (n <= primes.size())
-        return primes[n - 1];
+    vector<number_t> primes = {3, 5, 7, 11, 13};
 
-    primes.reserve(n);
+    if (n - 2 < primes.size())
+        return primes[n - 2];
+
+    primes.reserve(n - 1);
 
     if (auto_sieve_size == sieve_size) {
 
         sieve_size = min(size_t(32 * 1024),
-                         size_t(n * (log(n) + log(log(n))) + 0.5));
+                         size_t(0.5*(n * (log(n) + log(log(n)))) + 0.5));
     }
 
     vector<char> sieve(sieve_size, false);
 
-    sieve[0] = sieve[1] = true;
+    sieve[0] = true;
 
-    size_t first_number = 0;
+    size_t first_number = 1;
 
     while (true) {
 
         for (auto p : primes) {
 
-            size_t reminder = first_number % p;
-            size_t begin = reminder ? p - reminder : 0;
+            size_t reminder = (first_number % (2*p));
+            size_t begin    = reminder > p ? 3*p - reminder : p - reminder;
+
+            begin /= 2;
 
             for (size_t i = begin; i < sieve_size; i += p) {
 
@@ -52,10 +57,10 @@ number_t nth(size_t n, size_t sieve_size)
             if (sieve[i])
                 continue;
 
-            number_t p = first_number + i;
+            number_t p = first_number + 2*i;
             primes.push_back(p);
 
-            if (primes.size() == n)
+            if (primes.size() == n - 1)
                 return p;
 
             for (size_t j = i; j < sieve_size; j += p) {
@@ -64,7 +69,7 @@ number_t nth(size_t n, size_t sieve_size)
             }
         }
 
-        size_t next_first_number = first_number + sieve_size;
+        size_t next_first_number = first_number + 2*sieve_size;
 
         if (next_first_number < first_number)
             throw runtime_error("failed to reach prime number");