diff --git a/lib/primesieve/include/primesieve/StorePrimes.hpp b/lib/primesieve/include/primesieve/StorePrimes.hpp
index 7a28a194f..60bad7d3f 100644
--- a/lib/primesieve/include/primesieve/StorePrimes.hpp
+++ b/lib/primesieve/include/primesieve/StorePrimes.hpp
@@ -33,8 +33,8 @@
 
 namespace primesieve {
 
-/// primeCountApprox(x) >= pi(x)
-inline std::size_t prime_count_approx(uint64_t start, uint64_t stop)
+/// prime_count_upper(x) >= pi(x)
+inline std::size_t prime_count_upper(uint64_t start, uint64_t stop)
 {
   if (start > stop)
     return 0;
@@ -83,7 +83,7 @@ inline void store_primes(uint64_t start,
   if (stop > std::numeric_limits<V>::max())
     throw primesieve_error("store_primes(): " + getTypeName<V>() + " is too narrow for generating primes up to " + std::to_string(stop));
 
-  std::size_t size = primes.size() + prime_count_approx(start, stop);
+  std::size_t size = primes.size() + prime_count_upper(start, stop);
   primes.reserve(size);
 
   primesieve::iterator it(start, stop);
diff --git a/lib/primesieve/include/primesieve/pmath.hpp b/lib/primesieve/include/primesieve/pmath.hpp
index 16924fce6..d59f64a0d 100644
--- a/lib/primesieve/include/primesieve/pmath.hpp
+++ b/lib/primesieve/include/primesieve/pmath.hpp
@@ -138,15 +138,15 @@ inline B inBetween(A min, B x, C max)
   return x;
 }
 
-/// primeCountApprox(x) >= pi(x).
+/// primeCountUpper(x) >= pi(x).
 /// In order to prevent having to resize vectors with prime numbers
 /// (which would incur additional overhead) it is important that
-/// primeCountApprox(x) >= pi(x). Also for our purpose, it is
-/// actually beneficial if primeCountApprox(x) is a few percent
+/// primeCountUpper(x) >= pi(x). Also for our purpose, it is
+/// actually beneficial if primeCountUpper(x) is a few percent
 /// larger (e.g. 3%) than pi(x), this reduces the number of memory
 /// allocations in PrimeGenerator::fillPrevPrimes().
 ///
-inline std::size_t primeCountApprox(uint64_t start, uint64_t stop)
+inline std::size_t primeCountUpper(uint64_t start, uint64_t stop)
 {
   if (start > stop)
     return 0;
@@ -163,9 +163,9 @@ inline std::size_t primeCountApprox(uint64_t start, uint64_t stop)
   return (std::size_t) pix;
 }
 
-inline std::size_t primeCountApprox(uint64_t stop)
+inline std::size_t primeCountUpper(uint64_t stop)
 {
-  return primeCountApprox(0, stop);
+  return primeCountUpper(0, stop);
 }
 
 /// Approximation of the maximum prime gap near n
diff --git a/lib/primesieve/src/EratSmall.cpp b/lib/primesieve/src/EratSmall.cpp
index 7be6feef3..a473c38dd 100644
--- a/lib/primesieve/src/EratSmall.cpp
+++ b/lib/primesieve/src/EratSmall.cpp
@@ -41,7 +41,7 @@ void EratSmall::init(uint64_t stop,
   stop_ = stop;
   maxPrime_ = maxPrime;
   l1CacheSize_ = (std::size_t) l1CacheSize;
-  std::size_t count = primeCountApprox(maxPrime);
+  std::size_t count = primeCountUpper(maxPrime);
   primes_.reserve(count);
 }
 
diff --git a/lib/primesieve/src/PrimeGenerator.cpp b/lib/primesieve/src/PrimeGenerator.cpp
index 029a90141..ed6701789 100644
--- a/lib/primesieve/src/PrimeGenerator.cpp
+++ b/lib/primesieve/src/PrimeGenerator.cpp
@@ -164,7 +164,7 @@ void PrimeGenerator::initPrevPrimes(Vector<uint64_t>& primes,
     // When sieving backwards the number of primes inside [start, stop]
     // slowly increases in each new segment as there are more small
     // than large primes. Our new size has been calculated using
-    // primeCountApprox(start, stop) which is usually too large by 4%
+    // primeCountUpper(start, stop) which is usually too large by 4%
     // near 10^12 and by 2.5% near 10^19. Hence if the new size is less
     // than 1% larger than the old size we do not increase the primes
     // buffer as it will likely be large enough to fit all primes.
@@ -177,7 +177,7 @@ void PrimeGenerator::initPrevPrimes(Vector<uint64_t>& primes,
     }
   };
 
-  std::size_t pix = primeCountApprox(start_, stop_);
+  std::size_t pix = primeCountUpper(start_, stop_);
 
   if (start_ <= maxCachedPrime())
   {
@@ -235,7 +235,7 @@ void PrimeGenerator::initNextPrimes(Vector<uint64_t>& primes,
       // algorithm aborts as soon as there is not
       // enough space to store 64 more primes.
       std::size_t minSize = *size + 64;
-      std::size_t pix = primeCountApprox(start_, stop_) + 64;
+      std::size_t pix = primeCountUpper(start_, stop_) + 64;
       pix = inBetween(minSize, pix, maxSize);
       pix = std::max(*size, pix);
       resize(primes, pix);
@@ -252,7 +252,7 @@ void PrimeGenerator::initNextPrimes(Vector<uint64_t>& primes,
     // algorithm aborts as soon as there is not
     // enough space to store 64 more primes.
     std::size_t minSize = 64;
-    std::size_t pix = primeCountApprox(start_, stop_) + 64;
+    std::size_t pix = primeCountUpper(start_, stop_) + 64;
     pix = inBetween(minSize, pix, maxSize);
     resize(primes, pix);
   }
diff --git a/lib/primesieve/src/nthPrimeApprox.cpp b/lib/primesieve/src/nthPrimeApprox.cpp
index 09cd93e3d..757acb5d7 100644
--- a/lib/primesieve/src/nthPrimeApprox.cpp
+++ b/lib/primesieve/src/nthPrimeApprox.cpp
@@ -267,6 +267,12 @@ uint64_t Ri_inverse(uint64_t x)
   return (uint64_t) res;
 }
 
+/// primePiApprox(x) is a very accurate approximation of PrimePi(x)
+/// with |PrimePi(x) - primePiApprox(x)| < sqrt(x).
+/// Since primePiApprox(x) may be smaller than PrimePi(x) it
+/// cannot be used to calculate the size of a primes array, for
+/// this use case primeCountUpper() should be used.
+///
 uint64_t primePiApprox(uint64_t x)
 {
   // Li(x) is faster but less accurate than Ri(x).
@@ -277,6 +283,11 @@ uint64_t primePiApprox(uint64_t x)
     return Ri(x);
 }
 
+/// nthPrimeApprox(n) is a very accurate approximation of the nth
+/// prime with |nth prime - nthPrimeApprox(n)| < sqrt(nth prime).
+/// Please note that nthPrimeApprox(n) may be smaller or larger than
+/// the actual nth prime.
+///
 uint64_t nthPrimeApprox(uint64_t n)
 {
   // Li_inverse(n) is faster but less accurate than Ri_inverse(n).