feat(numerics): add is_prime function

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/tests/util/numerics/primes.cpp

@@ -24,8 +24,20 @@ static void tst1() {
     std::cout << "\n";
 }
 
+static void tst2() {
+    prime_iterator it;
+    for (unsigned i = 0; i < 100000; i++) {
+        uint64 p = it.next();
+        lean_assert(is_prime(p));
+        if (i % 1000 == 0)
+            std::cout << p << " "; std::cout.flush();
+    }
+    std::cout << "\n";
+}
+
 int main() {
     tst1();
+    tst2();
     return has_violations() ? 1 : 0;
 }
 

src/util/numerics/primes.cpp

@@ -106,4 +106,21 @@ uint64 prime_iterator::next() {
         return g_prime_generator(idx);
     }
 }
+
+bool is_prime(uint64 p) {
+    // Naive is_prime implementation that tests for divisors up to sqrt(p),
+    // and skips multiples of 2 and 3
+    if (p == 2 || p == 3)
+        return true;
+    uint64 i = 5;
+    while (i*i <= p) {
+        if (p % i == 0)
+            return false;
+        i += 2;
+        if (p % i == 0)
+            return false;
+        i += 3;
+    }
+    return true;
+}
 }

src/util/numerics/primes.h

@@ -7,13 +7,14 @@ Author: Leonardo de Moura
 #include "util/uint64.h"
 
 namespace lean {
-/**
-   \brief Prime number iterator. It can be used to enumerate the first LEAN_PRIME_LIST_MAX_SIZE primes.
-*/
+/** \brief Prime number iterator. It can be used to enumerate the first LEAN_PRIME_LIST_MAX_SIZE primes. */
 class prime_iterator {
     unsigned m_idx;
 public:
     prime_iterator();
+    /** \brief Return the next prime */
     uint64 next();
 };
+/** \brief Return true iff \c p is a prime number. */
+bool is_prime(uint64 p);
 }