From 3d938e880307869483aaa8fd1fffbc2c48cb690c Mon Sep 17 00:00:00 2001
From: pudepiedj <pudepiedj@gmail.com>
Date: Fri, 8 Mar 2024 09:55:28 +0000
Subject: [PATCH] New Carmichaels

---
 examples/cmap-example/CMakeLists.txt  |  4 ++
 examples/cmap-example/Carmichael.cpp  | 24 +++++++
 examples/cmap-example/Carmichael2.cpp | 93 +++++++++++++++++++++++++++
 3 files changed, 121 insertions(+)
 create mode 100644 examples/cmap-example/Carmichael2.cpp

diff --git a/examples/cmap-example/CMakeLists.txt b/examples/cmap-example/CMakeLists.txt
index 1fbfcf603..fa06a49d9 100644
--- a/examples/cmap-example/CMakeLists.txt
+++ b/examples/cmap-example/CMakeLists.txt
@@ -6,6 +6,10 @@ set(TARGET Carmichael)
 include_directories(${CMAKE_CURRENT_SOURCE_DIR})
 add_executable(${TARGET} Carmichael.cpp)
 
+set(TARGET Carmichael2)
+include_directories(${CMAKE_CURRENT_SOURCE_DIR})
+add_executable(${TARGET} Carmichael2.cpp)
+
 install(TARGETS ${TARGET} RUNTIME)
 target_link_libraries(${TARGET} PRIVATE common llama ${CMAKE_THREAD_LIBS_INIT})
 if (WIN32)
diff --git a/examples/cmap-example/Carmichael.cpp b/examples/cmap-example/Carmichael.cpp
index eb2f60260..c0e3eae07 100644
--- a/examples/cmap-example/Carmichael.cpp
+++ b/examples/cmap-example/Carmichael.cpp
@@ -50,6 +50,30 @@ static bool is_prime(size_t n) {
     return is_prime;
 }
 
+static bool is_carmichael_korselt(size_t n) {
+  if (n <= 1) return false;
+  if (n % 2 == 0 && n != 2) return false; // Even numbers except 2 can't be Carmichael
+
+  // Check for square-free property
+  size_t sqrt_n = sqrt(n);
+  for (size_t i = 3; i <= sqrt_n; i += 2) {
+    if (n % (i * i) == 0) return false;  // Perfect square factor found
+  }
+
+  // Check Korselt's condition for each prime factor
+  vector<size_t> factors;
+  for (size_t p = 3; p * p <= n; p += 2) {  // Check only odd primes
+    if (is_prime(p) && n % p == 0) {
+      factors.push_back(p);
+      if ((p - 1) % (n - 1) != 0) return false; // Doesn't satisfy Korselt's criterion
+    }
+  }
+
+  // All prime factors satisfy Korselt's condition - n might be Carmichael
+  // You can optionally do additional checks here or return true;
+
+  return true; // Replace with further checks or return based on your needs
+}
 
 
 // Function to check if a number is Carmichael
diff --git a/examples/cmap-example/Carmichael2.cpp b/examples/cmap-example/Carmichael2.cpp
new file mode 100644
index 000000000..dae8301eb
--- /dev/null
+++ b/examples/cmap-example/Carmichael2.cpp
@@ -0,0 +1,93 @@
+// Claude 3 CN generator using Korselt's criteria
+
+#include <iostream>
+#include <vector>
+#include <cmath>
+
+using namespace std;
+
+// Function to check if a number is prime
+static bool isPrime(size_t n) {
+    if (n <= 1)
+        return false;
+    if (n <= 3)
+        return true;
+    if (n % 2 == 0 || n % 3 == 0)
+        return false;
+
+    for (size_t i = 5; i * i <= n; i += 6)
+        if (n % i == 0 || n % (i + 2) == 0)
+            return false;
+
+    return true;
+}
+
+// Function to calculate the value of (a^n) % n
+static size_t modularExponentiation(size_t a, size_t n, size_t modulus) {
+    size_t result = 1;
+    a %= modulus;
+
+    while (n > 0) {
+        if (n & 1)
+            result = (result * a) % modulus;
+        a = (a * a) % modulus;
+        n >>= 1;
+    }
+
+    return result;
+}
+
+// Function to check if a number is a Carmichael number
+static bool isCarmichael(size_t n) {
+    if (isPrime(n))
+        return false;
+
+    vector<size_t> divisors;
+    for (size_t i = 2; i * i <= n; i++) {
+        if (n % i == 0) {
+            divisors.push_back(i);
+            if (i != n / i)
+                divisors.push_back(n / i);
+        }
+    }
+
+    for (size_t a = 2; a < n; a++) {
+        if (isPrime(a)) {
+            bool isCarmichael = true;
+            for (size_t d : divisors) {
+                if (modularExponentiation(a, d, n) != 1) {
+                    isCarmichael = false;
+                    break;
+                }
+            }
+            if (isCarmichael)
+                return true;
+        }
+    }
+
+    return false;
+}
+
+int main() {
+    size_t upperLimit;
+    cout << "Enter the upper limit: ";
+    cin >> upperLimit;
+
+    vector<size_t> carmichaelNumbers;
+
+    for (size_t i = 2; i <= upperLimit; i++) {
+        if (isCarmichael(i))
+            carmichaelNumbers.push_back(i);
+    }
+
+    if (carmichaelNumbers.empty())
+        cout << "No Carmichael numbers found up to " << upperLimit << endl;
+    else {
+        cout << "Carmichael numbers up to " << upperLimit << ":" << endl;
+        for (size_t n : carmichaelNumbers)
+            cout << n << " ";
+        cout << endl;
+    }
+
+    return 0;
+}