Data update

Task/Circular-primes/JavaScript/circular-primes.js

@@ -0,0 +1,167 @@
+// Check if a number is prime (works with Number type)
+function isPrime(n) {
+  if (n < 2) return false;
+  if (n % 2 === 0) return n === 2;
+  if (n % 3 === 0) return n === 3;
+  for (let p = 5; p * p <= n; p += 4) {
+    if (n % p === 0) return false;
+    p += 2;
+    if (n % p === 0) return false;
+  }
+  return true;
+}
+
+// Rotate the digits of a number: 197 -> 719 -> 971
+function cycle(n) {
+  const s = n.toString();
+  if (s.length === 1) return n;
+  return parseInt(s.slice(1) + s[0], 10);
+}
+
+// Check if a number is a circular prime
+function isCircularPrime(p) {
+  if (!isPrime(p)) return false;
+
+  // Quick check: multi-digit circular primes cannot contain 0,2,4,5,6,8
+  const s = p.toString();
+  if (s.length > 1 && /[024568]/.test(s)) return false;
+
+  let p2 = cycle(p);
+  while (p2 !== p) {
+    if (p2 < p || !isPrime(p2)) return false;
+    p2 = cycle(p2);
+  }
+  return true;
+}
+
+// Modular exponentiation: (base^exp) % mod
+function powerMod(base, exp, mod) {
+  let result = 1n;
+  base = base % mod;
+  while (exp > 0n) {
+    if (exp % 2n === 1n) result = (result * base) % mod;
+    exp >>= 1n;
+    base = (base * base) % mod;
+  }
+  return result;
+}
+
+// Generate random BigInt in range [min, max] (inclusive)
+function generateRandomBigInt(min, max) {
+  if (max < min) throw new Error("Invalid range");
+
+  const range = max - min + 1n;
+  // If range is small enough, use Math.random
+  if (range <= BigInt(Number.MAX_SAFE_INTEGER)) {
+    return min + BigInt(Math.floor(Math.random() * Number(range)));
+  }
+
+  // For large ranges, generate a random number with appropriate digit length
+  const maxStr = max.toString();
+  const len = maxStr.length;
+
+  let randomStr;
+  do {
+    // Generate a number with one fewer digit than max
+    randomStr = '';
+    for (let i = 0; i < len - 1; i++) {
+      randomStr += Math.floor(Math.random() * 10).toString();
+    }
+    // Remove leading zeros and ensure it's not empty
+    randomStr = randomStr.replace(/^0+/, '');
+    if (randomStr === '') randomStr = '0';
+  } while (BigInt(randomStr) > max);
+
+  const result = BigInt(randomStr);
+  return result >= min ? result : min;
+}
+
+// Miller-Rabin primality test for BigInt
+function isProbablePrime(n, k = 15) {
+  if (n === 2n || n === 3n) return true;
+  if (n < 2n || n % 2n === 0n) return false;
+
+  // Write n-1 as d*2^s
+  let d = n - 1n;
+  let s = 0;
+  while (d % 2n === 0n) {
+    d /= 2n;
+    s++;
+  }
+
+  // Witness loop
+  for (let i = 0; i < k; i++) {
+    // Generate random BigInt a in range [2, n-2]
+    const a = generateRandomBigInt(2n, n - 2n);
+
+    let x = powerMod(a, d, n);
+    if (x === 1n || x === n - 1n) continue;
+
+    let composite = true;
+    for (let r = 0; r < s - 1; r++) {
+      x = (x * x) % n;
+      if (x === n - 1n) {
+        composite = false;
+        break;
+      }
+    }
+
+    if (composite) return false;
+  }
+
+  return true;
+}
+
+// Create a repunit: digits=3 -> 111n
+function repunit(digits) {
+  return (10n ** BigInt(digits) - 1n) / 9n;
+}
+
+// Test repunit primality
+function testRepunit(digits) {
+  const r = repunit(digits);
+  if (isProbablePrime(r, 15)) {
+    console.log(`R(${digits}) is probably prime.`);
+  } else {
+    console.log(`R(${digits}) is not prime.`);
+  }
+}
+
+// Main execution
+console.log("First 19 circular primes:");
+let p = 2;
+let count = 0;
+while (count < 19) {
+  if (isCircularPrime(p)) {
+    if (count > 0) process.stdout.write(", ");
+    process.stdout.write(p.toString());
+    count++;
+  }
+  p++;
+}
+console.log();
+
+console.log("Next 4 circular primes:");
+let digits = 1;
+let repunitVal = 1n;
+while (repunitVal < BigInt(p)) {
+  digits++;
+  repunitVal = repunit(digits);
+}
+
+count = 0;
+while (count < 4) {
+  if (isProbablePrime(repunitVal, 15)) {
+    if (count > 0) process.stdout.write(", ");
+    process.stdout.write(`R(${digits})`);
+    count++;
+  }
+  digits++;
+  repunitVal = repunitVal * 10n + 1n;
+}
+console.log();
+
+testRepunit(5003);
+testRepunit(9887);
+testRepunit(15073);
+testRepunit(25031);