Data update

Task/Chernicks-Carmichael-numbers/JavaScript/chernicks-carmichael-numbers.js

@@ -0,0 +1,154 @@
+const bigInt = require('big-integer');
+class ChernicksCarmichaelNumbers {
+    static main() {
+        for (let n = 3; n < 10; n++) {
+            let m = bigInt(0);
+            let foundComposite = true;
+            let factors = [];
+            while (foundComposite) {
+                const increment = (n <= 4)
+                    ? bigInt(1)
+                    : bigInt(2).pow(n - 4).times(5);
+                m = m.add(increment);
+                factors = this.U(n, m);
+                foundComposite = false;
+                for (let i = 0; i < factors.length; i++) {
+                    if (!this.isPrime(factors[i])) {
+                        foundComposite = true;
+                        break;
+                    }
+                }
+            }
+            console.log(`U(${n}, ${m}) = ${this.display(factors)} = ${this.multiply(factors)}`);
+        }
+    }
+    static display(factors) {
+        return factors.map(f => f.toString()).join(" * ");
+    }
+    static multiply(factors) {
+        return factors.reduce((acc, val) => acc.times(val), bigInt(1));
+    }
+    static U(n, m) {
+        const factors = [];
+        factors.push(bigInt(6).times(m).add(1));
+        factors.push(bigInt(12).times(m).add(1));
+        for (let i = 1; i <= n - 2; i++) {
+            factors.push(bigInt(2).pow(i).times(9).times(m).add(1));
+        }
+        return factors;
+    }
+    static MAX = 100000;
+    static primes = new Array(ChernicksCarmichaelNumbers.MAX);
+    static SIEVE_COMPLETE = false;
+    static isPrimeTrivial(test) {
+        const num = test.toJSNumber();
+        if (!ChernicksCarmichaelNumbers.SIEVE_COMPLETE) {
+            ChernicksCarmichaelNumbers.sieve();
+            ChernicksCarmichaelNumbers.SIEVE_COMPLETE = true;
+        }
+        return ChernicksCarmichaelNumbers.primes[num];
+    }
+    static sieve() {
+        for (let i = 2; i < ChernicksCarmichaelNumbers.MAX; i++) {
+            ChernicksCarmichaelNumbers.primes[i] = true;
+        }
+        for (let i = 2; i * i < ChernicksCarmichaelNumbers.MAX; i++) {
+            if (ChernicksCarmichaelNumbers.primes[i]) {
+                for (let j = i * i; j < ChernicksCarmichaelNumbers.MAX; j += i) {
+                    ChernicksCarmichaelNumbers.primes[j] = false;
+                }
+            }
+        }
+    }
+    static isPrime(testValue) {
+        if (testValue.equals(2)) return true;
+        if (testValue.isEven()) return false;
+        if (testValue.lesser(ChernicksCarmichaelNumbers.MAX)) return ChernicksCarmichaelNumbers.isPrimeTrivial(testValue);
+        let d = testValue.minus(1);
+        let s = 0;
+        while (d.isEven()) {
+            s += 1;
+            d = d.divide(2);
+        }
+        const valNum = testValue.toJSNumber();
+        if (testValue.lesser(1373653)) {
+            if (!ChernicksCarmichaelNumbers.aSrp(2, s, d, testValue)) return false;
+            if (!ChernicksCarmichaelNumbers.aSrp(3, s, d, testValue)) return false;
+            return true;
+        }
+        if (testValue.lesser(4759123141)) {
+            if (!ChernicksCarmichaelNumbers.aSrp(2, s, d, testValue)) return false;
+            if (!ChernicksCarmichaelNumbers.aSrp(7, s, d, testValue)) return false;
+            if (!ChernicksCarmichaelNumbers.aSrp(61, s, d, testValue)) return false;
+            return true;
+        }
+        if (testValue.lesser("10000000000000000")) {
+            if (!ChernicksCarmichaelNumbers.aSrp(3, s, d, testValue)) return false;
+            if (!ChernicksCarmichaelNumbers.aSrp(24251, s, d, testValue)) return false;
+            return true;
+        }
+        // Try 5 "random" primes
+        if (!ChernicksCarmichaelNumbers.aSrp(37, s, d, testValue)) return false;
+        if (!ChernicksCarmichaelNumbers.aSrp(47, s, d, testValue)) return false;
+        if (!ChernicksCarmichaelNumbers.aSrp(61, s, d, testValue)) return false;
+        if (!ChernicksCarmichaelNumbers.aSrp(73, s, d, testValue)) return false;
+        if (!ChernicksCarmichaelNumbers.aSrp(83, s, d, testValue)) return false;
+        return true;
+    }
+    static aSrp(a, s, d, n) {
+        let modPow = ChernicksCarmichaelNumbers.modPow(bigInt(a), d, n);
+        if (modPow.equals(1)) {
+            return true;
+        }
+        let twoExpR = bigInt(1);
+        for (let r = 0; r < s; r++) {
+            if (ChernicksCarmichaelNumbers.modPow(modPow, twoExpR, n).equals(n.minus(1))) {
+                return true;
+            }
+            twoExpR = twoExpR.times(2);
+        }
+        return false;
+    }
+    static SQRT = bigInt(3037000499); // Approximate sqrt of MAX_SAFE_INTEGER
+    static modPow(base, exponent, modulus) {
+        let result = bigInt(1);
+        let b = bigInt(base);
+        let e = bigInt(exponent);
+        while (e.greater(0)) {
+            if (e.isOdd()) {
+                if (result.greater(ChernicksCarmichaelNumbers.SQRT) || b.greater(ChernicksCarmichaelNumbers.SQRT)) {
+                    result = ChernicksCarmichaelNumbers.multiplyInternal(result, b, modulus);
+                } else {
+                    result = result.times(b).mod(modulus);
+                }
+            }
+            e = e.shiftRight(1);
+            if (b.greater(ChernicksCarmichaelNumbers.SQRT)) {
+                b = ChernicksCarmichaelNumbers.multiplyInternal(b, b, modulus);
+            } else {
+                b = b.times(b).mod(modulus);
+            }
+        }
+        return result;
+    }
+    static multiplyInternal(a, b, modulus) {
+        let x = bigInt(0);
+        let y = a.mod(modulus);
+        let bInt = bigInt(b);
+        while (bInt.greater(0)) {
+            if (bInt.isOdd()) {
+                x = x.add(y);
+                if (x.greaterOrEquals(modulus)) {
+                    x = x.minus(modulus);
+                }
+            }
+            y = y.shiftLeft(1);
+            if (y.greaterOrEquals(modulus)) {
+                y = y.minus(modulus);
+            }
+            bInt = bInt.shiftRight(1);
+        }
+        return x.mod(modulus);
+    }
+}
+ChernicksCarmichaelNumbers.main();