51: prime digit replacements

51_prime_digit_replacements/51.py

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+import array, math
+# Given integer x, this returns the integer floor(sqrt(x)).
+def sqrt(x):
+    assert x >= 0
+    i = 1
+    while i * i <= x:
+        i *= 2
+    y = 0
+    while i > 0:
+        if (y + i)**2 <= x:
+            y += i
+        i //= 2
+    return y
+
+# Returns a list of True and False indicating whether each number is prime.
+# For 0 <= i <= n, result[i] is True if i is a prime number, False otherwise.
+def list_primality(n):
+    # Sieve of Eratosthenes
+    result = [True] * (n + 1)
+    result[0] = result[1] = False
+    for i in range(sqrt(n) + 1):
+        if result[i]:
+            for j in range(i * i, len(result), i):
+                result[j] = False
+    return result
+
+
+# Returns all the prime numbers less than or equal to n, in ascending order.
+# For example: listPrimes(97) = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ..., 83, 89, 97].
+def list_primes(n):
+    return [i for (i, isprime) in enumerate(list_primality(n)) if isprime]
+
+def compute():
+    isprime = list_primality(1000000)
+    for i in range(len(isprime)):
+        if not isprime[i]:
+            continue
+
+        n = [int(c) for c in str(i)]
+        for mask in range(1 << len(n)):
+            digits = do_mask(n, mask)
+            count = 0
+            for j in range(10):
+                if digits[0] != 0 and isprime[to_number(digits)]:
+                    count += 1
+                digits = add_mask(digits, mask)
+
+            if count == 8:
+                digits = do_mask(n, mask)
+                for j in range(10):
+                    if digits[0] != 0 and isprime[to_number(digits)]:
+                        return str(to_number(digits))
+                    digits = add_mask(digits, mask)
+    raise AssertionError("Not found")
+
+
+def do_mask(digits, mask):
+    return [d * ((~mask >> i) & 1) for (i, d) in enumerate(digits)]
+
+
+def add_mask(digits, mask):
+    return [d + ((mask >> i) & 1) for (i, d) in enumerate(digits)]
+
+
+def to_number(digits):
+    result = 0
+    for d in digits:
+        result = result * 10 + d
+    return result
+
+
+if __name__ == "__main__":
+    print(compute())

51_prime_digit_replacements/main.go

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+package main
+
+import (
+	"math"
+)
+
+func main() {
+}
+
+func isPrime(n int) bool {
+	res := int(math.Sqrt(float64(n)))
+	divider := 2
+	for divider <= res {
+		if n%divider == 0 {
+			return false
+		}
+		divider++
+	}
+	return true
+}

51_prime_digit_replacements/main_test.go

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+package main