import algorithm, math, system const wheel: array[1..8, int] = [ 4, 2, 4, 2, 4, 6, 2, 6 ] wheel_primes: array[1..8, int] = [ 7, 11, 13, 17, 19, 23, 29, 31 ] wheel_indices: array[1..31, int] = [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7 ] proc wheel_index(n: int): int = let d: int = (n - 1) div 30 r: int = (n - 1) mod 30 result = 8 * d + wheel_indices[r + 2] proc wheel_prime(n: int): int = let d: int = (n - 1) shr 3 r: int = (n - 1) and 7 result = 30 * d + wheel_primes[r + 1] proc primemask(limit: int): seq[bool] = let n: int = wheel_index(limit) m: int = wheel_prime(n) var sieve: seq[bool] = newSeq[bool](n + 1) p: int q: int j: int sieve.fill(true) for i in 1..wheel_index(sqrt(limit.float).int): if sieve[i]: p = wheel_prime(i) q = p ^ 2 j = ((i - 1) and 7) + 1 while q <= m: sieve[wheel_index(q)] = false q += wheel[j] * p j = (j and 7) + 1 return sieve proc prime(n: int): seq[int] = var ret: seq[int] if n >= 2: ret.add(2) if n >= 3: ret.add(3) if n >= 5: ret.add(5) if n < 7: return ret var sieve: seq[bool] = primemask(n) for i in 1..