Пример #1
0
def get_prime_v2(primePosition):
	"""
	Sieve the numbers.

	>>> get_prime_v2(6)
	13
	"""
	maxCandidate = 64
	minPrime = 3

	primes = [2]
	nonPrimes = set()

	while primePosition > len(primes):
		maxCandidate *= 2

		for factor in range(2, 1 + ceil(sqrt(maxCandidate))):
			if Prime.is_prime(factor):
				nonPrime = factor * 2
			else:
				nonPrime = factor

			while nonPrime <= maxCandidate:
				nonPrimes.add(nonPrime)
				nonPrime += factor

		primes.extend([n for n in range(minPrime, maxCandidate+1, 2) if n not in nonPrimes])
		minPrime = maxCandidate + 1
	
	return primes[primePosition - 1]
Пример #2
0
def larget_prime_factor_v1(n):
    """
	>>> larget_prime_factor_v1(6)
	3
	>>> larget_prime_factor_v1(8)
	2
	>>> larget_prime_factor_v1(13195)
	29
	"""
    return max(Prime.prime_factors(n))
Пример #3
0
def larget_prime_factor_v1(n):
	"""
	>>> larget_prime_factor_v1(6)
	3
	>>> larget_prime_factor_v1(8)
	2
	>>> larget_prime_factor_v1(13195)
	29
	"""
	return max(Prime.prime_factors(n))
Пример #4
0
def least_common_multiple_v1(maxDivisor):
	"""
	>>> least_common_multiple_v1(10)
	2520
	>>> least_common_multiple_v1(20)
	232792560
	"""
	primeFactorsCounter = Counter()
	for divisor in range(1, maxDivisor+1):
		# Get the union of the currently-used prime factors and the prime factors of divisor.
		primeFactorsCounter |= Counter(Prime.prime_factors(divisor))
	return product(primeFactorsCounter.elements())
Пример #5
0
def get_prime_v1(primePosition):
	"""
	>>> get_prime_v1(6)
	13
	"""
	n = 3
	primeNumbersSeen = 1 # 2 is prime
	while True:
		if Prime.is_prime(n):
			primeNumbersSeen += 1
			if primeNumbersSeen == primePosition:
				return n
		n += 2