Created
April 10, 2013 11:21
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Trying to find a Nth prime number (for a http://projecteuler.net/problem=7)
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def get_primes(start, end, primes=[]): | |
'''Get the numbers starting from start with the count based on primes | |
''' | |
sieve = range(start, end) | |
for prime in primes: | |
# Get the start value for primes striking | |
start_value = prime ** 2 | |
if start_value > end: | |
break | |
if start_value < start: | |
num = start / prime | |
if start % prime: | |
num += 1 | |
start_value = num * prime | |
# Strike out complex | |
for index in xrange(start_value, end, prime): | |
sieve[index - start] = False | |
# Get the numbers was not striked out | |
return [number for number in sieve if number] | |
def get_prime_by_number(number): | |
'''Get the n-th prime number''' | |
primes = [2, 3] | |
last_num = 0 | |
primes_num = 2 | |
end_value = step = 5 | |
while primes_num < number: | |
# Get a new step size for prime sieve | |
last_num = primes_num | |
primes_num = len(primes) | |
last_prime = primes[primes_num - 1] | |
start_value = end_value | |
end_value = last_prime ** 2 | |
if primes_num > last_num: | |
step *= (number - primes_num) * 1. / (primes_num - last_num) | |
if start_value + step < end_value: | |
end_value = start_value + int(step) | |
else: | |
step = end_value - start_value | |
# Get new primes | |
primes += get_primes(start_value, end_value, primes) | |
return primes[number - 1] | |
print get_prime_by_number(100001) |
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