def get_prime_list_true_prime(max_num):
# need to be at least 2
assert(max_num >= 1)
init_list = []
for i in range(2, max_num + 1):
init_list.append(i)
# print init_list
j = 0
new_list = init_list
new_list_len = len(new_list)
sqrt_of_max_num = int(math.sqrt(max_num))
while(1):
checkNum = new_list[j]
# show the progress of each iteration
# print 'j = %5d checkNum %5d, new_list_len %5d'%(j, checkNum, new_list_len)
# we only need to sieve up to sqrt(max_num)
if (checkNum > sqrt_of_max_num):
break
new_list = erato_siev_one_round(new_list, checkNum)
# print new_list
j = j+1
new_list_len = len(new_list)
if(new_list_len <= j):
break
print 'number of primes: %d'%(new_list_len)
# print 'prime list:', new_list
return new_list
def get_num_count_in_M_set_not_divisible_by_prime_less_than_xi(M_set, xi):
# need to be at least 2
target_num = len(M_set)
assert target_num >= 1
prime_list = get_prime_list(xi)
init_list = deepcopy(M_set)
# print init_list
j = 0
# construct initial list. Initial list may include [1] at beginning, we skip it.
if init_list[0] == 1:
new_list = init_list[1:]
else:
new_list = init_list
while 1:
checkNum = prime_list[j]
# show the progress of each iteration
# print 'j = %5d checkNum %5d, new_list_len %5d'%(j, checkNum, new_list_len)
new_list = erato_siev_one_round(new_list, checkNum)
# print new_list
j = j + 1
if j == len(prime_list):
break
sift_left_cnt = len(new_list)
print "number not_divisible_by_prime_less_than_xi: %d \n" % (sift_left_cnt)
# print 'number not_divisible_by_prime_less_than_xi:', new_list, '\n'
return sift_left_cnt