Okay so background: I'm solving a question which requires me to find a number 'n' such that n-9, n-3, n+3, n+9 are consecutive prime numbers and n-8, n-4, n+4, n+8 are practical numbers and then I have to add the first four n that satisfy this condition.
The problem: Whether the logic of the code is correct or incorrect is irrelevant here because my code crashes before it reaches 100 million. I can't even check the output of the code, it works fine for 1million but doesn't scale to well for larger numbers.
What i did: I used the sieve of erath... to get the prime numbers up to 100 million which we will call M. And since practical numbers are divisible by 6 or by 4, I created another set to store those numbers and from that list i then created a set that contained the numbers that satisfy this condition: 'n-8, n-4, n+4, n+8 are practical numbers' which we will call N. Finally I iterate through each element, a, in N and check whether a - 9, a - 3, a + 3, a + 9 are part of the prime number set.
If anyone has any tips on how i can speed this up or any better algorithms it would be greatly appreciated
code
def SieveOfEratosthenes(n):
m = set()
prime = [True for i in range(n + 1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * 2, n + 1, p):
prime[i] = False
p += 1
prime[0]= False
prime[1]= False
for p in range(n + 1):
if prime[p]:
m.add(p)
return m
#creates set that stores multiples of 4 and 6
def ps1(n):
s = set()
for i in range(1, n+1):
if i%4 == 0 and i%6 == 0:
s.add(i)
return s
#checks whether any number satisfies n -8, n-4, n+4, n+8 must be practical and stores it in a set
def ps2(l):
q = set()
for i in l:
if ((i-8) in l) and ((i-4) in l) and ((i+4) in l) and ((i+8) in l):
q.add(i)
return q
#using the numbers stored in the prev set, i check the last condition n-9, n-3, n+3, n+9 must be in the
prime list
def TotalSieve(k, l):
q = set()
inc = 0
for i in k:
if inc != 4:
if ((i-9) in l) and ((i-3) in l) and ((i+3) in l) and ((i+9) in l):
inc = inc + 1
q.add(i)
else:
print("Found 4")
return q
# driver program
if __name__=='__main__':
n = 1000000000
m = SieveOfEratosthenes(n)
p = ps1(n)
p = ps2(p)
f = TotalSieve(p, m)
elem1 = f.pop()
elem2 = f.pop()
elem3 = f.pop()
elem4 = f.pop()
#add the first four numbers that satisfy the conditions
tot = elem1 + elem2 + elem3 + elem4
print(tot)
