[Python] Goldbach's Conjecture - Find the number of ways an even number can be written as the...

I want to know the number of ways that a given positive even number can be written as the sum of two primes.

At the moment, I have this code:

n = int(input(">"))
def genprimes(n):#generate primes from 2 to n
primes = []
for i in range(2,n):
prime = True
for a in range(2,i):
if i % a == 0:
prime = False
if prime == True:
primes.append(i)
return primes

pairs = []
primes = genprimes(n)

for prime1 in primes:
for prime2 in primes:
if prime1 + prime2 == n and [prime1,prime2] not in pairs and [prime2,prime1] not in pairs:
pairs.append([prime1,prime2])
print(len(pairs))


It works, but it becomes a little slow when n goes above 10,000 ish. Can anyone think of a more efficient way to find this value, so that it yields quick results for high values?

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