Goldbach’s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: – Wikipedia

Every even integer greater than 2 can be expressed as the sum of two primes

Such a number is called a Goldbach number. Expressing a given even number as a sum of two primes is called a Goldbach partition of the number. For example,

In the article i have written a program to find the number of pairs of prime numbers are possible for every number from 4 to 20 and also 10000

import math,time
def isPrime(n):
root = int(math.sqrt(n))
for i in range (2,root+1):
if n % i == 0:
return 0
return 1
start = time.strftime('%s')
for n in range(4,21,2):
count = 0
for i in range (3,(n / 2)+1,2):
if isPrime(i) and isPrime(n - i):
count = count + 1
if n == 4:
print n,1
else:
print n,count
end = time.strftime('%s')
time = int(end) - int(start)
print "Time to execute the Algorithm =", time ,"Second(s)"