# Can A Number Be Expressed As A Sum Of Two Prime Numbers? | Python Program

## Number be expressed as a sum of two prime numbers in python

Here, we will discuss the program to check whether a number be expressed as a sum of two prime number in python. Prime number is a number which only have two divisors i.e. a number which can not be divided by any other number other than 1 or itself is a prime number. ### Theory

There are many theories which express numbers as a sum of two primes like Goldbach’s Conjecture which states that any even number greater than 2 can be expressed as a sum of two primes.

Prime number is a number which only have two divisors i.e. a number which can not be divided by any other number other than 1 or itself is a prime number.

Here we will check for all the numbers if they can be expressed as sum of two primes or not.

### Algorithm

• Take number as input in n
• Initialize a variable flag as 0
• Iterate using for loop from value of i between (2, n/2)
•  For each iteration Call a function sum_of_two_primes for value of i is it returns 1
• Call same function for value n-i and if it is also 1 then print i and n-i as answer increment the flag to 1
• If flag is 0 print not possible
• Create function sum_of_two_prime where check if passed number is prime return true else false ### Python code

Run
```# take input
Number = int(input('Enter the Number : '))
# initialize an array
arr = []
# find prime numbers
for i in range(2, Number):
flag = 0
for j in range(2, i):
if i % j == 0:
flag = 1
# append prime numbers to array
if flag == 0:
arr.append(i)
# possible combinations
flag = 0
for i in range(len(arr)):
for j in range(i + 1, len(arr)):
# if condition is True Print numbers
if arr[i] + arr[j] == Number:
flag = 1
print(str(arr[i]) + " and " + str(arr[j]) + ' are prime numbers when added gives ' + str(Number))
break
if flag == 0:
print('No Prime numbers can give sum of ' + str(Number))
```

### Output

```Insert the num: 15
15 can be expressed as the sum of 2 and 13```

### 4 comments on “Can A Number Be Expressed As A Sum Of Two Prime Numbers? | Python Program”

• Sonal

num=int(input(“Enter the number “))
count=0
def isprime(n):
fact=0
for i in range(1,n+1):
if n%i==0:
fact+=1
if fact==2:
return True
else:
return False
for j in range(2,num//2+1):
if isprime(j) and isprime(num-j):
count+=1
print(j,”+”,num-j,”=”,num)
if count==0:
print(num,”can’t be represented as a sum of two prime numbers”) 0
• Sonal

num=int(input(“Enter the number “))
def nextprime(n):
fact=0
for i in range(1,n+1):
if n%i==0:
fact+=1
if fact==2:
return True
else:
return False
for j in range(2,num//2+1):
if isprime(j):
if isprime(num-j):
print(j,”+”,num-j,”=”,num) 0
• Arun

val=int(input(“enter the value :”))
num=[]

for a in range(val):
if a > 1:
for x in range(2, a):
if a % x == 0:
break
else: num.append(a)

for x in range(len(num)):
for i in range(len(num)):
if num[x]+num[i]==val:
if num[x]<=num[i]:
print(num[x], " and ", num[i], " are prime numbers when added gives 30") 0
• Gunjan

c=0
p=[]
z=int(input(‘enter the no :’))
for i in range(2,z):
c=0
y=i//2+1

for j in range(2,y):
if(i%j==0):
c=c+1
if(c==0):
print(i,p.append(i),’is prime no’)
# t=p.append(i)
print(p)
for i in p:
for j in p:
if(i+j==z):
print(i,j,’are the no.s whose sem equals to’,z)
By-Gunjan soni 0