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Python: Accept an even number from the user and create a combinations that express the given number as a sum of two prime numbers

Python Basic - 1: Exercise-53 with Solution

Write a Python program that accept an even number (>=4, Goldbach number) from the user and create a combinations that express the given number as a sum of two prime numbers. Print the number of combinations.

Goldbach number: A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes.[4] Since four is the only even number greater than two that requires the even prime 2 in order to be written as the sum of two primes, another form of the statement of Goldbach's conjecture is that all even integers greater than 4 are Goldbach numbers.
The expression of a given even number as a sum of two primes is called a Goldbach partition of that number. The following are examples of Goldbach partitions for some even numbers:
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 7 + 5
...
100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53

Pictorial Presentation:

Python: Accept an even number from the user and create a combinations that express the given number as a sum of two prime numbers

Sample Solution:

Python Code:

import sys
from bisect import bisect_right
from itertools import chain, compress
print("Input an even number (0 to exit):") 
ub = 50000
is_prime = [0, 0, 1, 1] + [0]*(ub-3)
is_prime[5::6] = is_prime[7::6] = [1]*int(ub/6)
primes = [2, 3]
append = primes.append
 
for n in chain(range(5, ub, 6), range(7, ub, 6)):
    if is_prime[n]:
        append(n)
        is_prime[n*3::n*2] = [0]*((ub-n)//(n*2))
primes.sort()

for n in map(int, sys.stdin):
    if not n:
        break
    if n%2:
        print("Number of combinations:")  
        print(is_prime[n-2])
    else:
        print("Number of combinations:")  
        print(len([1 for p in primes[:bisect_right(primes, n/2)] if is_prime[n-p]]))

Sample Output:

Input an even number (0 to exit):
 100
Number of combinations:
6

Flowchart:

Flowchart: Python - Accept an even number from the user and create a combinations that express the given number as a sum of two prime numbers

Python Code Editor:

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Next: Write a Python program to create maximum number of regions obtained by drawing n given straight lines.

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Python: Tips of the Day

Python: The Zip() Function

>>> students = ('John', 'Mary', 'Mike')
>>> ages = (15, 17, 16)
>>> scores = (90, 88, 82, 17, 14)
>>> for student, age, score in zip(students, ages, scores):
...     print(f'{student}, age: {age}, score: {score}')
... 
John, age: 15, score: 90
Mary, age: 17, score: 88
Mike, age: 16, score: 82
>>> zipped = zip(students, ages, scores)
>>> a, b, c = zip(*zipped)
>>> print(b)
(15, 17, 16)