CODEWITHSUNDEEP
pythonoutput
Jose Herrera
Jose Herrera

Reputation: 13

Goldbach Python Output

I made a python code for Goldbach conjecture. The thing is my output looks like this 

Enter the lower limit: 8
Enter the Upper limit: 10
8 = 3 + 5
10 = 3 + 7
10 = 5 + 5

What I want my output to look like is 

8 = 3 + 5
10 = 3 + 7 = 5 + 5

Is there any way to format it as such?

I am posting only the for loop: 

for n in range (lo_limit, up_limit + 1): #lo_limit and up_limit is what you input
  if (n % 2 == 0):
    for a in range (1, n + 1): 
      if is_prime(a): #is_prime represent numbers that are prime
        for b in range(1, n + 1):
          if is_prime(b):
            if (a + b == n):
              if (a <= b):
                print(n, "=", a, "+", b)

main()

Upvotes: 1

Views: 794

Answers (3)

Andy Richter
Andy Richter

Reputation: 189

Here is my take. You just need to keep concatenating f" = {x} + {n-x}" to a string then print the string:

def is_prime(n):  
    if (n <= 3): return n > 1      
    if n%6 not in [1,5]: return False # 6k numbers
    limit = int(n**.5)+1
    for i in range(5,limit+1,6): 
        if (n%i == 0 or n%(i+2) == 0): return False          
    return True  

def goldbach2(lo_limit,up_limit): 
    lo_limit = lo_limit+lo_limit%2 # next even 
    for n in range (lo_limit,up_limit + 1,2): #lo_limit and up_limit is what you input
        ans = "" 
        if n == 4: ans += " = 2 + 2"
        if is_prime(n-3): ans += f" = 3 + {n-3}" 
        for p,q in ((i,i+2) for i in range(5,n//2+1,6)):
            if is_prime(p) and is_prime(n-p): ans += f" = {p} + {n-p}" 
            if is_prime(q) and is_prime(n-q): ans += f" = {q} + {n-q}"
        print("\n",n, "=", ans)
 
goldbach2(110,124)

Output:

$ python3 gold_range.py 

 110 =  = 3 + 107 = 7 + 103 = 13 + 97 = 31 + 79 = 37 + 73 = 43 + 67

 112 =  = 3 + 109 = 5 + 107 = 11 + 101 = 23 + 89 = 29 + 83 = 41 + 71 = 53 + 59

 114 =  = 5 + 109 = 7 + 107 = 11 + 103 = 13 + 101 = 17 + 97 = 31 + 83 = 41 + 73 = 43 + 71 = 47 + 67 = 53 + 61

 116 =  = 3 + 113 = 7 + 109 = 13 + 103 = 19 + 97 = 37 + 79 = 43 + 73

 118 =  = 5 + 113 = 11 + 107 = 17 + 101 = 29 + 89 = 47 + 71 = 59 + 59

 120 =  = 7 + 113 = 11 + 109 = 13 + 107 = 17 + 103 = 19 + 101 = 23 + 97 = 31 + 89 = 37 + 83 = 41 + 79 = 47 + 73 = 53 + 67 = 59 + 61 = 61 + 59

 122 =  = 13 + 109 = 19 + 103 = 43 + 79 = 61 + 61

 124 =  = 11 + 113 = 17 + 107 = 23 + 101 = 41 + 83 = 53 + 71

Upvotes: 0

tzaman
tzaman

Reputation: 47820

Your function can be simplified and sped up a ton with some simple changes:

def goldbach(lo, hi):
    # 1. just step by 2 instead of checking for even numbers
    for n in range(lo, hi + 1, 2):
        # 2. keep a list of found matches instead of building up a string 
        matches = [str(n)] 
        # 3. for any 'a', you can just subtract to find 'b' instead of looping
        # 4. instead of testing for a <= b, just run the 'a' loop halfway
        for a in range(1, n // 2 + 1):
            if is_prime(a) and is_prime(n-a):
                matches.append('{} + {}'.format(a, n-a))
        # 5. join up the matches and print at the end
        print(' = '.join(matches))

The entire inner for loop could be expressed as a list-comprehension as well, for more brevity.

You could easily optimize this further by generating a list of primes in your range beforehand, and then just iterating over those and checking membership for the complements, instead of doing repeated primality testing.

Upvotes: 1

Ben Morris
Ben Morris

Reputation: 626

Try this:

for n in range (lo_limit, up_limit + 1):
    if (int(n) % 2 == 0):
        printedstring=str(n)
        for a in range (1, n + 1): 
            if is_prime(a):
                for b in range(1, n + 1):
                    if is_prime(b):
                        if (a + b == n):
                            if (a <= b):
                                printedstring = printedstring + str(" = ", a, " + ", b)
        print(printedstring)

Upvotes: 0

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