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POPython- Prime summands to an even number
 

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    <p>This is the assignment my professor gave me. I have no idea where to start or what to do! The point is to use loops to figure this out and I can do the loops, but this is blowing my mind. </p> <p>Even numbers and primes.</p> <p>A prime number is one that has 1 and itself as its only divisors. 2, 3, 5, 7 and 11 are the first several. Notice that 'being prime' is purely a multiplicative condition -- it has nothing to do with addition. So it might be surprising that if we start listing even numbers, they seem to be the sum (addition!) of two primes. 4 = 2 + 2, 6 = 3 + 3, 8 = 5 + 3, 10 = 3 + 7, 12 = 7 + 5, 14 = 7 + 7, 16 = 13 + 3, ...</p> <p>Is this always the case? Can every even number be written as the sum of two primes?</p> <ol> <li>Write a is_prime(n) function. It should accept a positive integer n>1 as input, and output True or False, depending on whether n is or is not a prime number. Do this with a loop that checks whether for any integer d, 1 &lt; d &lt; sqrt(n), d divides n. I'd suggest a while loop -- think carefully about the conditional for the loop, and when you want to change this conditional inside the loop. (Use a boolean for your condition).</li> <li>Write a prime_sum(n) function. It should accept an even number n>1 as input, and via a loop search for primes p &amp; q with p + q = n. Hint: start with p = 3. If (p) and (n-p) are prime you are done. If not, set p+=2 and try again. Make sure you do not search forever!</li> <li>Main. <ul> <li>Ask the user for an even number n. Continually ask them until they do give you a positive even number.</li> <li>Search for the summands p &amp; q, and either print them out (if they exist) or say they don't. </li> <li>Ask the user if they wish to try with another even, and let them continue until they quit.</li> </ul></li> </ol> <hr> <p>I didn't know I could edit this! :) So this is what I have so far. I have not tested it yet to debug it b/c I want to get it all down and when the errors pop up I will address them, but if you see any immediate problems let me know. </p> <pre><code>def is_prime(n): d=2 while n&gt;1 and d&lt;n**0.5: if n%2==0: c=False d+=1 return c def prime_sum(n): p=3 while n&gt;1: q=n-p if q&lt;=0: p+=2 q=n-p is_prime(q) else: is_prime(q) is_prime(p) while True: print("The prime summands of", n, "are", p, "and", q) while False: print("There are no prime summands of", n) def main(): n=eval(input("Gimme an even number please: ")) while True: n=eval(input("That is not a positive even number. Try again: ")) #not sure how to combine yet, but I am still finishing. #will edit again when I have it all down. </code></pre>
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    1. COSo what have you tried so far?
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    2. CO"I can do the loops" suggests to me that you understand the prompt, but I guess that's not the case. What exactly in the assignment don't you understand, if not the way to organize the loops?
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    3. COWhat's the question? You have the steps. Write the is_prime function. Then move on to the next step. We won't do your homework for you. You have to write your own code.
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