Problem 51077. List composite numbers that cannot be written as the sum of two primes

Created by ChrisR

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The number 32 is a composite number that can be written as the sum of two primes in two ways: 3+29 and 13+19. The number 33 can be written as the sum of two primes in one way: 2+31. The number 35 cannot be written as the sum of two primes at all.
Write a function to list the composite numbers less than or equal the input that cannot be written as the sum of two primes. Remember that 1 is neither prime nor composite.
Problems that might be related include Cody Problem 60 and Cody Problem 46582.

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Last Solution submitted on Jul 28, 2025

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William on 20 Mar 2021

Chris, there may be something I am missing, but it seems that the solutions in the test suite are only including every second correct value. e.g. I get 10 results for problem 1. I think it is clear that something is wrong because problems 1 and 2 don't contain any of the same numbers (they each contain the alternate ones of the full set for values less than 100), and none of the lists contain the number 1.

William on 20 Mar 2021

Oh, and BTW, the example of the number 35, which is given in the problem description, does not appear in the list for the solution of the first problem.

ChrisR on 20 Mar 2021

William, I don't consider 1 as a prime or composite number, and I've added that note to the problem. Also, rather than list all of the numbers, the test suite checks some of them. For example, the first problem has y(1:2:end), and the second has y(2:2:end). I haven't looked at your solutions, but I suspect the problem is including 1; there are nine numbers less than or equal to 100, not ten.

William on 21 Mar 2021

Thanks. I missed the fact that you were only checking alternate values. It's a clever problem!

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Problem 51077. List composite numbers that cannot be written as the sum of two primes

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Problem 51077. List composite numbers that cannot be written as the sum of two primes

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