likely to use a machine instruction underneath; prefer this over the current top solution

Can you stop the rounding in any way?

python new test framework is required. updated in this fork

done!

Python:

• import of math.dist should be removed from sample tests.
• please add pass to initial code so it doesn't crash.

There seems to be some issues regarding the expected values of the tests.

It isn't possible for x=6 and y=18, as a and b would be complex

Actually, the solution for the equation is $a=b=3$, so there is a real solution for $a^7+b^7$

For x=5 and y=35, correct answer is 1576.6106018024825 with maximum deviation of 1e-06

The solution for these equations are $a=\frac {5 + 3 \sqrt 5} {2}$ and $b=\frac {5 - 3 \sqrt 5} {2}$, or vice versa, and $a^7+b^7=235625$, not $1576.6..$

Think of how would you solve on paper, and addapt to code. I agree that doesn't require much programming, it's just math

how do you solve the 3 equations? what method?

I disagree, mathematics is not very difficult, the level of high school is approximately, quite pulling on 6 kyu. But the kata itself is boring - just a mathematical problem from some school test, where 8 kyu programming plays only the role of a calculator.

Others may think differently.

I don't think this kata as 6kyu, more like 5kyu, hard math, but very satisfying to solve;

See the new description

The description still does not say it expects an array of AP numbers, even though the example assumes you do, but without context it makes no sense why 15(7+8) is part of the answer for start=7 but 27(10+17) is not.

11, 13, 17, 19, 23, 29 are natural numbers so they can't be divided any way.

Every integer >0 is a natural number. Did you mean something like regular prime numbers?

Changed

The result is the set of numbers that can be decomposed from the sum of two prime numbers, considering the provider number (start param) and the next one (start+1) as primes, and all numbers smaller than the provided one are not.

The result is the set of prime (in the problem definition) numbers that can be decomposed from the sum of two distinct prime numbers. These should be in the problem description.(not true for start 0 or 1, but is the answer for every number greater than that)

All test inputs are going to be > 0.

There are cases where the random tests test for start = 0

This should have a performance tag.

I have no idea how could this problem work for start 0 or 1, maybe put one of them in the sample tests?