are the random tests even generating proper molecules?. If I print the first 10 chars I get things like "H)4305C)59".

This is a duplicate: https://www.codewars.com/kata/52f831fa9d332c6591000511

Duplicate:

• https://www.codewars.com/kata/56cf0eb69e14db4897000b97
• https://www.codewars.com/kata/578dec07deaed9b17d0001b8

There is a theorem [...]. We can't prove it, [...]

If we can't prove it then it's a conjecture, not a theorem.

to find the 2 prime numbers

"to find 2 prime numbers" - there may be more than one possibility, and you show it in the very next sentence.

to find how much possible pairs of prime havinh their sum equal to an interger argument

"to find how many pairs of primes sum to the integer given as an argument"

the given number will not bigger than 10000000 and you must check if no pairs of prime is satisfied

"be bigger"
"1e7", "10^7", "10**7", "10 000 000", or "10_000_000", please. I don't want to count zeroes.
I don't know what you even mean by "no pairs of prime is satisfied"; it's incorrect but I couldn't figure out how to correct it.

I may have overlooked something; these just jumped out at me.