#[0] check out ChatGPT response for Polignac's Conjecture!
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We know that these primes are not congruent to 0, 2, 3, or 4 modulo 6. Therefore, they must be congruent to either 1 or 5 modulo 6.
If all primes were congruent to 1 modulo 6, then there would be no prime pairs with a difference of 2, as both primes would be odd. However, if all primes were congruent to 5 modulo 6, then they would alternate between being 2 more or 2 less than a multiple of 6. This would imply the existence of infinitely many prime pairs with a difference of 2, supporting Polignac's Conjecture.
