No Integer Solutions

Can you find the not-so-obvious error in a statistic about coffee and tea drinkers?
Part 1: Mertens’ Conjecture
How many different paris of prime numbers are there for which the sum is 999?
Can you make a long number sequence so that each number is a factor or a multiple of its predecessor?
Can you divide a parliament of MPs into two chambers, ensuring each MP has at most one enemy in their own chamber?
A nice proof problem with a possible interpretation in four-dimensional space.