Bounded gaps between primes

Key Points

• The aim is to establish a bound on the gaps between consecutive prime numbers.
• Proving the lim inf of the gaps between consecutive primes (pn+1 - pn) is less than 7 x 10^7.
• Utilizing mathematical techniques from number theory to derive the inequality.
• The established limit is lim inf n (pn+1 - pn) < 7 x 10^7, indicating bounded gaps between consecutive primes.