Green-Tao theorem

The Green-Tao theorem states that within the infinite set of prime numbers, there exist arbitrarily long sequences of consecutive primes spaced evenly apart, known as arithmetic progressions. In simple terms, no matter how long a sequence you want (like 3, 4, or 10 primes in a row), you can find such a pattern among primes, with each prime separated by the same difference. This discovery shows that primes, though seemingly sporadic, can form structured, repeating patterns over long stretches, revealing unexpected order within the apparent randomness of prime numbers.