Do Infinito a 70 Milhões: A Prova da Twin Prime Conjecture

The twin prime conjecture says that there is an infinite number of such twin pairs. Some attribute the conjecture to the Greek mathematician Euclid of Alexandria, which would make it one of the oldest open problems in mathematics. That goal is the proof to a conjecture concerning prime numbers. Those are the whole numbers that are divisible only by one and themselves. Primes abound among smaller numbers, but they become less and less frequent as one goes towards larger numbers. In fact, the gap between each prime and the next becomes larger and larger — on average. But exceptions exist: the ‘twin primes’, which are pairs of prime numbers that differ in value by 2. Examples of known twin primes are 3 and 5, or 17 and 19, or 2,003,663,613 × 2195,000 − 1 and 2,003,663,613 × 2195,000 + 1. The twin prime conjecture says that there is an infinite number of such twin pairs. Some attribute the conjecture to the Greek mathematician Euclid of Alexandria, which would make it one of the oldest open problems in mathematics. (...) The new result, from Yitang Zhang of the University of New Hampshire in Durham, finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on unproven conjectures. Although 70 million seems like a very large number, the existence of any finite bound, no matter how large, means that that the gaps between consecutive numbers don’t keep growing forever. The jump from 2 to 70 million is nothing compared with the jump from 70 million to infinity.