On Thu, 16 May 2013 16:31:20 -0700 (PDT), Pubkeybreaker <firstname.lastname@example.org> wrote:
>On May 16, 12:03 pm, Sam Wormley <sworml...@gmail.com> wrote: >> First Proof That Infinitely Many Prime Numbers Come in Pairs >> >> >> >> >http://www.scientificamerican.com/article.cfm?id=first-proof-that-inf... >> > 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 × 2^195,000 - 1 and >> > 2,003,663,613 × 2^195,000 + 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.- Hide quoted text - >> >> - Show quoted text - > >This is a gross misstatement of the proof. It did NOT prove that there >were infinitely many prime pairs. What it did prove was that the gap >between primes is FINITELY BOUNDED infinitely often. The bound is 70 >x 10^6. >While this will probably be improved it is a long way to proving a >bound of >2.
Some years ago there was something in Scientific American about the difficulty of factoring large primes.
Makes you wonder how accurate they are on topics where you can't immediately see the errors...