Proof involving pairs of prime numbers

[Greg Bernhardt]

It’s a result only a mathematician could love. Researchers hoping to get ‘2’ as the answer for a long-sought proof involving pairs of prime numbers are celebrating the fact that a mathematician has wrestled the value down from infinity to 70 million.

“That’s only [a factor of] 35 million away” from the target, quips Dan Goldston, an analytic number theorist at San Jose State University in California who was not involved in the work. “Every step down is a step towards the ultimate answer.”

http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989

 

[fresh_42]

So it doesn't involve twins of primes, which is important to distinguish. Only that the gap between primes is less than 70,000,000.

 

[mfb]

Still a major step forward, and often a new method like this can be improved over time. And it happened. Within just one year the upper bound could be reduced to 246.
It can be reduced to 12 or 6 if the Elliott–Halberstam conjecture or its generalization can be shown to be true.