Posted by: Paul A. Forsyth | June 11, 2013

Twin Primes, Quantum Links Between Photons, Imaging Molecules, and Other Sciency Links

1. From Wired: “Unknown Mathematician Proves Elusive Property of Prime Numbers.” Professor Yitang Zhang (University of New Hampshire) was looking into patterns among prime numbers — for example, the occurrence of pairs of primes (prime numbers that are “close together,” if you will). Mathematicians these days are dealing with some very large prime numbers; I’ve read that the largest prime number identified so far contains over 17 million decimal digits. The best known prime pairs are twin primes — two prime numbers that differ only by 2, such as 5 and 7, or 17 and 19, or 59 and 61.

The Twin Prime conjecture (one of Landau’s problems) states that there exist an infinite number of twin prime pairs. In 1849, Alphonse de Polignac put forth a more generalized form of the conjecture, stating that for every positive even number n, there are infinitely many cases of two consecutive prime numbers with difference n.

Prof. Zhang has shown “that there is some number N smaller than 70 million such that there are infinitely many pairs of primes that differ by N.” This takes us one step closer to proving (or disproving) the Twin Prime conjecture and its more generalized form, Polignac’s conjecture.

2. “Physicists Create Quantum Link Between Photons that Don’t Exist at the Same Time”: “experimenters in Israel have shown that they can entangle two photons that don’t even exist at the same time.”

3. Alex Tabarrok makes an argument for pharmaceutical reciprocity between the US FDA and its European counterparts.

4. These images of molecules, showing covalent bonds before and after reactions, are pretty cool! (Via In the Pipeline and 3 Quarks Daily.)

5. Also from In the Pipeline: “Kudzu of Chemistry”: “Chemistry, like any other human-run endeavor, goes through cycles and fads. At one point in the late 1970s, it seemed as if half the synthetic organic chemists in the world had made cis-jasmone. … There are still an awful lot of nanostructure papers, but I think that it’s a bit harder, compared to a few years ago, to just publish whatever you trip over in that field.” And then: what organic chemistry out there deserves to be more famous?

6. Stuart Benjamin (Duke) on Algorithms and Speech.

7. Noah Smith (SUNY Stony Brook): “What does it mean to have ‘predicted the crisis’?” His bottom line: “Predictions are hard, especially about the future. Sometimes people get things right because they understand how the world works, and sometimes they get things right by luck. The idea of a brilliant Cassandra-like sage, shouting in the wilderness while everyone ignores his or her trenchant warnings, is occasionally true, but not as much as we would like to think.”

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