User blog comment:Vel!/Call for math facts/@comment-5529393-20140731034954


 * On May 13, 2013, Yitang Zhang presented the proof to a weak form of the twin prime conjecture. On the same day, Harold Helfgott submitted a paper to the ArXiv proving a weak form of the Goldbach conjecture.


 * Yitang Zhang proved that there are infinitely pairs of primes of distance D or less, with D = 70,000,000. D has since been lowered to 246, and assuming the Elliot-Halberstam conjecture, one can take D = 6.

John Conway introduced the "look-and-say sequence" 1,11,21,1211,... and proved that it eventually splits into a sequence of 92 "atomic elements" that never interact with each other. Only the digits 1,2,3 appear in the sequence.

The automorphism group of the symmetric group S_n consists solely of inner automorphisms, unless n = 6. S_6 has 720 inner automorphisms and 720 outer automorphisms.