(Last April fools day I posted four links to stories that seemed absurd and asked which one was false. They all were true. I recently came across five stories that all seem absurd but are all real, but three of them can't wait until April 1 since they are about current political events. Here they are:
Amazon to open many brick-and-mortar stores.
Why John Kasich got second place in New Hampshire (whch was better than expected).
Jim Gilmore's (who?) low expectations,
Why Ben Carson left Iowa.
airpnp- not about P vs NP
Donald Trump defends.... (I added this one on March 14)
And now back to our regularly scheduled blog)
A while back Larry Washington (number theorist at UMCP) showed me a simple proof that
∑p ≤ n 1/p = ln(ln(n)) + o(1)
(p goes through all the primes ≤ n.)
Recently I tried to remember it and could not so I looked on the web and... I could not find it! I found proofs that the sum is at least ln(ln(n)) as part of a proof that the series diverges, but could not find a simple proof of the equality.
I asked Larry Washington to email me the proof, and then (and this happens often) while waiting for the response I came up with it.
Anyway, to try to avoid what Lance pondered, the deterioratation of math over time, I post the proof here.Read it here since you probably can't find this proof elsewhere.
I continue to be amazed at both what IS and IS NOT on the web.
(ADDED LATER- one of the comments pointed to links on the web that DO contain the proofs I could not find.)