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Peter Luschny
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Peter Luschny
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For n>0, f(n) = 2^(2^n)+2^(2^(n-1))+1 has at least n+1 distinct prime factors, hence, the # of primes is infinite

http://www.cut-the-knot.org/proofs/InfinitudeOfPrimesViaPowersOfTwo.shtml
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Will do (in a couple of days). Still exploring. I'll point out that the first differences (1, 1, 1, 2, 2, 1, 2, 2, 4, 2, 2, ...) are of course the number of new factors at each step. Those new factors are the factors of http://oeis.org/A220294 . :)
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How a Lone Hacker Shredded the Myth of Crowdsourcing

"...just two individuals had accounted for almost all the destruction, eviscerating the completed puzzle in about one percent of the moves and two percent of the time it had taken a crowd of thousands to assemble it."

"All the motivation generated by weeks of good PR, a fun task and a smart financial incentive scheme evaporated in the face of attacks by a single person lasting, in total, no more than a couple of hours."

Link: https://medium.com/backchannel/how-a-lone-hacker-shredded-the-myth-of-crowdsourcing-d9d0534f1731
High-tech analysis of a 2011 DARPA Challenge suggests that far from being wise, crowds can’t be trusted
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Peter Luschny

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Newly released documents show the extent of the links between corporate interests and the published work of Wei-Hock Soon, a Smithsonian-affiliated scientist who has tried to debunk the consensus about global warming.
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Peter Luschny
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W H A T   I S . . .  an Automatic Sequence?
Eric Rowland, Notices of the AMS Volume 62, Number 3
http://www.ams.org/notices/201503/rnoti-p274.pdf
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Kempe's Universality Theorem tells us that you can find for any algebraic curve a linkage such that the curve is the trajectory of one of its nodes. This is a very impressive result that is for example covered in the book of Demaine and O"Rourke (it's quite elementary, I have covered this once in class).

Today I spotted a paper on the arxiv that improves Kempe's result for parametrized curves. In particular, the constructed linkage has a smaller complexity. They also have a nice webside with examples, animations and even a Mathematica script that lets you reproduce their results.
Planar Linkages Following a Prescribed Motion. (by Matteo Gallet, Christoph Koutschan, Zijia Li, Georg Regensburger, Josef Schicho, and Nelly Villamizar). Linkage drawing an ellipse. Abstract. Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that ...
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Peter Luschny

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What's going on at G+?

I am flooded by new 'followers' which obviously share no interests with me. Others tell me that the same is happening with them.
#G+
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Good, honest solution would be that no person A could ask to connect to person B, unless both had gmail-accounts and B had sent at least once mail to A. But I'm not expecting it. First time I realized that Google's policy was clearly something else than "Do not do evil" was when Google-Plus started advertising in "You might know" corner above people who do not have Gmail-accounts and instead sends the connection-request somewhere else, which then effectively is just an advertisement-spam for asking that person to change his mail-account. (And you can't even see from those Add-buttons who has a gmail-account and who has not!)
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Peter Luschny
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Solve an open problem on the Online Encyclopedia of Integer Sequences and become eligible to win a $1000 prize!
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#GoogleMaps helps Oceana and +SkyTruth reel in a global view of illegal overfishing activities. #MapsHack goo.gl/umlez1
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This is pretty cool: the authors attempted to prove the correctness of a common sorting implementation and discovered it was in fact flawed.  Seems an input has to be rather carefully crafted to trigger a failure, though.
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Risks That Threaten Human Civilisation

From the introduction: "This report has, to the best of the authors’ knowledge, created the first list of global risks with impacts that for all practical purposes can be called infinite. It is also the first structured overview of key events related to such risks and has tried to provide initial rough quantifications for the probabilities of these impacts."

"The real focus is not on the almost unimaginable impacts of the risks the report outlines. Its fundamental purpose is to encourage global collaboration and to use this new category of risk as a driver for innovation."

"The idea that we face a number of global risks threatening the very basis of our civilisation at the beginning of the 21st century is well accepted in the scientific community, and is studied at a number of leading universities. But there is still no coordinated approach to address this group of risks and turn them into opportunities."

The report can be downloaded from:
http://globalchallenges.org/publications/globalrisks/about-the-project/
The Global Challenges Foundation wants to facilitate decisions for efficient actions against the greatest global risks facing humanity, that we are unable to manage in the current political system.
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Database of interesting graphs

From the welcome page: 
"Most graph theorists will agree that among the vast number of graphs that exist there are only a few that can be considered really interesting."

"It is the aim of this House of Graphs project to find a workable definition of 'interesting' and provide a searchable database of graphs that conform to this definition. And to allow users to add additional graphs which they find interesting."

"We would also like to serve as a repository for lists of graphs (which can be downloaded in several formats) and graph generators."

See also: http://arxiv.org/abs/1204.3549
The House of Graphs. Database of interesting graphs. Most graph theorists will agree that among the vast number of graphs that exist there are only a few that can be considered really interesting. It is the aim of this House of Graphs project to find a workable definition of 'interesting' and ...
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Kaspersky: What is the Equation group?

The Equation group is probably one of the most sophisticated cyber attack groups in the world; and they are the most advanced threat actor we have seen.

The Equation group is a highly sophisticated threat actor that has been engaged in multiple CNE (computer network exploitation) operations dating back to 2001, and perhaps as early as 1996.
The Equation group uses multiple malware platforms, some of which surpass the well-known “Regin” threat in complexity and sophistication. 

Here the report from kaspersky.com: http://goo.gl/8o9SvV

http://www.zeit.de/digital/datenschutz/2015-02/equation-group-stuxnet-kaspersky #EquationGroup
Sie versteckt sich unlöschbar auf Festplatten und spioniert hochrangige Ziele aus: Antivirenspezialisten entdecken extrem ausgefeilte Malware mit Parallelen zu Stuxnet.
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