The prime tuples conjecture, sieve theory, and the work of Goldston-Pintz-Yildirim, Motohashi-Pintz, and Zhang

I am free blogging dairy cow Terry Tao WordPress article Zhang and builds on it roughly contemporaneous. in like fashion and especially due to polymath 8 the size of the so-called ruler was reduced from 70 million – 246?and just as there was a flurry of activity on the twin primes conjecture after Zhang the recent screening of a documentary film counting from infinity by George si si si se ry I mean csicseri whycarol I guess carol I s capitalize causes some progress in defiance of the first law idea nurse a I that is inertia progress with the film about call jake owen call paul p a u l jason jacob j as in chipotle jack o b call wade c o h e a n c o h p n call in c o h n call colin call colin call call paul colin towing colin siding coincidence bug hug oh my god steve and eric o n sons of the feels prize winner fieldshad started filming their dad talking about 1963 and the Continuum Hypothesis. I bought a cassette of the film and then viewing it as I write this digressing too around tap around pack pack like a chicken with his head cut off on my stupid handheld all those thanks to Sr for showing me the freaking dictation buttonI am sending Steve this film actually we could say that the work in progress is a joint issue by Steve Eric and Paul it’s tough to film Paul Cohen without him taking over no offense

Torito was profile last monthterry towel was profiled in the New York Times Magazine just last month here’link

Terry Tao


I spent about 6 hours today from 10 a.m. till 2:30 p.m. on a Friday screening the Jean film and cross referencing with my stupid hand held having seen the film earlier this week at Cubberley and chatting up a couple interesting people about post film the Cohen family production for work in progress. here ar15 sources in the excellent film:

A film by George Csicsery, editing and service natural by Kyung Lee

A film by George Csicsery, editing and service natural by Kyung Lee

What's new

Suppose one is given a $latex {k_0}&fg=000000$-tuple $latex {{mathcal H} = (h_1,ldots,h_{k_0})}&fg=000000$ of $latex {k_0}&fg=000000$ distinct integers for some $latex {k_0 geq 1}&fg=000000$, arranged in increasing order. When is it possible to find infinitely many translates $latex {n + {mathcal H} =(n+h_1,ldots,n+h_{k_0})}&fg=000000$ of $latex {{mathcal H}}&fg=000000$ which consists entirely of primes? The case $latex {k_0=1}&fg=000000$ is just Euclid’s theorem on the infinitude of primes, but the case $latex {k_0=2}&fg=000000$ is already open in general, with the $latex {{mathcal H} = (0,2)}&fg=000000$ case being the notorious twin prime conjecture.

On the other hand, there are some tuples $latex {{mathcal H}}&fg=000000$ for which one can easily answer the above question in the negative. For instance, the only translate of $latex {(0,1)}&fg=000000$ that consists entirely of primes is $latex {(2,3)}&fg=000000$, basically because each translate of $latex {(0,1)}&fg=000000$ must contain an even number, and the only even prime is $latex {2}&fg=000000$. More generally…

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About markweiss86

Mark Weiss, founder of Plastic Alto blog, is a concert promoter and artist manager in Palo Alto, as Earthwise Productions, with background as journalist, advertising copywriter, book store returns desk, college radio producer, city council and commissions candidate, high school basketball player; he also sang in local choir, and fronts an Allen Ginsberg tribute Beat Hotel Rm 32
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