Monthly Archives: July 2011

Prime rich and prime poor

A short excursion –

The well-known Euler’s Polynomial $latex x^2 – x + 41$ generates 40 primes at the first 40 natural numbers. It is sometimes called a prime-rich polynomial. There are many such polynomials, and although Euler’s Polynomial is perhaps the best-known, it is not the best. The best that I have heard of is $latex (x^5 – 133 c^4 + 6729 x^3 – 158379 x^2 + 1720294x – 6823316)/4$, which generates 57 primes. But this morning, I was reading an article on Ulam’s Spiral when I heard of the opposite – a prime-poor polynomial. The polynomial $latex x^{12} + 488669$ doesn’t produce a prime until $latex x = 616980$. Who knew?

And to give them credit, that prime-rich polynomial was first discovered by Jaroslaw Wroblewski & Jean-Charles Meyrignac in one of Al Zimmerman’s Programming Contests (before being found by a few other teams too).

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Giving Journals

Firstly, I wanted to note that keeping a frequently-updated blog is hard. It has its own set of challenges that need to be overcome. Bit by bit.

But today, I talk about a sort of funny experience. Suppose for a moment that you had acquired a set of low-level math journals throughout the undergrad days, journals like the College Mathematics Journal, Mathematics Magazine, etc. Presuming that you didn’t want to keep them in graduate school (I don’t – they’re heavy and I have online access), what would you do with them?


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Back and Forum-ing: Beating a dead horse

I’m back! Croatia, Greece, Turkey… all behind me. In the meantime, I’ve fallen even more in love with math.stackexchange and have ended up as a temporary moderator for philsophy.stackexchange (check them out). To announce my return, a little fun:

from Loers
Hey everyone thanx for the amazing effort that u provide us with , over here . :)
just gotta a simple questions
why cannot we differentiate |x|when x = 0 ?
or let’s say |x+2| when x = -2
this is really annoying me :mrgreen: I cannot see a proper reason for it
thanx again :)

We strive to develop our humor. The Chaz (quite the internet sensation, if you haven’t run across him) writes: (more…)

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