Storms…

Workout notes No swimming this morning due to large thunderstorms; in fact the thunderstorms knocked out our power for several hours.

We weren’t affected (we have a few scattered twigs here and there) but other houses got creamed by large tree limbs, loose shingles, etc.

But I do have a head lamp (for use in long ultras) and so used my manual Sportech treadmill and ran about 5 miles (55 minutes of easy running; I run about 1 minute per mile slower on this thing than I do on the road) and followed it by 20 minutes of cycling.

When I finished, I was completely drenched in sweat; just dripping.

Articles:

Mathematics Recursivity reports that a Rutgers grad student found a concise formula that generates only “1s” or primes:

For a long time mathematicians have sought a simple formula that would generate all the prime numbers, or even infinitely many distinct prime numbers. Some have even gone so far as to claim that no such formula exists — a statement of very questionable veracity that depends entirely on one’s definition of “formula”. If you define formula to mean “polynomial with integer coefficients”, then it’s not hard (and I leave it as a challenge to the reader) to prove that no such polynomial can generate only primes, other than the trivial example of a constant polynomial. Euler’s polynomial x2 + x + 41 comes close: it generates primes for x = 0, 1, 2, …, 39, but fails at x = 40. [...]

Rutgers graduate student Eric Rowland has defied the odds, however, and has found a new one. In a paper just published in a journal I edit, the Journal of Integer Sequences, Rowland defines his formula and proves it generates only 1’s and primes. (1 is generally not accepted as a prime number, for a variety of reasons. For one thing, if 1 were a prime, then positive integers would not have a unique factorization into primes.) To be precise, I should say that the unusual property of the formula was originally conjectured by a team led by Matt Frank at a mathematics summer school in 2003 where Rowland was attending, but it was not proved until now.

Here is Rowland’s formula. We define a(1) = 7, and for n ≥ 2 we set

a(n) = a(n-1) + gcd(n,a(n-1)).

Here “gcd” means the greatest common divisor. So, for example, we find a(2) = a(1) + gcd(2,7) = 8. The prime generator is then a(n) – a(n-1), the so-called first differences of the original sequence.

For example, here are the first 23 values of the a sequence:
7, 8, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69

and here are the first differences of these values:
1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23

If we ignore the 1’s, then, the Rowland formula starts by generating the primes 5, 3, 11, 3 (again), and 23. The reader can easily program up the formula and find lots more primes. Removing duplicates, the first few are
5, 3, 11, 23, 47, 101, 7, 13, 233, 467, 941, 1889, 3779, 7559, 15131, 53, 30323, …

Surf to Recursivity’s article for the rest; there are some interesting questions here. Don’t be fooled however; these number theory questions may be easy to state, but difficult to do.

Local Politics Who is the Republican in the IL-18 race? Aaron Shock’s campaign says that HE is more like Obama and Colleen Callahan!

It seems that Colleen Callahan, the Democrat running for the 18th Congressional District job, recently pointed that it’s a little inconsistent, in her opinion, for Schock to market himself as being for “change” while attaching himself to President Bush as a fundraising tool. Bush is, after all, what most Americans want change from.

To which Shearer replied:

Shearer said Schock is like Obama in that he represents change and people are inspired by him. Callahan, he said, is showing she’s more of a Hillary Clinton supporter.

“This is a Hillary Clinton, throw-the-kitchen-sink blistering negative attack playbook that Sen. Obama has railed against as the broken part of politics right now. Is (Callahan) running because she has a vision for what this country should be or is she nitpicking on Aaron and constantly being nasty?”

Really? Is “nasty” the word Shearer (and by association, Schock) wants to use about this well-liked, well-regarded broadcaster, farm wife and mother?

Wow…even Republicans are trying to identify with Obama, and not just in Illinois either.

Hey, do any of you know any Democrat (no Lieberman doesn’t count!) running for office that is saying that they would be more like McCain than their opponent?

Perhaps this is one reason why you don’t hear about this:

psst: Iraq doesn’t border Pakistan though Iran does.

Back to the Illinois 18′th Congressional District race: Peoria Pundit sees this as competitive. I have to agree: why else would they be bringing in The Decider to raise money?

For an amusing take, here is another blog tidbit (hat tip to Peoria Pundit)

So, let me get this straight.

Aaron Schock is an anti-choice, Bush-loving neocon who thinks selling nuclear weapons to Taiwan is a swell idea, and proudly trumpets the historic achievements of the Gingrich Congress on his website.

Yeah, sounds just like Obama to me.

For the record, what was so kitchen-sinky about Callahan’s campaign? Apparently, she posted on her blog that President Bush was doing a fundraiser for Schock, and aligning oneself with this horrendous administration didn’t sound like “change” to her.

Imagine that.

So how is the general election looking at the moment? Here are the political future numbers:

Obama vs. McCain:
Obama: 65.2 McCain: 29.8. What this means is: if you want to buy a contract that pays out 100 dollars if your selected candidate wins (and zero if your candidate loses), an Obama contract costs 65.20 (that is, you bet 65.2 to win your money back plus 34.8 dollars), and a McCain contract costs 29.8 (that is, you win your 29.8 back plus 70.2 dollars).

Presidential party:
Democrats: 68.3, Republicans 31.4 (Intrade)
Democrats: 66.0, Republicans 35.1 (Iowa Electronic)

Religion/Issues. I have to admit that my current religious beliefs have not stopped me from enjoying Rosemary’s Baby (the director’s cut) on DVD. It remains one of my favorite “horror” movies, even though not believing in deities precludes me from believing in devils, demons and the like.

Trailer:

But I digress.

What I wanted to comment on is how atheists are often called “haters” because we dismiss (sometimes acerbically) the supernatural beliefs of theists. But those who call us “haters” have no problems labeling us as wicked, immoral, etc.