Saturday, September 27, 2014

Closed Circuit

Movie Review : Closed Circuit
Director : John Crawley
Genere : Thriller
Starring : Eric Bana, Rebecca Hall
Released : August 2013
My Rating : 6 out of 10

It seems to me that there are two clear approaches of making movies categorized as "thrillers". One has dazzling action sequences, fast moving story that tries to not give the viewer any time to find any plot holes and a few twists thrown in to wow them. Second type is based on slow build up, believable characters and maintaining intrigue till the end. "Closed Circuit" is of the second type.

A bomb explodes in a busy market in London killing many people. A tip allows the police to capture the alleged mastermind of the attack and he is put on a trial. This is the starting point of the story. We are given an explanation about the complicated legal procedure for trials involving national security, where some sensitive evidence can be presented only in a closed courtroom. As per the British legal system, there need to be two lawyers for the defense. One for the open trial, and one for the closed trial, and they cannot have contact with each other during the trial.

Martin Rose (Eric Bana) gets chosen as the defense attorney for the open trial, because the previously chosen lawyer commits suicide. The defense attorney for the closed trial is Claudia (Rebecca Hall). They had an affair in the past, but they chose to keep that knowledge to themselves in order to get the rare chance to fight a case with the national spotlight. As Martin digs deeper, he starts getting suspicious that things are quite different than what was being publicly acknowledged. Claudia also starts to feel that she is being constantly monitored. As the movie progresses we get more and more clarity about what actually happened.

Director John Crawley maintains the tension very well. Many times throughout the movie, we see the protagonists being constantly monitored via closed circuit cameras, as referenced by the movie title. The pacing is perfect.

The cast selection here is successful. Almost every one gives a believable performance. Eric Bana has acted well in many movies. He was the only bright spot in Troy for me, while Black Hawk Down and Munich were perhaps his most memorable performances. I had never noticed Rebecca Hall before, and she has provided perfect chemistry to Eric Bana here. Ciran Hinds (The Debt, Rome) and others provide able support.

The movie still falls very short of a satisfying experience. The problem is the shallow plot and lack of good surprising twists. We have seen these themes before. We can guess the secret very early, and it’s also revealed much before the movie is over. So the only question that remains once everything is out in the open is, what will be the final resolution? The ending is grounded in reality to some extent, but it’s still pedestrian. It will not leave you excited at the end, rather you will be feeling, “meh”. The same team produced "Tinker, Tailor, Soldier, Spy", which was far more satisfying.

I can neither recommend for watching this movie, nor against it. It’s a short movie, and doesn’t stray much. For example, the past relation between the leads is covered only in few dialogues. So time passes briskly, but without much payoff. It’s rated R, and should be fine for most teenagers.

Thursday, September 18, 2014

Sum Of Consecutive Primes - Part 2

When I wrote the blog post on “Sum Of Consecutive Primes” I said that it was a pure D! activity. This is D!^2 :-)

One of the comments on the post suggested to do the analysis to find even more special primes. I liked the suggestion and modified my code to look for even more special primes. What kind of specialty are we talking about?

Please read the original blog post for more details. As a quick recap, we are looking for primes that can be written as sum of consecutive primes.

Obtaining primes from adding consecutive primes is just beautiful. As the analysis shows, many of these prime numbers can be written as multiple different sequences of consecutive primes. Some of these sequences are surprisingly large.

Within such primes, how about finding some more specializations, as follows.
1. The length of at least one the sequence itself is prime.
2. More specialization of the first, length of EVERY sequence is prime.
3. For a particular prime, the number of different generating sequences is also a prime.
4. Intersection of 2, and 3 : the number of sequences is prime, and length of every sequence is also prime.

In each case, we are looking for the primes below an arbitrary limit, which is 1 million for Problem 50 in Project Euler.

So here are the answers.

1. At least one sequence with prime length

The largest prime is
999983 = 34337 + 34351 + … + 34613 (29 primes)

The largest sequence is for
981391 = 71 + 73 + … + 3917 (523 primes)

The prime 442019 is noteworthy, as it has the six generating sequences, maximum for this subset. Only the first sequence is of prime length.
442019 = 419 + 421 + … + 2621 (301 primes)
442019 = 7529 + 7537 + … + 8017 (57 primes)
442019 = 13229 + 13241 + … + 13567 (33 primes)
442019 = 17569 + 17573 + … + 17807 (25 primes)
442019 = 49069 + 49081 + … + 147347 (9 primes)

2 All generating sequences are of prime length
There have to be more than 1 generating sequences to be qualified for this criterion.

The largest is
999863 = 13723 + 13729 + … + 14447 (71 primes)
999863 = 199933 + … + 200003 (5 primes)

The largest sequence in this subset is for
973691 = 61 + 67 + … + 3907 (523 primes)
Interestingly it’s the same length (523) for the largest sequence for the previous subset above.

Most prime sequences are for
999049 = 4801 + 4813 + … + 6337 (179 primes)
999049 = 7013 + 7019 + … + 8231 (131 primes)
999049 = 21019 + 21023 + … + 21493 (47 primes)
999049 = 199799 + … + 199819 (5 primes)

3. Number of generating sequence is prime
The largest is same as above 999863.

The largest sequence is for a prime that is an answer to the Project Euler : Problem 50, so I cannot give it here.

The most sequences are for
988321 = 113 + 127 + … + 3923 (515 primes)
988321 = 4673 + 4679 + .. + 6247(181 primes)
988321 = 5107 + 5113 +  … + 6577 (169 primes)
988321 = 89797 + 89809 + … + 89899 (11 primes)
988321 =  329419 + 329431 + 329471
Note that 2nd and 3rd of the above are overlapping sequences!

4. Primest of primes
Now let’s see which are the most special of these. These have ONLY a prime number ways of generating sequences, and length of each of these sequences is also prime.

The largest is 999863, same as subset 2 above.

The largest sequence in this subset is also for the same prime as for subset 2 above.
973691 = 61 + 67 + … + 3907 (523 primes)
973691 = 6841 + 6857 + …  + 8039 (131 primes)
So there are 2 sequences, each has prime number of primes.

And the most sequences are for
993367 = 13679 + 13681 + … + 14387 (71 primes)
993367 = 141863 + 141871 + … + 141941 (7 primes)
993367 = 331099 + 331127 + 331141
Now that’s one beautiful number. It’s the largest prime below 1 million that can be written in most prime number of different ways as sum of prime number of consecutive primes :-)



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