Problem: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 3, 1 1 3, etc. are all valid factorizations of 3.

The property of being prime (or not) is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and . Algorithms much more efficient than trial division have been devised to test the primality of large numbers. These include the MillerRabin primality test, which is fast but has a small probability of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of January 2016[update], the largest known prime number has 22,338,618 decimal digits.
1. what is primality?
2. is trial division less efficient than an algorithm
3. what have the algorithms been developed for?
4. name one
5. is it known as error free?
6. name another?
7. which is faster?
8. what are non prime numbers called?
9. is 1 prime?
10. how many digits in the largest prime number?
Answer: 1. a number that con only be divided by 1 and itself
2. yes
3. test the primality of large numbers
4. Miller Rabin
5. no
6. AKS
7. Miller Rabin
8. composite numbers
9. no
10. 22,338,618

Problem: CHAPTER V

HOME AGAIN

Following Brick Simpson's directions, they came into Union Street, and without further mishap gained the Hill. From the brow they looked down into the Pit, whence arose that steady, indefinable hum which comes from crowded human places.

"I 'll never go down there again, not as long as I live," Fred said with a great deal of savagery in his voice. "I wonder what became of the fireman."

"We 're lucky to get back with whole skins," Joe cheered them philosophically.

"I guess we left our share, and you more than yours," laughed Charley.

"Yes," Joe answered. "And I 've got more trouble to face when I get home. Good night, fellows."

As he expected, the door on the side porch was locked, and he went around to the dining-room and entered like a burglar through a window. As he crossed the wide hall, walking softly toward the stairs, his father came out of the library. The surprise was mutual, and each halted aghast.

Joe felt a hysterical desire to laugh, for he thought that he knew precisely how he looked. In reality he looked far worse than he imagined. What Mr. Bronson saw was a boy with hat and coat covered with dirt, his whole face smeared with the stains of conflict, and, in particular, a badly swollen nose, a bruised eyebrow, a cut and swollen lip, a scratched cheek, knuckles still bleeding, and a shirt torn open from throat to waist.

"What does this mean, sir?" Mr. Bronson finally managed to articulate.
1. Which door was locked?
2. What question did he get asked?
3. who asked the question?
4. whose directions did the group follow?
5. Fred never wanted to do what?
6. How dod Joe get into his house?
7. Was he clean?
8. Charley laughed at what?
9. Freddy didn;t know what happened to someone, who?
10. What injuries did the younger Bronson have?
Answer: 1. on the side porch
2. What does this mean, sir?
3. Mr. Bronson
4. Brick Simpson
5. go down there again
6. entered like a burglar
7. no
8. Joe
9. Joe
10. badly swollen nose, a bruised eyebrow, a cut and swollen lip, a scratched cheek,

Problem: Steven Spielberg's new movie Lincolnpaints a vivid and breath-taking picture of the 16th U.S. president and his determination to end slavery. Spielberg based his film on parts ofTeam of Rivals, a book by Doris Kearns Goodwin. He makes Abraham Lincoln relevant today by presenting a cunning political mind trying to overcome Washington's all too familiar political divisions.

In previous movies, Lincoln was shown as a simple yet almost perfect man. But Spielberg's Lincolnis different. "I was determined to make a movie about a working president dealing with real problems. Not some angel," Spielberg said.

We watch the president first ending slavery and then the war.

The film's adviser, historian Eric Martin, explains how Lincoln's thinking evolved.

"His main objective when the war began was not the freeing of the slaves but to keep the country united. Lincoln realizes that in order to keep the country together, the question of slavery will have to be addressed," Martin said.

The film focuses on the last four months of his presidency.

In the movie, the arguments among political enemies seem very similar to the problems we see in Washington today. The disagreements were bitter.

The film turns to Lincoln's relationships with his wife and kids, his beliefs and constant self-examination. Daniel Day-Lewis, the actor who plays Lincoln, offers an Oscar-worthy performance as the 16th President. Not only is his physical similarity to the president incredible, he is able to capture many of Lincoln's mannerisms and his high-pitched, almost lady-like voice.

"I found it very easy to play the role of Lincoln because the real man himself was so open. When I was researching his history to prepare for the part, one of the most surprising things I found was just how accessible he was. Even in war-time, when he was in great danger, he was always willing to meet with others and share his ideas," Day-Lewis said.

Spielberg's Lincolnwill head to the Oscars. But more important it will make history.
1. What is the name of the movie in the story
2. whose movie is it?
3. Which months of his presidency does the film focus on?
4. Which months of his presidency?
Answer:
1. Lincolnpaints
2. Steven Spielberg's
3. Abraham Lincoln
4. last four months