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: (CNN) -- Cristiano Ronaldo underlined just why Real Madrid agreed to pay him the big bucks on a scintillating evening of European football.

The 28-year-old, who inked a new five-year deal with the Spanish club on Sunday, completed a brilliant hat trick as Real raced to a 6-1 rout against Galatasaray.

Ronaldo had the final say in Istanbul as he danced past three defenders before blasting the ball into the net for his hat-trick.

Summer signing Isco had got Los Blancos off the mark when he picked up a long ball hit from beyond the halfway line by Angel di Maria and hit home after 33 minutes.

From then on it was one way traffic as Karim Benzema and Ronaldo added two goals apiece before Umut Bulut pulled one back for the Turkish champions.

The away victory saw the nine time European champions kick off a new era of European football under manager Carlo Ancelotti in some style.

A pulsating opening round of Champions League group matches featured a flurry of firsts.

Former Barcelona boss Pep Guardiola safely negotiated his first match in charge of Bayern Munich's title defence with an emphatic 3-0 win over CSKA Moscow.

David Alaba hit home a dipping free kick to set the Germans on their way before Mario Mandzukic powered in a header in a dominant first half.

Arjen Robben volleyed in a scooped pass from Alaba to tick off a first European win for Guardiola and his defending champions.

David Moyes also came through his first game as Manchester United manager unscathed as the club made its first European outing without Sir Alex Ferguson at the helm since 1985.
1. How old is Ronaldo?
2. Who does he play for?
3. How long is his contract?
4. Who won on Sunday?
5. What was the score on Sunday?
6. Who did they play against?
Answer: 1. 28
2. Real Madrid
3. five-year deal
4. unknown
5. unknown
6. Galatasaray

Problem: (CNN) -- Lying low.

Three of the key anti-war members of Congress are considering supporting expanded military action against ISIS -- but the key word there is "considering."

Rep. Barbara Lee said she "can't say" if she'd oppose expanded military operations.

The California Democrat was the only member of Congress to vote against giving President George W. Bush -- and subsequent presidents that would follow him -- nearly unlimited authority to wage war just days after the September 11 terror attacks.

This time around, she said there's "no question" that ISIS needs to be stopped, but she's waiting to hear President Barack Obama's plan, which he's expected to unveil in an address Wednesday night.

Analysis: Obama speech a do-over 'no strategy' comment

To get her support, Obama has to outline a plan that is "strategic, targeted and limited," Lee told CNN.

Republican Walter Jones of North Carolina, who said he will go to his grave apologizing for his vote for war in 2002, couldn't commit his support -- or opposition -- to an expanded military operation either.

"I've always regretted that vote," he told CNN of his vote that authorized U.S. intervention in Iraq. "I think here we go again."

Jones said it "depends" on what the President says. "I'm opposed to spending money without a debate and a strategy."

Rounding out the vocal antiwar trio, Massachusetts Democrat James McGovern, said he's "very uneasy" about the prospect of expanded war but stopped short of opposing it. He said he has "a million questions" about potential action in Syria, the role of regional partners and the cost to U.S. coffers.
1. What is being considered by Congress?
2. Against whom?
3. Who is the current president in the article?
4. What does Obama think about it?
5. Who is someone he is trying to get support?
6. What is her job?
7. From where?
8. What is her party?
9. Did she support the war after 9/11?
10. How does she feel about ISIS?
11. Who is another congressman to be convinced?
12. Where is he from?
13. What party?
14. Did he vote for the war after 9/11?
15. When was that vote taken?
16. Was he at peace with his stance?
17. What is he really against?
18. Who is another antiwar congressman?
19. Where is he from?
20. What's his party?
Answer: 1. military action
2. ISIS
3. George W. Bush
4. unknown
5. Lee
6. Representative
7. California
8. Democrat
9. no
10. they need to be stopped
11. Walter Jones
12. North Carolina
13. Republican
14. yes
15. 2002
16. no
17. spending money without a debate and strategy
18. James McGovern
19. Massachusetts
20. Democrat

Problem: Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years. By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia.
1. How long did it take for Newton's laws to be corrected?
2. Whose theory had accurate predictions?
Answer:
1. nearly three hundred years.
2. Einstein