In this task, you are given a passage and a question regarding that passage. You must determine whether or not the question is answerable from the given passage. If a question is answerable, output should be 'True', otherwise 'False'. You must not consider any other information that is not provided in the passage while labelling True or False.

Passage: Modern primality tests for general numbers n can be divided into two main classes, probabilistic (or "Monte Carlo") and deterministic algorithms. Deterministic algorithms provide a way to tell for sure whether a given number is prime or not. For example, trial division is a deterministic algorithm because, if performed correctly, it will always identify a prime number as prime and a composite number as composite. Probabilistic algorithms are normally faster, but do not completely prove that a number is prime. These tests rely on testing a given number in a partly random way. For example, a given test might pass all the time if applied to a prime number, but pass only with probability p if applied to a composite number. If we repeat the test n times and pass every time, then the probability that our number is composite is 1/(1-p)n, which decreases exponentially with the number of tests, so we can be as sure as we like (though never perfectly sure) that the number is prime. On the other hand, if the test ever fails, then we know that the number is composite. Question: What type of algorithm is trial division?
True

Passage: There are hints in the surviving records of the ancient Egyptians that they had some knowledge of prime numbers: the Egyptian fraction expansions in the Rhind papyrus, for instance, have quite different forms for primes and for composites. However, the earliest surviving records of the explicit study of prime numbers come from the Ancient Greeks. Euclid's Elements (circa 300 BC) contain important theorems about primes, including the infinitude of primes and the fundamental theorem of arithmetic. Euclid also showed how to construct a perfect number from a Mersenne prime. The Sieve of Eratosthenes, attributed to Eratosthenes, is a simple method to compute primes, although the large primes found today with computers are not generated this way. Question: What is the name of the Egyptian papyrus that suggests that they may have had knowledge of prime numbers?
True

Passage: In addition to the Riemann hypothesis, many more conjectures revolving about primes have been posed. Often having an elementary formulation, many of these conjectures have withstood a proof for decades: all four of Landau's problems from 1912 are still unsolved. One of them is Goldbach's conjecture, which asserts that every even integer n greater than 2 can be written as a sum of two primes. As of February 2011[update], this conjecture has been verified for all numbers up to n = 2 · 1017. Weaker statements than this have been proven, for example Vinogradov's theorem says that every sufficiently large odd integer can be written as a sum of three primes. Chen's theorem says that every sufficiently large even number can be expressed as the sum of a prime and a semiprime, the product of two primes. Also, any even integer can be written as the sum of six primes. The branch of number theory studying such questions is called additive number theory. Question: Which theorem states that every large even integer can be written as a prime summed with a semiprime?

True

