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Chapter 10: Problem 1

If a prime number, \(p,\) is squared and the result is added to the next prime number greater than \(p\) which of the following integers could be the resulting sum? Indicate all such integers. A. $$3$$ B. $$4$$ C. $$7$$ D. $$14$$ E. V$$58$$ F. $$60$$ G. $$65$$ H. $$69$$

Short Answer

Expert verified
The correct answers are C. \(7\) and D. \(14\)

Step by step solution

01

Identify the first few prime numbers and find the next prime number of each

The first few prime numbers are \(2, 3, 5, 7, 11, 13, 17, 19, 23, \ldots\). The next prime number greater than each of these are \(3, 5, 7, 11, 13, 17, 19, 23, 29, \ldots\) respectively.
02

Square each prime number and add it to the next prime number

Calculating the square of each prime number and adding it to the next prime number, we get the following: \(2^2+3=7\), \(3^2+5=14\), \(5^2+7=32\), \(7^2+11= 62\), \(11^2+13=134\) and so on.
03

Compare the result with the given options

For each of these sums, check if they are in the given options. If they are, mark that option as a valid answer. From the results, it can be seen that 7 (from \(2^2+3=7\)) and 14 (from \(3^2+5=14\)) are in the given options.

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Most popular questions from this chapter

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