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In this problem, we want to use the test for primality to determine whether the following numbers are prime or not.
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The test of primality goes as follows.
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For any integer n greater than 1, we want to check if it is divisible by any prime number less or equal to its square root.
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If it is not divisible by any of these numbers, then our integer n here is a prime number.
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So the first thing you want to do is to determine or to calculate the square root.
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Of our integers here because that will determine the upper limit of the prime numbers we want to test.
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It's the visibility.
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So the square root of 493 corresponds to 22 .2.
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The square root of 653 corresponds to 25 .5.
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Next, the square root of 437 is equal to 20 .9.
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And lastly, the square root of 521 is is equal to 22 .8.
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So we see here that our maximum integer is equal to 25.
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So let's find all the prime numbers up until that integer.
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This corresponds to the set p equal to the prime numbers 3, 5, 7, 11, 13, 17, 19, 21, and 23.
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The next prime number after 23 is 29, and this is too big to be considered.
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So now, the next thing we want to do is to take our integer, and a, our integer corresponds to 9 ,4003, that we want to test for primality...