Problem:
Pierre de Fermat (1601–1665) conjectured that there are infinitely many prime numbers of
the form n = 2 2p+1 for some integer p. These numbers are called Fermat primes. For example,
5 is a Fermat prime because it is a prime number and it has the form +1. Write a program
that finds all the Fermat primes that are in the range of the int type. Use the Primes
class from Problem 2.22 and the Math.pow() method. Your first 5 lines of output should
look like this:
the form n = 2 2p+1 for some integer p. These numbers are called Fermat primes. For example,
5 is a Fermat prime because it is a prime number and it has the form +1. Write a program
that finds all the Fermat primes that are in the range of the int type. Use the Primes
class from Problem 2.22 and the Math.pow() method. Your first 5 lines of output should
look like this:
Output:
2^2^0 + 1 = 3
2^2^1 + 1 = 5
2^2^2 + 1 = 17
2^2^3 + 1 = 257
2^2^4 + 1 = 65537
2^2^1 + 1 = 5
2^2^2 + 1 = 17
2^2^3 + 1 = 257
2^2^4 + 1 = 65537
Solution:
public class TestFermat {
public static void main(String[] args) {
Primes.setSize(1000);
for (int p = 0; p < 5; p++) {
int n = (int)Math.pow(2,Math.pow(2,p)) + 1;
if (Primes.isPrime(n)) {
System.out.println("p = "+p+", n = 2^2^p = "+n);
}
}
}
}
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