For example, the sixth Fermat number is 2 2 5 + 1 ( or 2 32 + 1 ).
12.
As part of the ongoing worldwide search for factors of Fermat numbers, some Pierpont primes have been announced as factors.
13.
This argument is not a rigorous randomly ", yet we have already seen that the factors of Fermat numbers have special properties.
14.
In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers.
15.
Generalized Fermat numbers can be prime only for even a, because if a is odd then every generalized Fermat number will be divisible by 2.
16.
Generalized Fermat numbers can be prime only for even a, because if a is odd then every generalized Fermat number will be divisible by 2.
17.
If a is a perfect power with an odd exponent, then all generalized Fermat number can be algrabic factored, so they cannot be prime)
18.
Even if it wasn't known at the time of the quote that the 20th Fermat number is composite, this number is 315653 digits.
19.
Notable examples include the set of all prime numbers, the set of elements in Sylvester's sequence, and the set of all Fermat numbers.
20.
Famous examples of Lucas sequences include the Fibonacci numbers, Mersenne numbers, Pell numbers, Lucas numbers, Jacobsthal numbers, and a superset of Fermat numbers.
