Smarandache function, the Fermat number
, lower bound estimate, elementary method.
Papadopoulos of the University of Maryland at College Park performed a massive calculation to prove that the 24th Fermat number, which is more than 5 million digits long, is not a prime.
No one has yet found even one prime factor of the 24th Fermat number, for example.
In 1990, Lenstra and a colleague used the method to factor a 155-digit Fermat number
Two computer scientists factored a record-breaking, 155-digit Fermat number
(137: 389; 138: 90).
Using a Fermat number as the divisor in modular arithmetic provides a handy way of speeding up certain types of calculations and circumvents the need to deal with real numbers.
Thus, the answer is always exact and correct, provided it's less than the Fermat number used in the operations.
finished factoring the tenth Fermat number, proving that this 155-digit behemoth is the product of three prime numbers.
A century later, however, Leonhard Euler successfully factored the next Fermat number in the sequence.
His exploration of elementary and advanced topics in classical number theory covers a range of numbers, including Fermat numbers
, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, and voracious numbers.
More recently analysis of these so-called Fermat numbers
have found no other primes above [F.
Almost all number theorists consider the first Fermat prime to be [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], so that the first five Fermat numbers