Factor 12 is what?

Answer 1

F12, that is the twelfth Fermat number, or 2^(2^12)+1 is equal to 24096+1.

In decimal, the number has one thousand two hundred and thirty-four digits. Such a number is impossible to completely factorise (for comparison, the number F9(10) or 10512+1 is still not completely factored), but we do know six prime factors of F12 and that the cofactor is composite.

This means F12 must have at least eight distinct prime factors, as compared to no more than five for F11, four for F10, three for F9 and two for F8, F7, F6 and F5.

The known prime factors of F12 are:

1. 114689, the second smallest Fermat divisor and was discovered in 1877 well before computers by Edouard Lucas
2. 26017793 and
3. 63766529, both discovered in 1903 by Western
4. 190274191361, discovered in 1974
5. 1256132134125569, discovered in July 1986, and
6. 568630647535356955169033410940867804839360742060818433, discovered in March 2010

Before the sixth factor of F12 was found it was known after extensive use of the Elliptic Curve Method that there could be no factor of the 1,187 digit composite factor of F12 with under 45 digits.

Answer 2

1, 2, 3, 4, 6, 12