I am slightly confused by the following:

Fact: 54410972897 is a prime. Set p = 54410972897.

560 is the least power of 2 such that 2^{560}= 1 (mod. p). [2^{280 }= -1 (mod. p).]

So, according to Euler 560 should divide p-1 but it does not.

Can anyone give a correction to this?