This can be verified from the factorization

p_{27} - 1 = 2^{19} . 51309697 . 11878566851267

The fact that p_{27} - 1 is divisible by 2^{19}
is not surprising.
Since p_{27} is a factor of the Fermat number
F13,
a well-known theorem implies that p_{27} - 1 is divisible
by 2^{15}.

Richard Brent

30 June 1995