Question

Show that 2047 is a strong pseudoprime to the base 2 by showing that is passes Miller’s test to the base 2, but is composite.

Short answer

$2^{1023}={\left(2^{11}\right)}^{93}={2048}^{93}\equiv 1^{93}=1(mod2047)$

Step-by-step solution

Step: 1

First, 2047=23.89 is composite. Write 2047-1=2046

2046=2. 1023,

So s = 1 and t = 1023 in the definition.

Then $2^{1023}={\left(2^{11}\right)}^{93}={2048}^{93}\equiv 1^{93}=1(mod2047)$as desired.