Problem of the day
 Secret message =
"Y,B>j0rB\xca?x3A+Yb\xc4& m".
f(x) = ax mod N, a = 19,
N = 1,000,000, block size = 3. What is the message?
 Is the number N1 =
18811277023211276170
87679512659599640999
58352014316332881290
46662122067416818277
286993
prime or composite? Why?

Find the continued fraction expansion of the square roots
of 2, 3, 5, 6, ... . What patterns do you see? Compute
convergents of these continued fractions. How do they
relate to solutions of Pell's equation?
 Find a prime number larger than 10^{100}.
Find the next five primes. How sure are you of your
results?
 I have encoded my PIN using the function f(x) = x^{3} mod 12347.
The result is 6803. What is my PIN?