6. Sophie Germaine primes A prime number p > 2 is called a Sophie Germaine prime if 2 p+1 is also prime. A 32-bit Sophie Germaine prime is p = 2008465313 with prime 2 p +1 = 4016930627 (found after 644 trials). It took 2253 trials to generate a 64-bit Sophie Germaine prime p = 10155921358726090901 with prime 2.p+1=20311842717452181803.

(a) Compute another 32-bit Sophie Germaine prime p.

(b) Compute another 64-bit Sophie Germaine prime p.

(c) What is the largest Sophie Germaine prime you can generate (without upsetting your systems administrator)?

(d) A natural number is a palindrome in decimal representation if its string of deci- mal digits is symmetric with respect to reading it from the left or the right. For example, 131 and 314413 are each palindromes. Find a Sophie Germaine prime that is a palindrome in decimal representation.