Problem 10 (a) Suppose the primes p and q used in the RSA algorithm are consecutive primes. How would you factor n = pq? (b) If you knew even more that q = p + 2, describe an alternative way to factor n. The ciphertext 10787770728 was encrypted using 3 = 113 and n = 10993522499. The factors of p and q were chosen so that q-p = 2. Decrypt the message. (c) The following ciphertext c was encrypted mod n using the exponent e:

n = 152415787501905985701881832150835089037858868621211004433

e = 9007

c = 141077461765569500241199505617854673388398574333341423525.

The prime factors p and q of n are consecutive primes. Decrypt the message.