Assignment I

# 1 RSA

The following is an example RSA system. (We have used chunks of 4 digits to break up large numbers).
 What Number Modulus 1120 3636 1351 5716 6077 1438 9947 7366 2821 0498 6262 4870 2237 7405 1359 1447 2052 5841 5977 Public Key 0015 8597 Secret 0029 9734 7246 2576 1241 7972 6959 1999 9270 7786 7766 5723 3432 0430 7514 6108 7174 6174 9337
The following was sent over the channel

 1009 7905 9122 7717 7609 5230 5257 6744 5876 5952 5469 5306 9587 5797 6021 7482 3100 3064 5451

Decrypt the (date) that is the message. Then add a date of your own in the same format; encrypt it and send it to me!

# 2 Trial Division

Find the first number larger than 232 that is not divisible by the first 1000 primes. Is this number a prime?

# 3 Twin primes

The twin prime conjecture says that there are infinitely many pairs of primes (p, q) so that p - q = 2. Try to verify this conjecture by finding a pair (p, q) larger than 100000000001 ( = 1011 + 1) which is likely to be a prime pair.

Kapil H. Paranjape 2002-01-26