Reminder: fill out the form (link in last daily) about poster groups.
Reminder: Test Wednesday!! See Tests tab above.
I’ll post the proof of infinitude of primes based on Komolgorov complexity in the overleaf notes [edit: done, see section 3.7] — this is the solution to the last daily post.
Use Fermat’s Primality Test to detect whether 2001 and 2003 are composite or probably prime. Show your work (but you can use a calculator like Sage for the exponentiation).
If one of them is probably prime, then try a different a and explain what you learn.
Use Fermat Factoring to factor $n=16080$. Show the steps.
I wish to factor $n=38191$. How do I do it, if I have the following info:
196 ^2 - n factors as 3^2 * 5^2
201 ^2 - n factors as 2 * 5 * 13 * 17
214 ^2 - n factors as 3^2 * 5 * 13^2
227 ^2 - n factors as 2 * 3^3 * 13 * 19
229 ^2 - n factors as 2 * 3 * 5^3 * 19
241 ^2 - n factors as 2 * 3^2 * 5 * 13 * 17
254 ^2 - n factors as 3^4 * 5^2 * 13
If you aren’t familiar with for loops and if statements in Python/Sage, please visit these super quick tutorials: Python: For Loops and Python: If Statements.
Play around with Sage to see if you can find Carmichael numbers. This might require writing a for loop in python.