Factor the number 184507 using the p-1 factoring method from today’s class. Tell me what you choose for a, and tell me what powers of a you compute, and tell me what gcd you tried, and what factor you found (you may need to keep lengthening the chain and trying again). You could use the Sage command “factorial(n)” if that seems useful. You can use the command “is_prime(n)” to check that you’ve factored it all the way. Do not ever use the command “factor(n)” since that’s cheating (except to check your answer after you’re done).
Use EC Factoring Tools to factor n = 290265623. You might want to increase the size of the loop! Use the result to factor n (that is, take the gcd of the non-invertible residue with n to get a non-trivial factor).
Now do it again with a different choice of curve and point (revisit lecture for some advice on finding random curve + point pairs). Factor n.
Now try modifying one of the middle digits of n, and see how long it takes. Factor n.
Try modifying one of the digits a couple more times and see how long it takes. Factor n.
Report to canvas on how long it took (what multiple of P) on different curves and points, and different n. Explain why you think it was fast sometimes and slow other times.