Numbers

 Working through Lesson 6, on algorithms. No joking, finding quantum advantage

cannot be in terms of seconds to run a certain program...

Interesting look at prime factorization. Python's math module accepts this code, and

outputs quickly:

                                                        

For instance, if you input the number 650, the output will be 2 5 5 13, representing the prime factors of 650. Feel free to try it out! 😊

you

what does n//= i mean?

Copilot

Certainly! The expression n //= i is a shorthand for integer division with assignment. It divides the value of n by i and assigns the result back to n. In other words, it updates n to be the floor division of n by i.

For example:

If n is initially 10 and i is 3, then n //= i results in n becoming 3 (since 10 divided by 3 is 3 with no remainder).

If n is initially 15 and i is 4, then n //= i results in n becoming 3 (since 15 divided by 4 is 3 with a remainder of 3).

Feel free to ask if you have any more questions! 😊

                                                                    *     *     *

  The **RSA Factoring Challenge** was a significant initiative by RSA Laboratories to encourage research in computational number theory and the practical difficulty of factoring large integers used in cryptography. Here are the key points:

1. **Challenge Overview**:

   - RSA Laboratories published a list of semiprimes (numbers with exactly two prime factors) known as the **RSA numbers**.

   - The challenge was to factorize these numbers into their prime components.

   - The smallest of these, **RSA-100**, a 100-decimal digit number, was factored by April 1, 1991.

   - Larger numbers remained unfactored for quite some time.

2. **Purpose and Application**:

   - The challenge helped track the cutting edge in integer factorization.

   - It provided insights into choosing key lengths for the RSA public-key encryption scheme.

   - RSA Laboratories used it as an incentive for the academic community to test the strength of their solutions.

3. **Challenge Numbers**:

   - The RSA numbers were generated without any network connection.

   - The computer generating them had its hard drive destroyed to prevent any record of the solutions.

   - The challenge included both decimal and binary representations of numbers.

4. **Legacy and Conclusion**:

   - The RSA Factoring Challenges ended in 2007.

   - Only RSA-576 and RSA-640 were factored from the 2001 challenge numbers.

   - Advances in quantum computers (such as Shor's algorithm) may impact future factorization efforts.

In summary, the RSA Factoring Challenge played a crucial role in understanding the security of RSA-based encryption. 🌟

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The first bit in a binary just codes 0 or 1, but the subsequent ones are all powers of 2.

possible values:   8   4   2   1

my_num:             1   1   0   0  thus represents 12, and the 8 is 2^3.

So what is 2^1023??