Step by Step solution about How to resolve the algorithm Euclid-Mullin sequence step by step in the Mathematica/Wolfram Language programming language

Overview:

This Wolfram code generates a list of integers and performs certain operations on them.

Implementation:

1. Initialization:

   • list = {2}: Initializes a list containing a single element, which is 2.

2. For Loop:

   • Do[... , {21 - 1}]: Executes the following block of code 20 times, from 1 to 20 (excluding 21).

3. Operations Inside the Loop:

   • prod = Times @@ list: Calculates the product of all elements in the list.
   • prod++: Increments the prod by 1.
   • new = Min[FactorInteger[prod][[All, 1]]];:
     • FactorInteger[prod]: Factors the prod into its prime factors.
     • [[All, 1]]: Extracts the smallest prime factor.
     • Min[]: Gets the minimum of the extracted prime factor.
   • AppendTo[list, new]: Adds the new value to the list.

4. Output:

   • list: After the loop completes, the code prints the final value of the list.

Explanation:

The code starts by initializing a list with a single element, 2. It then iteratively generates a sequence of integers by performing the following operations:

1. Multiplies all elements in the list to get the prod.
2. Increments prod by 1.
3. Factors prod into prime factors and takes the smallest one (new).
4. Adds new to the list.

This process is repeated 20 times. The resulting list contains the sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

list = {2};
Do[
  prod = Times @@ list;
  prod++;
  new = Min[FactorInteger[prod][[All, 1]]];
  AppendTo[list, new]
  ,
  {21 - 1}
  ];
list