Problem 57417. Easy Sequences 86: The "real" Hyperprimorials

Ramon Villamangca

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In Easy Sequences 85, we define the hyperprimorial of n, as a exponent ladder of primes numbers from the n-th prime down to first prime (2). OEIS, however, defines hyperprimorial differently. In OEIS sequence #A076265, the hyperprimorial of n, ()  defined as follows:
                             
                             where:  is the i-th prime number.
Using the above formula, we want to calculate , which is the sum of all hyperprimorials from 1 to n:
                            
For example:
                            
                                
                                .
Since this will involve large integers, please output a vector containing first 6, last 6, and the number of digits of . Therefore, the final function output should be:  .