Make a list of distinct prime numbers, using the decimal digits from 0 to 9 exactly twice each in the list. What is the minimum sum of all the numbers in such a list? What's the minimum product of all the numbers in such a list? (None of the primes may admit leading zeroes).

Bonus Question:

Make a list of distinct prime numbers, using the duodecimal digits from 0 to B exactly twice each in the list. What is the minimum sum of all the numbers in such a list? What's the minimum product of all the numbers in such a list? (None of the primes may admit leading zeroes).

Note: Think of this problem as an extension of Pretty Potent Primes.

No computer, no spreadsheets... just some numbers (decimal 0-9 only, two of each) to get things rolling!

Lowest sum: 2+23+89+109+463+487+557+601 = 2,331

These same numbers might produce the minimum product as well:

2*23*89*109*463*487*557*601 = 33,683,247,440,588,782 

 

Posted by rod hines on 2008-12-09 18:08:10