Make a list of distinct prime numbers, using the hexadecimal digits 1,3, 5, 7, 9, B, D, F exactly once 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?

Bonus Question:

Make a list of distinct prime numbers, using the hexadecimal digits from 1 to F exactly once 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?

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

2+3+5+7+BF+91D = 9ED

The UBASIC immediate mode playing around leading to this:

b=11
OK
d=13
OK
f=15
OK
bs=16
OK
x1=bs*b+f:?x1,prmdiv(x1)
 191     191
OK
x2=bs*9+d:?x2,prmdiv(x2)
 157     157
OK
x3=bs^2*9+bs*1+d:?x3,prmdiv(x3)
 2333    2333
OK
?2+3+5+7+x1+x3
 2541
OK
?2541\16,2541 @ 16
 158     13
OK
?158\16,158 @ 16
 9       14
OK

 

Posted by Charlie on 2010-10-26 17:59:58