Double Primes II - The Fives Mystery Cache
Double Primes II - The Fives
Please note Use of geocaching.com services is subject to the terms and conditions
in our disclaimer.
There is absolutely nothing wrong with the coordinates above.
I'm sure they would take you to a very nice location where you
could enjoy God's creation. However, if you want to find this
cache, I don't recommend going there; I recommend solving the
puzzle instead.
Good job, class! So now you've learned about primes and double
primes. For any of you who were absent and didn't catch the lesson,
you can review it at
GC2NX0A Double Primes.
Today we will learn about a special case of the double primes. I
call them "the Fives." The Fives are prime numbers, which are also
double primes. But when you recursively add up the digits, the
digits total 5. If you recall, the first 8 double primes are (2, 3,
5, 7, 11, 23, 29, 41). Of these, only 5, 23, and 41 belong to the
Fives. The first 8 Fives are (5, 23, 41, 113, 131, 311, 401, 599).
Note that for the 8th one, 599, the digits sum to 23, which makes
it a double prime. But if I repeatedly sum the digits until the sum
is less than 10, the 23 becomes 2+3 = 5, and thus 599 is a member
of the Fives.
You can see where this is going. If I were to ask you for the 2nd
Five, 2nd digit, you should say 3. If I ask you for the 8th Five,
3rd digit, you should say 9. If I ask you for the 55th Five, 1st
digit, you should simply say "goodnight" and go to bed. I mean ...
it's just not worth it, right? Well I guess we'll find out. Here
goes:
2nd Five, 2nd digit
8th Five, 3rd digit
7th Five, 1st digit
62nd Five, 3rd digit
14th Five, 3rd digit
# Fives < 10,000, 2nd digit
Largest Five < 5000, 3rd digit
25th Five, 3rd digit
20th Five, 3rd digit
89th Five, 3rd digit
77th Five, 4th digit
29th Five, 1st digit
38th Five, 3rd digit
1st Five
I remind you once again: please don't try this by hand! I've told
you this before, and you just won't listen. Maybe this time you
will! BYOP.
You can check your answers for this puzzle on
Geochecker.com.
Additional Hints
(No hints available.)
Treasures
You'll collect a digital Treasure from one of these collections when you find and log this geocache:
Loading Treasures