Perfect Numbers and The Wrekin Mystery Cache
geohatter: As the owner has not responded to my previous log requesting that they check this cache I am archiving it.
If you wish to email me please send your email via my profile (click on my name) and quote the cache name and number.
Regards
Paul
geohatter
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Perfect Numbers and The Wrekin
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Puzzle cache hidden on the Wrekin, Telford, Shropshire. You will need to Google a few things before you leave to translate the coordinates !
Happy caching !
Here at TonySamBen we all love maths and numbers. It’s what makes the world tick. Perfect Numbers are pretty rare, which makes them very special to mathematicians. This cache is also special as it has permission to be on the Wrekin, hence the name of the cache.
First, a quick lesson on Perfect numbers !
Perfect Numbers are numbers that equal the sum of their divisors. The first perfect number is 6, as 6 = 1 + 2 + 3 (1, 2 and 3 all divide into 6).
The next perfect number is 28 (28 = 1 + 2 + 4 + 7 + 14). Then 496, then 8,128. And from that point on they become increasingly rare (and big !).
If you can find a big Mersenne Prime number, which is of the form 2^p – 1 (where p is a prime number), then it is easy to prove that 2^(p-1) . (2^p -1) is Perfect. There are 47 known Perfect Numbers so far, the largest has p = 43,112,609. Every time a new big Mersenne Prime is found, you get a Perfect Number for free ! Big Primes are used in cryptology, especially in coding credit card transactions. For more info, check out the Great Internet Mersennse Prime Search, or GIMPS for short.
Anyway, back to the cache !
The coordinates are
North 52. 40.abc’
West 2. 32.def’
where a, b, c, d, e and f are as follows.
a = last digit of the sixth perfect number
b = first digit of the fifth perfect number
c = first digit of the sixth perfect number
d = last but one digit of the seventh perfect number
e = fourth digit of the seventh perfect number
f = third digit of the fifth perfect number.
If you start from the waypoint listed, which is the car park area at the bottom of the Wrekin, simply head up the hill and follow the path.
The cache is a standard lunchbox cache with a smaller box inside (weatherproofing a speciality !). It contains the usual log book and trinkets, with a special place in the book for FTF, STF and TFT.
Happy caching !
Tony Sam & Ben
Additional Hints
(Decrypt)
Jvguva n fnja gerr fghzc.
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