Two things conspired to create this math puzzle: I spotted a hiding place with such beautiful coordinates that I had to do something with it; and just after that a cacher told me that they wish to see more Uilebheist math puzzles: be careful what you wish for! This puzzle is all about prime numbers and the difficulty could be anything between 3 and 5 depending on whether you see how to do it or not: so I compromise and call it 4.
A prime number (or simply a "prime") is a natural number greater than 1 that has no positive divisors other than 1 and itself. So for example 5 is a prime number, but 15 isn't (it can be divided by 3 and 5).
Cache is at:
North AB°CD.EFG
West HJK°LM.NPQ
and the (straight line) distance from the above coordinates is RST metres or URST feet (note: three different GPSs gave me three slightly different values for the distance between the above coordinates and the final location's waypoint, and they can't be all right: so consider RST and URST an approximation).
Each of the following numbers is a prime: ABCDEFG, E, EFG, HJK, LM, P, Q, NP, NPQ, HJKLMNPQ, ABCDEFGHJKLMNPQ, S, RS, RST, URST.
Each of the following numbers is the square of a prime: R, T.
F is the cube of a prime and FG is the fourth power of a prime.
Each of the following numbers is the product of two (distinct) primes: AB, CD, N, ST.
That's a lot of primes all in the same set of coordinates, so you can see how I just couldn't resist!
You don't need to look at the distance (RST or URST) at all as long as you have a reasonable guess about where the cache must be ("In Edinburgh" would be a good enough guess, but I'm sure you can do better!). I checked all possible values of A to Q which correspond to coordinates within 20 miles (32 kilometres) of the above coordinates, and there was only one possible value matching the requirements, and this even without calculating RST or URST... so all you need to do is to find this solution! And you already know you don't need to search a 32 kilometre radius, as RST can be at most 999 metres.
Finding the solution may be easier than you think... you should be able to figure out the values of AB, HJK and LM immediately. And the other numbers? Well, that's enough hints from me.
If in doubt, feel free to email me to check your calculations, tell me what you've done and I'll let you know if you are on the right track. You can also validate your puzzle solution with certitude but of course that'll only say "yes" or "no" and won't be able to answer questions.
If arriving by public transport, use bus number LM (naturally, a prime!) to the above coordinates, or bus number Q (of course, another prime) to Ferry Road; if a prime bus is not your thing, two multiples of Q (E * Q and K * Q) also get you to Ferry Road.
Wheelchairs and strollers can get to within Q metres of the cache using a tarmac path if they start from North AB°CD.GKG, West HJK°LM.PLM or from North AB°CD.EDF, West HJK°LM.RNC; however wheelchair users will need assistance to retrieve the container.
Cache meets the GAGB Urban Placement guidelines.
Congratulations to tele420 on being first to find (again!). They must be starting a collection of these FTF tags.