The cache is NOT at the listed co-ordinates; they are just the nearby shopping centre!
The foundation of today's internet security is the use of encryption systems developed in the 1970s. The first practical version of ‘public key cryptography’ was developed in 1977 and published in 1978 by Ron Rivest, Adi Shamir and Len Adleman from MIT. This subsequently became the ‘RSA’ cryptosystem (from the developers' surnames), and is now the standard used in all browsers for the SSL and TLS protocols.
These communication standards form the basis of the https protocol for secure websites (as used for internet banking, shopping etc) and exchange the cipher key to be used for subsequent data exchange using this public key encryption system. The security is mainly dependent on the difficulty of determining the factors of very large integers created by multiplying together two large prime numbers to create the algorithm key. The current standard for the size of these (asymmetric) keys is 1024 or 2048 bits i.e. 21024 or 22048. Once the main cipher key exchange is complete the data transfer under https is undertaken using a much faster symmetric cryptosystem (such as AES or Advanced Encryption Standard) which requires only 128-bit key length for equivalent security.
Current factorisation algorithms work well for smaller numbers such as the one below, but no one has developed a fast enough process for very large numbers to endanger the security of cryptography. RSA Security set a series of factoring challenges with significant prizes to monitor developments in this area, but these were withdrawn in 2007. The largest of these numbers that has been factored is RSA-768, a 232 decimal digit number. Factorisation was completed on December 12, 2009.
With this geocache puzzle, you have to find a way to factor a relatively small integer (at 46-bit equivalent it is tiny in cryptography terms, anyway). An internet search should provide a few options, or perhaps you could tackle it yourself with a bit of thought and a small amount of programming?
Find the cache in this prime position by determining the two prime factors of:
64,460,243,458,613
With decimal points in the appropriate places, these 2 prime numbers give the latitude and longitude (with decimal degrees) of the cache location.
The cache is a 500ml screw-top container with some swap items and a log book.
GZ hint: This song (mp3,midi) released the year after RSA cryptography was published.