... however (and this is a really dumb question), the block that has to be a factor of the origin of the prime, we just convert the hex of the previous block (so say we are trying to mine block 54320, we would convert the hex of block 54319 to decimal, correct?)
The nice thing about using bignums is that you don't have to convert them to decimal - since the internal representation of bignums is in a base of a power of 2 (usually the "digit" size of bignums is 1 or 2 bytes), and the hash is already in that format, we don't have to convert it to decimal. Unless you want a human-readable representation, the number is stored as raw bytes.e.g. If the prevhash is 0x000...0053, it is internally represented as {0x00, 0x00, ..., 0x53} (or in the opposite order). We can then use this to construct a bignum without converting it into its decimal representation 83.
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Oh, and another dumb question... What does '≡' mean? 
'≡' means "congruent". In this case it refers to modular congruence - if x ≡ y (mod z), it means that they both have the same remainder mod z. E.g. 3^4 ≡ 1 (mod 5) because 3^4=81 and 1 have the same remainder (1) mod 5.