Examples of Advanced Description Searches
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  Below we give many of the advanced search options available with the two fields description and comment.  The example I give are all aimed at the description field, but apply to either.  The key thing to note is that matches need only match part of the string--so a search using just 2 in the description field will match a prime with a 2 anywhere in its description.
An expression may begin with the word NOT (uppercase) to negate a search
Example:  NOT [2345] will match the primes without the digits 2, 3, 4 or 5 in their descriptions
Example:  NOT .^ will match primes without the exponentiation operator

An expression may contain the word OR (uppercase) to allow a boolean search
Example:  3^ OR 5^ will match the primes like Phi(3,-163195^8192) and 343372*3^178255-1
Example:  2^ OR 3^ OR 5^ will return mostly primes like 3*2^478785+1 (which greatly outnumber the previous types)

An expression may begin with the character ^ (carat) which will only match at the beginning of the prime description.  (Using ^ anywhere else in the description field will simply match the exponentiation operator.)
Example:  ^2 will match prime descriptions that begin with the digit 2.
Example:  .^2 will match prime descriptions that have an exponent that begins with the digit 2.

An expression may end with the character $ (dollar sign) which will only match at the end of the prime description. 
Example:  2$ will match prime descriptions that end with the digit 2.
Example:  $2 can not match any prime (how can 2 occur after the end?)

The character . (period) will match any single character
Example:  (..) will match primes with two characters in a pair of parenthesis (e.g., 43013#*R(23)^11+1)
Example:  .. will match everything on the list (as there are no one-character descriptions)
Example:  ^......$ will match every description with exactly six-characters.
Example:  ^.?3 will match description whose first or second character is 3.  (The couplet .? matches any 0 or 1 characters).

The character % (percent sign) will match any (0 or more) characters.
Example:  ^2%1$ will match descriptions beginning with the digit 2 and ending with the digit 1 (with anything else in between)
Example:  % will match everything on the list.
Many, GRE constructs will work.  The fact that +, *, ( and ) are quoted (to make searching for algebraic expressions easy) eliminates many, but you can get around this by being creative and using the fact MySQL represents many GRE expressions using [, ], {, }, >, < and :
Example: ^[123]{3,}[[:digit:]]{3,}* will match those beginning with at least three digits from the set {1,2,3} followed by at least three more digits (0 through 9).
Example: ^[[:alpha:]]{1,2}( will match those beginning with one or two letters followed by a parenthesis.
Internally % is translated to the GRE '.*'.