factoring

Prime factor of 300 000 000 000?

I need to find out the prime factors of over 300 billion. I have a function that is adding to the list of them...very slowly! It has been running for about an hour now and i think its got a fair distance to go still. Am i doing it completly wrong or is this expected?! (Please no solutions for my code to give it away, but some subtle hi...

How does being able to factor large numbers determine the security of popular encryption algorithms?

How is the an encryption algorithm's security dependent on factoring large numbers? For example, I've read on some math-programming forums that by using the Quadratic Sieve or the General Number Field Sieve, one can factor a 256 bit number with relative ease on commercially available hardware. How does this translate to being able to b...

How can I factor out repeated expressions in an SQL Query? Column aliases don't seem to be the ticket...

So, I've got a query that looks something like this: SELECT id, DATE_FORMAT(CONVERT_TZ(callTime,'+0:00','-7:00'),'%b %d %Y') as callDate, DATE_FORMAT(CONVERT_TZ(callTime,'+0:00','-7:00'),'%H:%i') as callTimeOfDay, SEC_TO_TIME(callLength) as callLength FROM cs_calldata WHERE customerCode='999999-abc-blahblahblah' AND ...