[QUOTE=R.D. Silverman;111888]Look up Dickman's function. See Knuth Vol. 2[/QUOTE]
Brian Murphy's disstertation on NFS polynomials also contains a large section on Dickman's function, and he uses it to estimate the number of NFS relations with large primes

David Broadhurst has found 8 consecutive completely factored 509-digit numbers (no primes). He used another approach with much harder factorizations: [url]http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm#factorizations[/url]

David Broadhurst has now found astonishing 10 509-digit numbers!

The Largest Consecutive Factorizations record page is now at [url]http://users.cybercity.dk/~dsl522332/math/consecutive_factorizations.htm[/url]
In the last month David Broadhurst found [URL="http://tech.groups.yahoo.com/group/primeform/message/9871"]11 515-digit numbers[/URL] and then [URL="http://tech.groups.yahoo.com/group/primeform/message/9882"]12 521-digit numbers[/URL]. Today Joe Crump and John Michael Crump announced [URL="http://tech.groups.yahoo.com/group/primeform/message/9938"]13 500-digit numbers[/URL].
Selected polynomials are used to get many algebraic factorizations.