Quote:
Originally Posted by robert44444uk
I'm wondering if the following is known, and if not, how to compute this quickly:
The minimum number of primes that are needed in a covering set that provide factors for every member of a integer range of 2310.

I have been exploring this a bit.
The primes to 739 produce a covering set over an integer range of 2310, as provided with the following range  (given as a pfgw file)
Code:
ABC2 739#851000256349765889295008041950222651166966896546372185059613326227806525122640671296401722521283286251647678570118376450038403980595559317197227223782617485823807110377855506648118651780073056285228902161980363975551530425485856513116025177545445198982939525456348688416730243149519392436370957298448398900$a
a: from 0 to 2309
This is almost certainly not the smallest range of 2310 where all integers are composite and all have factors of 739 or smaller.
Can anyone do better?