Despite my earlier post, there is a 6029 consecutive integer covering set with primes <= 1669. The n is

here. Can someone please verify that each integer in the range n, n+6028 has a prime factor <= 1669? I checked it myself once I found it but just want the verification of others too. Thanks.

(Also the modular congruence found

here may be helpful.)

Edit: I think less primes could be used for this range, I just didn't sort out the congruence to the EXACT level. All improvements, corrections, and suggestions on this record are welcome.