k's with consecutive small primes
I did some testing on k's with consecutive small primes, i.e. k's that have primes from n=1 thru 6, 1 thru 7, 18, etc. up to k=100M. Some of the k's that I found may be excellent candidates for people to search further so I'm listing them here. The ones that are prime for n=1 thru 7 and higher are listed below and I'm attaching a list of the k's that are prime for n=1 thru 6.
Up to k=100M, the following k's are prime for:
n=1 thru 9
42932385
n=1 thru 8
26277285
n=1 thru 7
1082115
1164735
5128905
5154945
7015155
12088065
14421825
18544365
31400085
44087025
47915595
52694085
60627945
69070365
91780965
94708605
95082405
The biggest surprise out of all of this that I found was that k=45 is the only k < 26K that is prime for n=15 and is the only k < 200K that is prime for n=16!! :surprised
If anyone knows the lowest k that is prime for n=110 or would like to do some testing to find it, I'd be interested in seeing the results. I think you'd probably have to test up to k=1G. I was lucky to find one that was prime for n=19 out of only 2 candidates that were prime for n=18.
Gary
