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Old 2007-07-27, 17:35   #1
gd_barnes
 
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May 2007
Kansas; USA

5·2,111 Posts
Default 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, 1-8, 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=1-5 and is the only k < 200K that is prime for n=1-6!! :surprised

If anyone knows the lowest k that is prime for n=1-10 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=1-9 out of only 2 candidates that were prime for n=1-8.


Gary
Attached Files
File Type: txt cons-small-prime-1-6.txt (1.4 KB, 229 views)
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