[seqfan] Left-Truncatable Primes
Hans Havermann
pxp at rogers.com
Wed Aug 17 04:21:30 CEST 2011
I've continued to explore A076623, A103463, and A103443, in various
bases, ever since I first noted, back in May, that the base-14 entry
for A103443 was incorrect. Today, I finally reproduced Martin Fuller's
2008 base-24 number for A076623 after a ten-day compute on my wife's
much-newer computer: It would have taken four times as long on my old
machine! I've collated my current results into a single file here:
http://chesswanks.com/num/LTPs/LTPs.txt
This could conceivably be used as a link to replace the current OEIS
in-house a-files for all three sequences. (I intend to add a few more
bases in the coming months.) I just noticed that Neil's June 2
correction of the a-file for A103443 (as per the attribution) did not
in fact correct the base-14 entry, which is still wrong, but created a
second error by replacing a base-24 question mark with the correct
entry for base-14.
For a more graphical approach to the sequences, I'll point the
interested reader to my "number of left-truncatable primes by digit
length" page, which illustrates all bases up to 120, here:
http://chesswanks.com/num/LTPs/
Finally, a challenge... It is unlikely (at least in my lifetime) that
the numbers for base 30 will ever be computed. The expected number of
digits in the largest base-30 left-truncatable prime is around 82.
Here's a 49-digit attempt at a large example that I grew through
random accretion:
{26, 27, 16, 17, 12, 26, 29, 19, 17, 5, 20, 18, 1, 26, 12, 12, 6, 18,
15, 19, 7, 26, 29, 5, 24, 23, 23, 14, 13, 28, 7, 3, 8, 28, 22, 25, 21,
25, 23, 13, 25, 15, 15, 8, 12, 19, 1, 25, 19} =
2147186882499459649456828050886961756168069394758485971705532390689634669
Can anyone do better?
More information about the SeqFan
mailing list