[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:


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:


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} =  

Can anyone do better?

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