Wednesday, August 31

Spoonful

David 'Honeyboy' Edwards died on Monday, so yesterday I listened to a bit of what I had of his in iTunes (mostly the Delta Bluesman album). One of the songs was Just a Spoonful, which brought me to list all of the 'Spoonful' covers that I had: about a dozen. Cream's short six-and-a-half-minute version from Fresh Cream played next and I was reminded that they had a long version on their Wheels of Fire double-album which, back in the day, I once owned. But the album was missing from my iTunes library, so I downloaded it — and am listening to it today. Catherine actually brought into our relationship the Fresh Cream album (along with The Incredible String Band's Wee Tam & The Big Huge), acquired back then from Kay Owen, her British cousin. Much appreciated music, even after all these years.

Tuesday, August 16

The largest base-24 left-truncatable prime

10594160686143126162708955915379656211582267119948391137176997290182218433

As previously aspired to, I have now replicated Martin Fuller's 2008 determination of all base-24 left-truncatable primes. I don't know if Martin thought to store the largest of these as part of his program, but I don't see it anywhere on the Net and more specifically not in the a-file for A103443, where it belongs. It's the 53-digit number {17, 22, 19, 14, 19, 15, 10, 3, 10, 7, 1, 13, 18, 13, 9, 22, 15, 22, 23, 15, 14, 3, 13, 3, 20, 19, 17, 10, 6, 1, 20, 17, 9, 2, 18, 15, 12, 10, 3, 21, 11, 8, 16, 15, 4, 4, 4, 15, 11, 11, 7, 10, 17}.

Bookends

Back on May 7, I created a 9 times 48969-digits-each, type-2 Belgian-numbers html-file to elegantly display solutions to Eric Angelini's second type of Self Belgian Numbers. On May 17, I published a list of thirteen type-2 Belgian primes plus six more probable primes, the largest composed of 27867 digits. By May 24, I had determined for what number-length (after length 1) all nine type-2 Belgian-number templates again produced solutions: length 1899283.

All that needed to be done now was to find all solutions to length 1899283 so that these might be as elegantly displayed as my initial length-48969 set. The calculation took about a week for each of the nine templates and, on July 31, I html-colourized the result. Only problem was, the numbers would not display properly in any of the browsers that I tried. The far-right digits did not align, even though all nine numbers have the same number of digits and they are rendered in a monospace font.

Thankfully, Firefox 6 has just been released and it did display the numbers correctly! The length-1899283 solutions turned out to be terms 3594728-3594736 of A107070 and because these nine solutions along with the first nine solutions form "bookends" to all the other solutions within the nine templates, that's what I ended up naming the over-80-MB file.