Sunday, March 27, 2016

Shiver in ecstasy


Cliff Pickover's voluminous twitter feed includes entries introduced with "shiver in ecstasy". This one is from last Friday. The hard part in verifying the claim is counting the nines. I see an eight with 252 nines in front and 253 nines behind, so 10^506-10^253-1. It's not quite a palindrome and it really isn't that large, but we can (courtesy of Darren Bedwell) fix that:

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Monday, March 21, 2016

Humber river erosion control


Work is progressing towards the building of a makeshift bridge across the river so that the current armourstone toe of the valley slope on my side (to the left in this looking-south photo) of the Humber river may be replaced with a better (presumably higher) version. The intention is to provide improved erosion control for a few properties at the top of the slope (on Sykes Avenue and Denison Road West). Roy Murray reports on the construction from his other-side-of-the-river (Raymore Park) vantage (March 16, March 23).

Tuesday, March 08, 2016

I get by with a little help

I have diverted some of my Leyland-prime-indexing processes in order to accelerate my smallest-primes-containing-a-certain-number-of-zeros compilation. Robert G. Wilson v had taken an interest in the latter and I thought to inform him of the imminent speed-up. I wrote: "I have now distributed the task." He replied: "Nice to have friends!"


A photo of my late-2012 main machine (display on) and its "friends", a late-2013 Mac Pro (behind), a late-2014 iMac (immediately left), and a late-2015 iMac (far left).

Saturday, February 20, 2016

The smallest primes containing a certain number of zeros

For example, what is the smallest prime containing exactly 10000 zeros? It is 10^10002 + 7*10^164 + 9. Robert Israel provided the procedure with which I am currently calculating the sequence for a large number of values. We'll see how far I get.

Saturday, January 23, 2016

Indexing the Leyland primes, reprise

When I wrote Indexing the Leyland primes last May, I suggested that (of the then-known Leyland primes) "the smallest 954 (or slighly more) are indexable". Letting a Leyland number L(x,y) = x^y+y^x, x≥y, and [excepting L(2,1)] y>1. Two and a half weeks ago, I found that L(12876,2447) was prime and that this wasn't a known Leyland prime. As a result of having now examined all 75545875 smaller Leyland numbers, I can say that 955 of the then-known Leyland primes were in fact indexable!

I had made a bit of a fuss over the three Leyland primes I discovered last October. So far this month, chronologically after L(12876,2447), I found L(13307,3442), L(13227,2200), L(13371,3068), and L(13051,2448). It seems that I'm picking low-hanging, perhaps mistakenly ignored fruit. Norbert Schneider is also looking for Leyland primes not far from where I'm currently searching, so I have competition! Regardless, I will continue my effort to close the gaps between known Leyland primes — extending their indices as far as I am able.