What's a heaven for?

The west-wall, floor-to-ceiling bookshelf in my room is compartmentalized into 62 sections, of which 59 are used for books. The picture is a composite of three of those sections. The upper shown section is on the left side of the bookshelf, one down from the top; the bottom two, horizontally adjacent at the top-right corner of the shelf. Most of these books are from Springer and were purchased in the book-buying mania of my 1980s (give or take).

Five of the books in the middle shown section are Berger's Geometry I and II, Weil's Basic Number Theory, Armstrong's Groups and Symmetry, and Gelbaum & Olmsted's Theorems and Counterexamples in Mathematics. They are all pretty much beyond my grasp and I was fortunate enough yesterday to be allowed to ship them to a mathematician who might actually benefit from their content.

A million-digit Leyland prime (reality check)

Having previously decided that finding a million-digit Leyland prime was doable and subsequently committing to a search thereof, it is time for a reality check.

The notion that I could scan the Leyland interval from L(999999,10) to L(1000099,10) by the end of September was predicated on an estimate of about 5 hours examination time per candidate (of some 59500 candidates). It turns out that the running time on my nine oldest Mac minis is closer to 11.5 hours and, for reasons I don't comprehend, three newer Mac minis are running at 18.5 hours per candidate. My 2020 iMacs, which I had assumed would be the most productive, still need 11 hours on my main machine (7 processes) and almost 15 hours on my helper machine (8 processes). I'm well into 2023 at this rate!

Early this morning Gabor Levai noted that he had discovered a 1000027-digit Leyland prime. Of my 108 running processes, this will have been found in about four months (by process #23 that happens to reside on one of the slower Mac minis). Disheartening, to say the least.

Aerial lies

my neighbourhood, looking toward downtown Toronto

The blue arrow at bottom-left points to a lot that seemed to me unfamiliar, as it is the location of what I had always considered a shallow pit waiting on the construction of a nine-storey building (1681 Weston Road). I most certainly was not conscious of a circular path therein. The drone image (taken by a realtor for an area house) appears filtered for effect and my inclination was to think that the lot might have been photoshopped. But I was wrong. I went there to take this over-the-fence photograph:

path in the metre-deep pit at 1681 Weston Road

Thirty

I turned on the air conditioning yesterday. In spite of that, my room registers at 30º — significantly above the ambient air temperature outside — because there are sixteen computers herein generating heat, 24/7, and there is insufficient air flow from the vents to make much of a difference. The living room is a little better (the ceiling fan helps) but even Bodie has taken to lying on the floor instead of his chair or the bed/couch. I expect that it will be like this most of the summer!

Goslings

My daughter dropped by today with some rescued goslings, wondering if I'd seen at the river any families that might be adoption candidates. Of course I hardly ever see the river these days since my Bodie walks are pre-dawn. I pointed out that historically there had always been such families above the weir in Raymore Park and she proceeded thereto and did in fact find such a family.

Bucket list

1. Wiener schnitzel (The Coffee Mill closed in 2014; Amber closed in 2021.)

2. China Town (Their online ordering system stopped working a few years ago.)

3. KFC (It's a bucket list! Like Domino's Pizza, I've been unable to generate a delivery.)

4. Tim Hortons (I know. How can something so ubiquitous be so difficult to reach.)

5. Harvey's (Overly motivated by a languishing old Ultimate Dining card.)

269 Rexdale Blvd., this morning (after seeing my endodontist)

Original combo, unoriginal price: $10.84

Ovenbird

There's a pair of robins that have been making daily forages around our backyard since at least mid-April, so it made for a pleasant change to see yesterday this ovenbird checking out a small corner-section of the venue.

The new high-rise

Prominent now on my morning walks home from Denison Park is "The Humber", an under-construction condominium at 10 Wilby Crescent — which any reasonably observant map enthusiast will decry as being more properly situated on Hickory Tree Road. The sad reality is that the latter has never properly connected Bellevue Crescent to Wilby, being instead a gated roadway to a couple of other high-rises with access only from the Bellevue side. The yellow structure in the below map outlines the building that used to be #10 (also street-view visible by rotating Google's 2015 no-access part of the road; also the location of my 2020 "breakout" blog):

Even though it still a handful of storeys short of its final height, the new condominium can already be seen from my home:

A million-digit Leyland prime (search start)

Last month I laid out a prognosis for setting up a million-digit Leyland prime search. That endeavour has now started its run!

I sieved my L(999999,10) - L(1000099,10) candidates to 2*10^11 resulting in a 59536-term file. Running the sieve from 10^11 to 2*10^11 was not really necessary. The 12.5 days that it took (on a 10-core machine) netted 1632 composites but a direct primality test would have netted ~50 composites per core in the same amount of time and, at 100 cores, would have resulted in three times the yield. At any rate, the effort was not wasted since nine of my Mac minis are still working on their previous project and are therefore not yet search-ready.

I have now initialized 54 cores on nine different computers to begin the search. In a week I will have added the 54 cores on those nine Mac minis finishing their assignments. So 108 cores on eighteen computers dedicated to the task! I am hoping for completion some time in September. Of course, prime finds (should I be so lucky) could happen at any time.