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.)
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| 269 Rexdale Blvd., this morning (after seeing my endodontist) |
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| Original combo, unoriginal price: $10.84 |
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.
Some three months ago, I suggested on Mathematica Stack Exchange that there are 39542 Leyland numbers with exactly one million decimal digits. On my earlier-this-month blog post, I pointed out that I had created a dictionary of 39556982 Leyland-number (x,y) pairs in order of increasing magnitude, starting with the smallest 1000000-digit L(999999,10). The Leyland number L(x,y) = x^y + y^x, x ≥ y > 1. It's easy to cull from this list the first 39542 entries and I present them now here. The final L(190793,174294) is the entry just prior the appearance of the 1000001-digit L(1000000,10).
At the end of my February 21 blog post I suggested that I might to try to find (starting in May) a Leyland prime with one million (or more) decimal digits. I am now in a position to assess what this would entail.
Specifically, I would try to see if there are any (probable) primes with 1000000 or more, but fewer than 1000100, digits. There are 3954322 Leyland numbers in this range but by sieving out ones that are divisible by small primes — say, up to 10^11 — only about 61000 should remain. The sieving can be done in three weeks and only then would I start the search. Each remaining candidate needs about five hours to decide if it was composite, which comes to 35 years overall but, fortunately, I can distribute this across 72 Mac-mini cores, so six months. I will likely add some cores to the job but still, five months!
Considering that I have now spent the last ten months charting 300000-digit Leyland primes, it seems doable. There's a possibility that there are no primes in my working range, in which case I would have to commit to the next-larger range. And so on.
I have created a dictionary of Leyland (x,y) pairs from (999999,10) to (1000999,10), sorted by magnitude and preceded by its Leyland-number index (21588818851 to 21628375832). The text file is more than a gigabyte so I don't see much utility in linking to it. Here is a much abridged version showing the initial-, middle-, and final-100 entries:
I was somewhat taken by this beautiful dappling on an apple skin. I wonder what caused it.
Taken on my Bodie walk early Tuesday morning, these are not the sort of tracks I am used to seeing in the snow at the side of the road. The river is not that far away so perhaps a heron or egret, I will guess. The Old/Middle French pie de grue is the origin of the word pedigree and the tracks naturally reminded me of the fact.
Update: It appears Laurie Mace, who lives on this stretch of road, had captured a photo of the culprit:
@metromorning an attempted break in across the street from us a few weeks ago. pic.twitter.com/N2gQSk6prN
— Denison Denizen (@LaurieMace) March 21, 2022
Six years ago I made Bell my internet provider. Bell's Fibe 25 service was then priced at $66 per month plus $10 for an unlimited usage promo. In my current bill, those prices were $92 plus $12.50. Mind, the Fibe 25 ran closer to 30 Mbps download (10 Mbps upload) after some supposedly-no-cost upgrade some time ago. I forget the details. At any rate, this was more than sufficient to service not only my internet needs but also Bell's television service to which I am also subscribed.
When I accessed my Bell bill I noticed that faster speeds were readily available. The Fibe 50 plan with unlimited usage built in was $100 per month. Wait, that's less than what I was paying now! A Fibe 150 plan was $105 per month, 50 cents more than what I was paying! So I decided to upgrade to the Fibe 150, which was installed yesterday. The installation required an optic cable to replace the copper one that was installed here only in January.
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| Justin, technician, prepares the new optic cable |
The new cabling didn't just end at the house. It entered the house and reached a new hub that sits on my desk. It even has a 10 Gigabit ethernet port if I wanted to connect it to a new computer that had the capability (none of my current computers do). A speed test suggests that I now get 185 Mbps download and over 160 Mbps upload. I doubt that either of those numbers will improve my life significantly, but what can one reasonably expect for 50 cents? The new hub needed to be paired with our TV receiver units in addition to our home phone. Unfortunately, the latter pairing somehow broke our home phone services: call display no longer worked and we were unable to access Bell's voicemail. I spent several hours today trying to assess the nature of the problem and have Bell fix it. Even after that, the indicator light for new (voicemail) messages was inoperative and this required yet another call to Bell.
Anyways, that's done and I can now concentrate on worrying about why we have not yet received our CPP and OAS T4As. I can't do our taxes without them!
I like to keep our grocery deliveries down to one-a-month which makes it difficult if ever they are out of something (or my personal shopper can't find it). One obvious remedy is to hoard more than a month's worth of staples so that out-of-stock items don't impact the unchanging (and somewhat inflexible) daily menu. Of course one can't really do that with milk and yogurt. Last summer I compensated by walking over to the nearby FreshCo for replacements. With the recent uptick in snow and Omicron, I perceived such a venture as too challenging. So last month I tried a second order, but from a different grocery delivery service. Even that was not able to procure me those big boxes of Bran Buds, so I resorted to asking Amazon for five of them (back on January 27). It was never going to be a fast delivery because (I think) they had to wait on Kellogg's but I still had a couple of big boxes and a couple of small ones on hand, so no problem. Then the Ambassador Bridge blockade made me worry a bit about it. The order arrived today! In the above photograph they are on the second shelf from the top.
This is a screen grab of today's probable-prime top-discoverers leaderboard that updates the one I posted on 7 May 2021. My production score now places me at #14. I am unlikely any time soon (if ever) to reach #13 and there is ample opportunity to be displaced downward by other people's efforts.* Of the 1584 PRPs noted, 1532 are Leyland primes. I reached my 1500th Leyland prime on 9 September 2021.
My worksheet (above) shows, at the bottom, the 74 cores currently working on Leyland interval L(302999,10) to L(303999,10) in which I have found so far 11 Leyland primes. It should be done in early March. After this I will do interval L(303999,10) to L(304999,10), taking me into May. This will then complete my attempt to find all Leyland primes in the interval L(299999,10) to L(304999,10). My thinking for what comes next has changed somewhat since the recent finds by the Levai brothers of five Leyland primes larger than 500000 decimal digits (at the bottom, here). I may to try to find a Leyland prime with one million (or more) decimal digits.
* Update (28 February 2022): Only one week later and I am again at #15 as Anonymous moved from #18 to #9.
An 80-year-old woman crossing the street died after being struck by an 80-year-old woman driving a Honda. Strikes me as a starting point for a science-fiction story or revenge drama.
As we entered the current calendar year, James Propp (in a math-fun forum) noted a Dan McQuillan tweet on the embedding of the integer 2022 in its base-three representation:
2202220
The property is not the sole domain of 2022, but rather of a sequence of such integers wherein 2022 is the sixteenth term. James wanted to find out if this sequence was infinite. His argument had it that for length-d integers there should be slightly more than d solutions. Actual number of solutions for d up to 26 are:
3, 3, 6, 4, 4, 0, 0, 3, 3, 10, 0, 15, 14, 20, 8, 13, 20, 25, 9, 21, 14, 20, 23, 17, 8, 18.
That's 281 solutions altogether, thus far. Here are the last 18 (26-digit) solutions:
[last updated 28 March 2022]
Every few years I manage to discover something previously unknown in my genealogical meandering. Recently it was the children of Wilhelmine Elisabeth Havermann Rademacher on an Ancestry website. Note that the site incorrectly positions her among the children. Elisabeth (known as Sette) was a sister of my grandfather Friedrich (known as Fritz) Havermann (1869-1945).
Sette's children are welcome additions to my personal "Havermann" family tree. There was another piece of information on that Ancestry website: Elisabeth's death date is given as 17.05.1943, supposedly in Arnsberg. A search for that specific date yields a number of hits related to Operation Chastise, wherein the dam at the Möhne reservoir was destroyed. Many of the deaths from the resulting flood occurred in Neheim (which, since 1975, is a part of Arnsberg). Neheim is not only where I was born, but also (I believe) the hometown of my grandaunt Elisabeth Rademacher. If Sette was a casualty of that flooding, this was not something of which I had been previously aware. Mind, prior to my father's death, his aunts and uncles (and their offspring) generally were not something of which I recall being really conscious. If he had ever talked about any of them, it failed to make a sufficient impression on me (i.e., that they were his relatives).
My research associate, Marlene Frost, has Ancestry access and was able to dig up the 1928 and 1936/37 address directories for Neheim showing that Elizabeth and some of her children lived at Möhnestraße 11, not far from the Möhne river (downstream from the reservoir). The Möhne joins the Ruhr in Neheim. Sette's death informant, instead of providing particulars, had simply made a reference to the Möhnekatastrophe, hence the date.
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| Möhnetalsperre 17 May 1943 (Fotarchiv Ruhrverband) |
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| 47.7º N, 117.5º W, approximation error box (in magenta), click to enlarge |
Local calls appeared to be getting through on our home-phone landline but not long-distance calls, as evidenced by a handful of instances over the course of a month. I was certain that the problem lay in some distant Bell relay device and that the technician likely wouldn't have to come into the house. I was wrong.
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| Ekene, technician, connecting a new cable to a nearby Bell hub |
