Glad Hobo Express
Sunday, September 03, 2023
Thursday, August 10, 2023
A million-digit Leyland prime (encore)
Tuesday, August 08, 2023
833719/265381
Based on the simple continued fraction of π, its convergents (rational approximations) are: 3/1, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, 208341/66317, 312689/99532, 833719/265381, 1146408/364913, ...
Prime numerators are at position 1, 5, 9, ... Prime denominators are at position 2, 4, 9, ... The ninth convergent therefore has both prime numerator and prime denominator, noted ~2003 in the OEIS. It seems unlikely that we will ever see another such.
I thought it might be useful to have here a listing of the positions of prime numerators (p/) and prime denominators (/p) so as to better assess the rarity of their confluence:
1/
/2
/4
5/
9/
/9
11/
16/
/33
87/
230/
334/
594/
/595
840/
853/
/1127
1149/
/2003
2726/
/3611
3788/
/4356
/6926
7442/
8751/
/25333
/27652
/32395
/37722
42038/
/114199
143753/
...
Thursday, July 20, 2023
A million-digit Leyland prime (I got lucky)
Back in April, I wished myself "better luck" in my current million-digit Leyland prime search. I've won that lottery, so to speak:
191319^170462+1*170462^191319 is 3-PRP!
The number has 1000910 decimal digits. The current top-five Leyland prime leaderboard now looks like this (the first column is the number of digits):
1717671 (1343238,19) Ryan Propper May 2023
1433792 (300102,59935) Ryan Propper May 2023
1268947 (1139148,13) Ryan Propper Jul 2023
1000910 (191319,170462) Hans Havermann Jul 2023
1000175 (218767,37314) Gabor Levai Mar 2023
Monday, July 10, 2023
Trouble above
Saturday, July 08, 2023
Thursday, July 06, 2023
Goodbye landline
My brand new iPhone 13 arrived yesterday. I wasted little time in trudging up to Freedom Mobile (1924 Weston Rd.) in the heat — twice (I didn't bring any identification the first time)! So now I have a cellphone number. This meant that I could lose the "home" phone which I had been using only as a two-factor authentication device. When I called Bell, they dragged out the cancellation process and finally offered me the landline (I'm paying $60 per month) for something closer to $10 per month (if I heard correctly). "Just cancel the fucking phone," I blurted out uncharacteristically.
Wednesday, June 14, 2023
Monday, May 29, 2023
Little free library
Ross and Laurie (beside Denison Park at Lippincott) have set up this very nice "little free library" box in a corner of their place. I should be able to donate a few books from my own mostly-reference library. Not everyone thinks that these things are a good idea.
Friday, May 19, 2023
Agent orange
This late-evening marauder comes as close to being "orange" (especially in the tail) as one might deem possible. Close inspection suggests that the effect might just be a whitened mixture of "brown". A search finds that the descriptive word for it is "erythrism". This particular raccoon paced our back- and side-yards for a half-hour or so before finally climbing the fence into a neighbour's yard. This included ventures onto the back deck and peering into the kitchen door. When I went out in order to scare it away, it was somewhat unconcerned by my approach — perhaps even attracted to it — as though it was tame. This leads me to suppose that it might be suffering from distemper.