Catherine is charging up the car's battery (by driving around for a half hour at this pre-dawn stretch of time on a Saturday morning). It's still a little too early for my walk with Bodie so I check with Find-My-Friends to see when she might arrive back. Bodie (who suffers from separation anxiety) has no such recourse and stares out the window (as he has done since she left) for a sign of her return.
The Johnny Strides video offering this morning had me reliving my daily trips to and from The Beer Store on St Clair Ave. W. by Lauder Ave. (currently the Fox & Fiddle pub), both before and after 2003 in which year I purchased my first DSLR camera — a Nikon "Coolpix" 5700. Unfortunately, Johnny stops walking at Northcliffe Blvd., a block short of where the store used to be.
By an uncanny coincidence, he boards a streetcar heading west, just as I did back in early-May 2003 at the same intersection — although I'm fairly certain the old stop was on the other side of Northcliffe. I had been trying out the Coolpix's one-minute video recording feature on that and the previous day (documenting some aspects of the Beer Store workplace) and I took another one boarding the streetcar on my way home after work. The recording is very poor in resolution and violently jerky, as I had the camera hung around my neck so as not to alert the streetcar passengers to the capture. The rustling is my plastic bag in which I carried my personal effects.
The photo shows four recently acquired Mac minis that were meant to complement my previously-existing Leyland prime search farm. The "silver" one is the new M1 Mac mini and I did not find it suitable for the task, so it is not part of the farm. The other three are Intel and add 18 cores to the previous 54, for a total of 72 cores. This will help with my current work on interval #18 which is checking for the probable primality of 1087659 terms ranging in size from 111532 to 121787 decimal digits. My updated-in-real-time search results are posted on my indexing the Leyland primes document.
This evening I found my 1000th Leyland prime. My 500th was only ten months ago! The above chart extends the graph that I posted back then. I have 579 red values found using Mathematica (from 3 October 2015 to 3 July 2020), followed by 421 blue values found using xyyxsieve & pfgw64 (from 6 July 2020 on). I have it in mind that I might actually achieve 1500 finds by later this year. It's a tough target to reach because I'll be picking all the remaining low-hanging fruit (< 150000 decimal digits) in the ongoing search and I don't believe that there are quite 500 of those left.
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| SWAT team entering a house across the street at 4:30 pm |
Happy New Year! (I did my first one ten years ago. My cheat sheet is good to 2101.)
2*3 = 6 in base 2 is 110: 1~10 = (1,2)
2*3 = 6 in base 4 is 12: 1~2 = (1,2)
3*5 = 15 in base 6 is 23: 2~3 = (2,3)
3*5 = 15 in base 13 is 12: 1~2 = (1,2)
5*7 = 35 in base 2 is 100011: 10~0011 = (2,3)
5*7 = 35 in base 4 is 203: 2~03 = (2,3)
5*7 = 35 in base 16 is 23: 2~3 = (2,3)
23*29 = 667 in base 6 is 3031: 30~31 = (18,19)
43*47 = 2021 in base 10 is 2021: 20~21 = (20,21)
53*59 = 3127 in base 5 is 100002: 1~00002 = (1,2)
59*61 = 3599 in base 2 is 111000001111: 1110~00001111 = (14,15)
59*61 = 3599 in base 4 is 320033: 32~0033 = (14,15)
59*61 = 3599 in base 16 is e0f: e~0f = (14,15)
67*71 = 4757 in base 3 is 20112012: 2011~2012 = (58,59)
67*71 = 4757 in base 9 is 6465: 64~65 = (58,59)
103*107 = 11021 in base 12 is 6465: 64~65 = (76,77)
113*127 = 14351 in base 2 is 11100000001111: 1110~0000001111 = (14,15)
113*127 = 14351 in base 4 is 3200033: 32~00033 = (14,15)
1319*1321 = 1742399 in base 11 is a900aa: a9~00aa = (119,120)
2729*2731 = 7452899 in base 14 is dc00dd: dc~00dd = (194,195)
3359*3361 = 11289599 in base 15 is ed00ee: ed~00ee = (223,224)
3593*3607 = 12959951 in base 3 is 220101102201012: 2201011~02201012 = (1975,1976)
3593*3607 = 12959951 in base 9 is 26342635: 2634~2635 = (1975,1976)
120181*120193 = 14444914933 in base 11 is 6142861429: 61428~61429 = (89691,89692)
189913*189929 = 36069986177 in base 3 is 10110002210001011000222: 1011000221~0001011000222 = (22624,22625)
833363*833377 = 694505556851 in base 13 is 50651050652: 50651~050652 = (143885,143886)
3329233*3329251 = 11083852294483 in base 2 is 10100001010010101001000101000010100101010011: 101000010100101010010~00101000010100101010011 = (1321298,1321299)
4999493*4999507 = 24995000249951 in base 10 is 24995000249951: 249950~00249951 = (249950,249951)
75991159*75991169 = 5774657006074871 in base 5 is 22023343440022023343441: 22023343440~022023343441 = (23652995,23652996)
756395819*756395821 = 572134636513472399 in base 15 is 148e98ed148e98ee: 148e98ed~148e98ee = (223238023,223238024)
5368703993*5368704007 = 28822982639615999951 in base 2 is 11000111111111111110011100000000000000001100011111111111111001111: 1100011111111111111001110~0000000000000001100011111111111111001111 = (26214350,26214351)
5368703993*5368704007 = 28822982639615999951 in base 4 is 120333333303200000001203333333033: 1203333333032~00000001203333333033 = (26214350,26214351)
5368703993*5368704007 = 28822982639615999951 in base 16 is 18fffce00018fffcf: 18fffce~00018fffcf = (26214350,26214351)
Robert Israel and Ed Pegg have posted other very large base-ten examples! I will provide herewith the initial (base 2-16) solutions where the consecutive integers are descending:
2*3 = 6 in base 6 is 10: 1~0 = (1,0)
3*5 = 15 in base 7 is 21: 2~1 = (2,1)
3*5 = 15 in base 15 is 10: 1~0 = (1,0)
5*7 = 35 in base 2 is 100011: 100~011 = (4,3)
5*7 = 35 in base 8 is 43: 4~3 = (4,3)
5*7 = 35 in base 11 is 32: 3~2 = (3,2)
7*11 = 77 in base 5 is 302: 3~02 = (3,2)
7*11 = 77 in base 12 is 65: 6~5 = (6,5)
11*13 = 143 in base 15 is 98: 9~8 = (9,8)
13*17 = 221 in base 6 is 1005: 10~05 = (6,5)
29*31 = 899 in base 7 is 2423: 24~23 = (18,17)
31*37 = 1147 in base 3 is 1120111: 112~0111 = (14,13)
31*37 = 1147 in base 9 is 1514: 15~14 = (14,13)
41*43 = 1763 in base 5 is 24023: 24~023 = (14,13)
67*71 = 4757 in base 11 is 3635: 36~35 = (39,38)
383*389 = 148987 in base 5 is 14231422: 1423~1422 = (238,237)
409*419 = 171371 in base 13 is 60005: 6~0005 = (6,5)
1499*1511 = 2264989 in base 12 is 912911: 912~911 = (1310,1309)
1889*1901 = 3590989 in base 7 is 42344233: 4234~4233 = (1495,1494)
4583*4591 = 21040553 in base 11 is 10971096: 1097~1096 = (1437,1436)
11827*11831 = 139925237 in base 13 is 22cb22ca: 22cb~22ca = (4899,4898)
38011*38039 = 1445900429 in base 6 is 355250355245: 355250~355245 = (30990,30989)
1079783*1079797 = 1165946444051 in base 11 is 40a52540a524: 40a525~40a524 = (658146,658145)
1628329*1628353 = 2651494412137 in base 5 is 321420230032142022: 32142023~0032142022 = (271513,271512)
193746481*193746491 = 37537700837348171 in base 5 is 303330120142303330120141: 303330120142~303330120141 = (153754422,153754421)
1008660187*1008660197 = 1017395382925476839 in base 7 is 1551530341515515303414: 15515303415~15515303414 = (514530735,514530734)
11999987983*11999988017 = 143999712000143999711 in base 10 is 143999712000143999711: 143999712~000143999711 = (143999712,143999711)
The scene this morning behind the west fence of Denison Park (Weston). The lights on the left are reflections of the camera flash. On the right, one of the vertical strings of lights (bottoming at 7 o'clock) was actually lit! Naively, I expected to find an extension cord nearby but failed to see one. The path drops somewhat steeply down to the Humber river.
Addendum: Found this twitter post...
Out for a late Sunday afternoon walk in Denison Park and found these two decorating a tree in the easement by the Humber River! Love my neighbourhood! #YSW pic.twitter.com/YaCN2tk4Ps
— Denison Denizen (@LaurieMace) December 6, 2020
