Number twenty

This morning I reached #20 in the production score of the probable-prime top-discoverers leaderboard. I was already at #20 by number of probable primes and it is relatively unusual to be in the same position in both lists. Of the 1438 probable primes noted, all but 52 are Leyland primes. My work on finding more Leyland primes continues unabated as my current worksheet clearly shows:

Intervals #18-#20 are done. Interval #22 shows 34 recent finds of an expected 100 or so by this time next month. That will push me to #19 on the number leaderboard and possibly to #18 on the production score list. Alas, I will still be several dozen short of my strived-for 1500 Leyland-prime finds. Being so close is incentive enough to continue. Once interval #22 is completed I will be looking at Leyland numbers ranging from 300000 decimal digits length up to 305000 decimal digits. I don't think there are enough probable primes in this region to make up the deficit but it will bring me much closer.

Much ado about directed energy attacks

I'm increasingly annoyed by the lack of skepticism in the current round of media hype about "directed energy attacks". After the first reports of an "acoustic attack" made their debut in 2017, I was certain that an element of mass hysteria was at play. I have just come across Robert Bartholomew's excellent analysis in Skeptic that arrives at a similar conclusion.

Dry run

A pre-registration for Pfizer vaccine appointments is being held at 1765 Weston Rd. today for two hours, starting at noon. Shown here is the starting lineup winding its way around the back of the building at left, then down to and along Weston Rd., snaking its way into the UP Express site, therein reaching Lawrence Ave. W. All for a measly 300 bookings!

Anticipation

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.

Johann schreitet

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.

Reinforcements

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.

My 1000th Leyland prime find

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.

A little excitement

SWAT team entering a house across the street at 4:30 pm

My guess is that this is related to the Oakville gun-shots incident. The woman that vacated the Oakville residence at 3 pm may have told police that the man still inside had a connection to this rooming house. Perhaps he (or a relative of his) is a tenant herein. I did spot a Halton police vehicle on the street after the SWAT team had left.

10/9*8*765/4+321

Happy New Year! (I did my first one ten years ago. My cheat sheet is good to 2101.)

On the product of consecutive primes being the concatenation of consecutive integers (base 2-16)

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)