Puzzle 1253 2026 a Prime
Productive Year
Lets' devote this puzzle to create some fun with
this new year:
2026
I will start with some curiosities that I got
somewhere out there:
a) 2026 is the
algebraic sum
of the first 34 odd (consecutive) primes, from 3 to 149, where
only two primes are negative summands: 11 & 113.
|
3 |
5 |
7 |
-11 |
13 |
17 |
19 |
23 |
29 |
31 |
37 |
41 |
43 |
47 |
53 |
59 |
61 |
67 |
71 |
73 |
79 |
83 |
89 |
97 |
101 |
103 |
107 |
109 |
-113 |
127 |
131 |
137 |
139 |
149 |
2026 |
b) 2026 is equal to the sum of the
following two primes, 23 + 2003 (the more apart),
1013+1013 (the more close) & 977+1049 (the closer
but distinct)
c) 2026 It is a
prime-productive number,
because
2*026+1, 20*26+1, 202*6+1, and 2026+1
are all prime numbers.
BTW, there are
only
193
such numbers under a billion (in
https://oeis.org/A089395 you may see the list of
the first 139 of them).
And you know
what?
193
is also a
prime,
weak,
but
happy
&
lucky
number!
d) You may construct a beautiful
carpet
using exactly
2026 sticks,
as shown below:
BTW, this image was "stolen" from the Giovanni
Resta's amazing place,
https://www.numbersaplenty.com/
Q. Q. Can you provide more/better prime-curios about
2026?
|
|
|
|
During Jan 3-9, 2026 contributions came from Ivan ianakiev, Emmanuel
Vantieghem
***
Ivan wrote:
2026 = floor(е^п + п^е)^(φ(777)/φ(666)) - e^(i*п)
Happy Eulerian year to you and your readers!
***
Emmanuel wrote:
2026 = 9*(8*7 - 6 - 5)*(4 + 3 -2) + 1
= 1 + (-2 + 3 +
4)*(5*6 + 7 + 8)*9
= (2 + 3)*5*7*11 + 13 + 17 + 19 + 23 + 29
(10 consecutive primes)
= 2^11 + 0^1 - 2^4 - 6^1
= 2^2 + 5^2 +7^2 + 11^2 + 13^2 + 17^2 + 37^2
= 2^2 + 5^2
+7^2 + 13^2 + 17^2 + 23^2 + 31^2
In
the mail list of the SeqFans you can find a lot of interesting facts about
2026.
...
In such
SeqFans I (CR) found two more interesting equations:
2026 =
2^11 -2*11, by Dave Consiglio
2026 = (2²+0²+2²+6²)²+(2+0+2+6)²-(2+0+2+6),
by zzllrr xiaole
***
