Did you know that a prime, regardless of its base, is always a prime?

I am looking for a prime. It’s the largest of its kind.

In solving this puzzle, the answer you may find.

Translated, that is, but a prime is a prime.

enter image description here

Note (and possibly a hint):

There was some confusion about the tiny black and white markings in the puzzle. These are not important in the puzzle. They are just the result of my poor graphic skills.

Hint 1 - an annotated version of the puzzle:

enter image description here

  • 6
    $\begingroup$ I'll take, who is Optimus Prime for $500, please. :) $\endgroup$ – Perpetual J Aug 30 '19 at 14:00
  • 2
    $\begingroup$ @PerpetualJ That surely is a large prime! ;) Just not quite what I'm looking for... $\endgroup$ – P1storius Aug 30 '19 at 14:12
  • 1
    $\begingroup$ @SayedMohdAli Lol I was just cracking a joke about the description was all. $\endgroup$ – Perpetual J Aug 30 '19 at 14:31
  • 1
    $\begingroup$ @Perpetual J I'll challenge that with who is Sentinel Prime for $750, please! $\endgroup$ – Rewan Demontay Aug 30 '19 at 16:21
  • 1
    $\begingroup$ @RewanDemontay Hahahaha I bring you Cybertron, your home, and still you choose humanity! $\endgroup$ – Perpetual J Aug 30 '19 at 16:24

Continuing from Bananenkopp's solution,

Reading off the rotations in base 4 gives 120122113, which translates to 99991 in base 10. This is a prime, and the "largest of it's kind": the largest prime below 100000.

  • $\begingroup$ Great job, that is the right answer! rot13(Gur onfr sbhe cneg zvtug unir orra n ovg gevpxl: Gur oybpxf pna bayl unir sbhe ebgngvba fgngrf, enatvat [mreb gb guerr]. Urapr gur pubvpr bs onfr sbhe) $\endgroup$ – P1storius Sep 3 '19 at 14:43
  • $\begingroup$ argh, to slow with all these formatting stuff $\endgroup$ – Bananenkopp Sep 3 '19 at 14:53

We have a 12x12 matrix $M$ divided into nine 3x3 matrices. Lets call them
$$\begin{pmatrix}A1 & A2 & A3\\B1 & B2 & B3\\C1 & C2 & C3\end{pmatrix}$$

and do the following

Rotate A1,B1 and C1 90 degree clockwise
Rotate A2 and B2 180 degree, C2 90 degree clockwise
Rotate B3 180 degree and C3 270 degree clockwise
or in short with r=rotate 90 degree clockwise
$\begin{pmatrix}r & rr & \\r & rr & rr\\r & r & rrr\end{pmatrix}$

The result should be something like this

Rotated Sub-Matrices
(thx to the "poor graphic skills" as a hint for doing this)

Now, what is this?

We now have an image with black dots at the prime numbers between 1 and 144!
You just have to add the x value to the y value.

Now back to the riddle:

Did you know that a prime, regardless of its base, is always a prime?

Yeah, seems to point us to primes in a different base. Here 12 is chosen. (a 12x12 matrix is a good way to show base12 numbers without using actual base12 numbers!) and base 4 is on its way.

In solving this puzzle, the answer you may find.

Remeber our rotational matrix? With numbers of rotations instead of the r

$\begin{pmatrix}1 & 2 & 0 \\1 & 2 & 2\\1 & 1 & 3\end{pmatrix}$

Reading the matrix in one row gives $120122113$
And $120122113_{4}$ is $99991_{10}$

I am looking for a prime. It’s the largest of its kind.

99991 is the largest prime with 5 digits in base 10

Translated, that is, but a prime is a prime.

Maybe a hint to the "cipher" used

  • $\begingroup$ Very impressive, you are definitely on the right track, but not completely there yet! rot13(Vaqrrq gurer vf zber gb gur chmmyr. Lbh fbyirq gur vzntr bs gur cevzrf. Ubjrire, gur nafjre qbrf abg yvr va gur erfhyg, ohg engure va gur xrl.) $\endgroup$ – P1storius Sep 3 '19 at 14:22
  • 1
    $\begingroup$ That's the correct answer, with all clues explained. The poster of the accepted answer was just a bit faster in posting the final answer. But the bounty will come your way when the 24 hours have passed. That is for providing a complete answer and cracking the largest part of the puzzle. $\endgroup$ – P1storius Sep 3 '19 at 15:06

Partial Answer

I believe that this may be:

A crossword style puzzle in which the words have been replaced with prime numbers of lengths 1, 2, 3, and 4.

With that in mind, the lower left hand single space in the first box of the first column could be either 2 or 3. I'm not sure what the significance would be yet as I'm still working on the rest as I have time.

A theory I have towards the final answer is:

That the final answer will probably be a representation of the largest known prime found to-date, which is (as of August 2019) $2^{82,589,933} − 1$.

The line stating Did you know that a prime, regardless of its base, is always a prime? is a little concerning though because this could be in any base which would definitely make the puzzle quite broad as there are many different bases to choose from. However, the most common are:

Binary, Octal, Decimal, and Hexadecimal

  • $\begingroup$ rot13(V guvax gur gval yvarf va orgjrra gur obkrf ner fvtavsvpnag, gbb, nf frcnengbef.) $\endgroup$ – Cloudy7 Aug 30 '19 at 16:13
  • $\begingroup$ @Cloudy7 rot13(Creuncf pyhrf yrnqvat gb ovanel; abg fher gubhtu. V ubcr gurl'er whfg cnvag reebef yby) $\endgroup$ – Perpetual J Aug 30 '19 at 16:19
  • $\begingroup$ I like the concept you mention, but unfortunately you are in the wrong direction. rot13(lbh qbag unir gb svyy nalguvat va gur chmmyr. Ohg gur chmmyr fubhyq or zbqvsvrq gb znxr vg pbeerpg.) $\endgroup$ – P1storius Aug 30 '19 at 18:02

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