7
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<=19

B: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, ...

P: <3 <3 <3 <3 <3 <3 <3 X X X X X X X X X X X X X X ...

AB: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

20

B: 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 2, 4, 8, 16, 32, 64, 128, ...

P: <3 <3 <3 <3 <3 <3 <3 X X X X X X <3 <3 <3 <3 <3 <3 <3 <3 <3 ...

AB: - - - - - - - - - - - - - - - - - - - - - - ^ - - - - - - - - - - - - - - - - - - -

21

B: 1, 2, 4, 8, 1, 2, 4, 1, 2, 4, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, ...

P: <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 X X X X X X X X X X X X X X X ...

AB: - - - - ^ - - - - ^ - - - - ^ - - - - - - - - - - - - - - - - ^ - - ^ - - ^ - - - ^ ^ ^ ^ ^ ^ ^ ^ ^ ^


Original puzzle above. Hints will be put down here.

Hint 1:

19th, 20th, 21st

Hint 2:

there is no math tag

Hint 3:

<3 means heart

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  • $\begingroup$ <3 = heart; ^--^ = happy face; X X = dizzy face; Wow, are you japaniizu? $\endgroup$ – WhatsUp Nov 11 at 1:47
  • $\begingroup$ rot13(Gur urneg vagrecergngvba vf pbeerpg, V qvq abg vagraq gur bgure flzobyf gb or vagrecergrq gung jnl. V qba'g guvax V'z wncnavvmh.) $\endgroup$ – jazhang Nov 11 at 4:27
  • $\begingroup$ rot13(Vs guvf jnf cerfragrq va n zbabfcnprq sbag, gur bhgchg jbhyq or fvtavsvpnagyl qvssrerag be vg jbhyq or gur fnzr?) $\endgroup$ – Victor Stafusa Nov 11 at 20:14
  • $\begingroup$ @VictorStafusa rot13(gur jnl guvatf ner yvarq hc znggref.) $\endgroup$ – jazhang Nov 12 at 0:39
1
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PARTIAL ANSWER

What it is 19, 20 and 21?

Centuries. Up to the 19th century (it is "<= 19", not only "19") it was all the same thing. Things started to change in the 20th century and changed really quickly in the 21st century and are still changing.

This is something about:

Perfect numbers and Mersenne numbers. A number is perfect if it is equal to the sum of its divisors excluding itself. A Mersenne number is a number in the form $2^n - 1$, some of which are prime numbers. They are mathematically related, as that for every Mersenne prime there is a perfect even number and vice-versa.

What is B, P and AB?

B means binary.
P means either perfect or prime.
Maybe AB is a composite number, so $2^{ab} - 1$ is divisible by both $2^a - 1$ and $2^b - 1$. Perhaps it points out important things that are happening through the time and sharply accelerating in the 21st century due to the use of computers.

What more?

Maybe "<3 <3 <3 <3 <3 <3 <3 X X X X X X" is a binary representation for 11111110000002 = 8128, a perfect number.

Also, "- - - - - - - - - - - - - - - - - - - - - - ^ - - - - - - - - - - - - - - - - - - -" has a "^" in the 23rd position, and the 23rd number in the B line would be 8192. 8191 is a Mersenne prime, which is also very close to the 8128.

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  • $\begingroup$ The reply to my joke-comment however confirms that there's something to do with rot13(urnegf). $\endgroup$ – WhatsUp Nov 12 at 0:21

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