Puzzling Stack Exchange

Clues to crossword perfection
Clues to crossword perfection

You pick up a discarded newspaper, hoping to satiate your need for puzzles with a cryptic crossword. But as you turn to the page, you feel something is awry – perhaps some elision?

Across
3. $F_6,F_7,F_8$ mixed $13\times3$ down${}- \sqrt{12\text{ across}}$
16. $3$ squares joined${}- 4$ and half of $3$ down
12. A square $6$ under $1$ across
20a. Multiple of $268727$ less than a square
8. Double $37+1019$a across – a square
19a. Code for a Lao $45$b down, head rooted
21. Twice $120$a across’ smaller prime factor
1. $17$ down${}+ 4163^\text{rd}$ prime
18. A square two-thirds of $5$d across
5d. Palindrome two-thirds of $1$ across${}+ 2$
19b. Multiple of $717$ down${}+ 10 $

Down
3. $\sqrt{x^{yz_{10}}}$ if $16$ across is $xyz_{10}+2^x,x\in\mathbb{N}$
15. The start of $20$a across${} – 10555_7$
13. $1$ across${} + 101042$ years ago
16. $3$ down reversed${} + 13010+{}$AP joined
5a. Undecimal $88840+3$ down
5b. Double $97-120$b down reversed${} + 61 $
20b. $4$ odd digits, or $5$ with flipped $19$b across
5c. A sum with the two summands${} – 4+6! $
17. AP joined, or a sum of the first $k$ primes

AP means Arithmetic Progression (of at least 3 terms)
Joined means concatenated

Text transcription of crossword here or see post source code

Hints for extraction:

I wonder why the clue numbers are labelled so weirdly… and what could fill in the blanks on the black spaces?

Perhaps the clues give a message? If only there were a convenient way to turn numbers into letters…

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