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…