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Link to the entire series.

The message:

3, 53, 48751, 9247757, 294914580539

The answer is a 13 letter word: UNDERSTANDING

Hint 1:

One mathematical operation is 50% of the puzzle.

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    $\begingroup$ After a quick search, they're all primes. Surely not an accident(?) $\endgroup$ Aug 25, 2023 at 19:03
  • $\begingroup$ @BenjaminWang - it's neither. Not an important detail, nor an accident. Them being primes doesn't matter. $\endgroup$ Aug 25, 2023 at 19:18
  • $\begingroup$ One hint please $\endgroup$ Aug 28, 2023 at 14:29
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    $\begingroup$ I try to sum each number and after converting each digit into a letter now I have this : cjejcecihhbaf but if i try do anagram I don't find nothing that have sense :/ $\endgroup$ Sep 6, 2023 at 19:09
  • $\begingroup$ @IlCorsaroNero - You are not far from solving it $\endgroup$ Sep 19, 2023 at 14:59

1 Answer 1

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Encoding

Following IlCorsaroNero's idea of adding all the numbers together, we instead try to multiply all the numbers in the message, to obtain the number 21140405181920011404091407.
We notice that this is a 26 digit number, exactly twice the length of our 13 letter word. By splitting the number into groups of two digits, we get 21, 14, 04, 05, 18, 19, 20, 01, 14, 04, 09, 14, 07.
Replacing each two digit group with its corresponding letter in the alphabet yields UNDERSTANDING.

Decoding

To decode a message, we do the reverse of encoding. The only difference is what numbers we factorise the initial number into. Following an observation made by Benjamin Wang that all the numbers are prime, we can guess that the initial number should be factorised into primes and then these primes organised into ascending order.

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    $\begingroup$ Your answer is correct for the most part :) However, numbers do not have to be primes, initial number can be broken up into non-prime factors (if possible). That is why numbers being primes is not important. $\endgroup$ Sep 20, 2023 at 12:07
  • $\begingroup$ I see, I thought that your comment about it not being an accident might have been a part of the decoding process. Does that mean they only have to be in ascending order, or is that also optional, considering they all give the same decoded message? $\endgroup$ Sep 20, 2023 at 12:18
  • $\begingroup$ The key part of this cipher is multiplication. The number containing letter numbers is factorized into primes or non-primes, which then have to be multiplied to get the initial number. Prime factorization simply was easier to code. Order of numbers does not matter since we need to multiply them. $\endgroup$ Sep 20, 2023 at 12:31

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