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The Wikipedia article on Gottfried Wilhelm Leibniz mentions, in the chapter on symbolic thought, that:

Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic, a striking anticipation of Gödel numbering. Granted, there is no intuitive or mnemonic way to number any set of elementary concepts using the prime numbers.

First of all, as far as I understand, Gödel numbering is an operation that does assign a prime number to every elementary symbol (or the elementary concept it represents) or logical operation (such as logical conjunction) , and therefore the second sentence is unclear to me.

Secondly, I'd like to get a reference about the manuscripts in which Leibniz anticipated Gödel numbering (of which the wikipedia claim is based). I guess it's in of his writings on "characteristic numbers" and the "calculus of propositions", but the Leibniz's nachlass is too vast and i don't know where to find the relevant material.

Everyone with useful information is welcome to contribute to the answer of my question.

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  • $\begingroup$ leibnizedition.de/reihen/reihe-vi $\endgroup$
    – sand1
    Sep 29, 2018 at 18:34
  • $\begingroup$ Best place currently is the Akademie Ausgabe, perhaps VI.4 A ( leibnizedition.de/reihen/reihe-vi ); Regulae ex quibus de bonitate consequentiarum judicari potest per numerum, p.242 $\endgroup$
    – sand1
    Sep 29, 2018 at 18:40
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    $\begingroup$ The link with memeory is exactly what is not relevant for Gödel's Arithmetization of syntax. $\endgroup$ Sep 30, 2018 at 8:45
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    $\begingroup$ Gödel numbering is a rather arbitrary way of assigning numbers to sentences of a particular formal language (Principia Mathematica originally, later Peano arithmetic), even if it did assign primes to primitives it would hardly be "intuitive or mnemonic". Leibniz would need some intrinsic relation between primitive concepts themselves (if there was such a thing), not formal sentences, and primes to assign the numbers canonically. $\endgroup$
    – Conifold
    Sep 30, 2018 at 21:03
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    $\begingroup$ On Gödel's obsession with characteristica universalis and paranoia about Leibniz see Why did Gödel believe that there was a conspiracy to suppress Leibniz's works? Dawson's book cited there mentions Leibniz's works that Gödel considered relevant. $\endgroup$
    – Conifold
    Oct 1, 2018 at 3:07

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No. Primes occur in many situations. With Liebniz's extraordinary intuition he is more likely to intuited that prome factorisation may apply elsewhere - and indeed it does - for example in prime knots.

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