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I have voted to close because this question is not in the scope of the site, as described in the FAQ linked at the top of the page. The proof of the incompleteness theorem is completely constructive and so, in principle, you could follow it step by step to write down a Goedel number of the Goedel sentence, given a Goedel numbering of formulas. However, it is unlikely that anyone has done so, because the actual number would be quite large.
– Carl MummertSep 19 '11 at 11:43

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You can use a Gödel numbering in which a given formula (e.g. your favorite Gödel sentence) has Gödel number equal to a given number (e.g. 17). So the answer to your question: the exact number you are looking for can be any number, it all depends on the Gödel numbering you use.
– GH from MOSep 19 '11 at 11:51

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I would be interested to see an answer to the question, if it provided the actual Gödel number of the original "I am not provable" statement using Gödel's coding scheme, which is of historical interest. I would view such an aswer as fundamentally similar to the results I have seen, published in one of the MAA journals, to compute the digits of the transcendental number Cantor produced in his original diagonalization against the algebraic reals.
– Joel David HamkinsSep 19 '11 at 12:19

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I would be interested to know if anyone has done this crazy thing, too. Please don't close. I just checked Russell O'Connors formalization in Coq (r6.ca/Goedel/goedel1.html), but unfortunately his program cannot do it (see section 8 of his web page).
– Andrej BauerSep 19 '11 at 12:51