Descartes number

Question

In 1638 Descartes wrote a letter to Mersenne where he talks about how the number $$D=3^2⋅7^2⋅11^2⋅13^2⋅22021$$ would be an odd perfect number if we mistakingly assume that $22021$ is prime. My question is, do we know what method Descartes used when he found his number and does anyone know where I can find a copy of the letter that he sent to Mersenne in November of 1638?

I've tried several searches online, and at our local academic library, but have had no luck. Any help would be greatly appreciated!

$D = 32\cdot72\cdot112\cdot132\cdot22021= 750 , 086 , 701 , 056$ ;$D_{\text{Peter}} = 198,585,576,189$ — R.W, Oct 24 '17 at 21:49
In fact, "$D_{Peter}$" WOULD be a perfect odd number, if $22021$ WERE prime. — Peter, Oct 24 '17 at 21:55
I found this. Helpful? http://faculty.missouri.edu/~bankswd/papers/2008_Descartes_Final.pdf — MBP, Oct 24 '17 at 22:23
Descartes à Mersenne, 15 novembre 1638 (lettre CXLIX), into Œuvres, éd. Adam et Tannery, Tome II, page 429. — Mauro ALLEGRANZA, Oct 25 '17 at 11:08
This question is related and the answer contained therein attempts to respond to your first inquiry. — Jose Arnaldo Bebita Dris, Oct 25 '17 at 12:01
@MauroALLEGRANZA, I think you should post your comment as an answer to this question, since it actually answers the OP's inquiry, so that the question does not remain unanswered. — Jose Arnaldo Bebita Dris, May 22 '18 at 10:32

score 4 · Accepted Answer · answered May 22 '18 at 11:22

4

The letter is :

Descartes à Mersenne, 15 novembre 1638 (lettre CXLIX).

We can find it into : Œuvres, éd. Adam et Tannery, Tome II, page 429.

answered May 22 '18 at 11:22

Mauro ALLEGRANZA

99,247

Descartes number

1 Answers1