# Descartes number

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!

• $D = 32\cdot72\cdot112\cdot132\cdot22021= 750 \, 086 \, 701 \, 056$ ;$D_{\text{Peter}} = 198\,585\,576\,189$ – Rafael Wagner Oct 24 '17 at 21:49
• $D_{Peter}$, nice idea :) – Peter Oct 24 '17 at 21:52
• I found this. Helpful? 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
• @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