Cogito, ergo sum is "Since I doubt, I think; since I think, I exist"; with rearrangement and compaction, "I doubt, therefore I think, therefore I am", or in Latin, "dubito, ergo cogito, ergo sum". A further expansion, ("…—a thinking thing") extends the "cogito" with Descartes's statement in the subsequent Meditation, , or, in English, "I am a thinking (conscious) thing, that is, a being who doubts, affirms, denies, knows a few objects, and is ignorant of many …". This has been referred to as "the expanded "cogito"". Neither nor indicate whether the verb form corresponds to the English simple present or progressive aspect.
Descartes number Descartes number In number theory, a Descartes number is an odd number which would have been an odd perfect number, if one of its composite factors were prime. They are named after René Descartes who observed that the number would be an odd perfect number if only were a prime number, since the sum-of-divisors function for would satisfy, if 22021 were prime, where we ignore the fact that reveals that 22021 is composite. A Descartes number is defined as an odd number where and are coprime and , whence is taken as a 'spoof' prime. The example given is the