[tnlhreue] Some boring interesting numbers

0 is the additive identity
1 is the multiplicative identity
2 is the smallest prime
3 is the smallest odd prime
4 is the smallest composite
5 is the smallest prime one bigger than a composite
6 is the smallest composite with distinct factors, and the smallest square-free composite, and smallest perfect number
9 is the smallest composite with only odd factors
15 is the smallest composite with distinct odd factors
Beyond this point, it is just "more of the same".

Applying the Mersenne and Fermat mappings:

2^2-1=3 is the smallest Mersenne prime
2^3-1=7 is the smallest Mersenne prime with odd exponent
2^11-1=2047=23*89 is the smallest composite Mersenne number

2^2^0+1=2^1+1=3 is the smallest Fermat prime
2^2^5+1=2^32+1=4294967297=641*6700417 is the smallest composite Fermat number