Limits
This web site analyzes numbers up to 1015 and identifies more than 170 properties. For each family of numbers I present some examples of numbers which also belong to other families.

Due to algorithmic and time constraints some properties cannot be tested in real-time up to 1015 and similarly, when I crossed the various families to find common members, often I cannot consider all the members up to 1015.

For those numbers families for which recognition and/or crossing is not performed up to 15 digits (1015), I report the actual limits I used in the table below.

Please note that in the "cross" section I disregard common numbers below 10, because, well..., they are too common.

FamilySearchCrossNotes
aban10121015
eban10151015
iban10151015
oban10151015
uban10151015
ABA10151013
a-pointer10151010
abundant10155×107
Achilles10155×1013
amicable10121014
alternating1015109
amenable1015109
anti-perfect3×1083×108
apocalyptic*30000Numbers over 3⋅106 are apocalyptic exponents with high probability
arithmetic1015107
dig.balanced10152×108
bemirp10152×1014
betrothed2.03×10102.03×1010
balanced p.10151010
binomial10151013
brilliant1015109
Carmichael10151012
congruent*107numbers whose squarefree part is < 107
Chen109108
Curzon10152×108
cyclic1015107
d-powerful107107
D-number70431337043133
deceptive10151011
deficient1015107
de Polignac1015108
droll10151015
Duffinian1015107
economical10152×107
emirp10152×108
emirpimes1012108
enlightened10155.57×1011
equidigital10152×107
eRAP10121012
esthetic10151015
evil1015109
fibodiv10151.14×1010
Friedman106106A few numbers may be missing
frugal1015109
gapful10151011
Gilda10151.61×1010
good prime10152×108
happy1015107
harmonic10151014
hoax1015108
Honaker109109
hungry108108
hyperperfect10154×1012
iccanobiF1.1×10141.1×1014
interprime1015108
inconsummate106106
junction1015108
Lehmer10151012
lonely10141014
lucky107107
modest10152×109
Moran1015108
nude10155×108
odious1015109
panconsummate106106Actually, it is conjectured that the largest term is 3097
pandigital10151010
palprime10151015
pernicious1015107
persistent10151011
power10155×1013
powerful10151015
practical1015106
prime10151012
primeval1.01×10111.01×1011
prim.abundant1015108
Proth10151012
pseudoperfect106106Some numbers larger than 106 are recognized using their properties
repdigit10151015
repunit10151015
Rhonda10151012
Ruth-Aaron10121012
self1015109
semiprime1015108
sliding10151015
Smith1015108
Sophie Germain1015108
sphenic1015108
strong prime1015108
super-d1015107
super Niven10155×1010
tau1015109
taxicab10151015
tcefrep10151013
truncatable prime10151015
twin1015109
Ulam107107
untouchable106106
unprimeable1015107
vampire10101010
wasteful1015107
weak prime1015108
weakly prime10151011
weird106106
Wieferich*1015The largest known number 16547533489305 is also the last, unless a third Wieferich prime exists.
Zuckerman10151010
Zumkeller105105Some numbers larger than 105 are recognized using their properties