# what is the name of this number? is it transcendental?

Consider the number with binary or decimal expansion

0.011010100010100010100...

that is, the $n$'th entry is $1$ iff $n$ is prime and zero else. This number is clearly irrational. Is it known whether it is transcendental?

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Wiki lists it as a "suspected transcendental" en.wikipedia.org/wiki/List_of_numbers#Suspected_transcendentals – Dan Brumleve Jun 2 '11 at 2:02
@Graham Enos: You mean of a transcendental number, in which case the answer is yes. By tradition, the first incommensurability proof involved $\sqrt{2}$, though some have argued it might have been the so-called golden number. – André Nicolas Jun 2 '11 at 2:23
@Dan, every number not known to be algebraic is suspected transcendental. – Gerry Myerson Jun 2 '11 at 3:10
I nominate Jonas to answer this because he found the name. – Dan Brumleve Jun 2 '11 at 3:30