# 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

I initially found it by googling "0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1", which brought me this link to the CRC concise encyclopedia of mathematics with references to OEIS. I could also have entered a similar search on oeis.org. I saw sequence A010051, the characteristic function of the primes. One of the cross references there is sequence A051006, also referenced in the encyclopedia article, which is the decimal expansion of the "prime constant", with that name given. Another Google search with name in hand brings up the Wikipedia article.