Is this number random?
CJam, 53 52 47 bytes

l~"X    0'ò"2/Dfb+:%"gÇâì6Ô¡÷Ç8nèS¡a"312b2b=


There's unprintables, but the two strings can be obtained by

[88 9 48 5 39 5 29 1 242]:c
[8 103 199 226 236 54 212 15 161 247 199 56 110 232 83 161 97]:c


respectively. This also shows that the code points are below 256.

This is a modulo chain answer, where we apply the following modulos to the input integer, in order:

[1153 629 512 378 242 136]


Since this list contains integers greater than 255, the list is encoded using two chars each. The decoding is done by 2/Dfb, which splits the string into chunks of length two and converts each from a base 13 number (e.g. 88*13 + 9 = 1153). However, there are two exceptions to the decoding:


The last number (136) is not included (see below),
The second-last number is represented by a single char, since the number (242) is less than 256 and splitting an odd-length array into chunks of size 2 will leave a size 1 array at the end. Thanks to @MartinBüttner for this tip!


Once the modulos have reduced the input integer to a relatively small number, we perform a lookup from a table. This table is encoded via the second string, which is converted to a base 312 number then decoded to base 2, which we index. Since CJam's array indexing wraps, we can leave out the final modulo as mentioned earlier.

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