I read "An illegal prime is a prime number that represents information whose possession or distribution is forbidden in some legal jurisdiction." on wikipedia , but I didn't get properly .
Can you explain what is it ? Is only one illegal prime number exist (that is given in link).
Suppose you have something in binary form that is illegal in some jurisdiction. This could be a text document in some countries, or as this was used, either code for simple encryption or a code to remove encryption. The details of which are not important to this discussion, but many US citizens believe(d) them to be government overreaches by the NSA and corporatations, so worthy of protest.
It is illegal to publish them. However, if you take the binary representation $k$ and then create a number $k*256^n+b$ with small values of $n$ and $b$, we could find a somewhat large prime. If the prime is large enough and we create a proof certificate for it, this may be computationally worthy of publication. There are web sites that publish large primes and their proof certificates.
Now we have a third party publishing a large prime number, which can be argued worthy of mathematical merit. This is not illegal. Someone can then mention, that by the way, taking entry 42, subtract $b$, writing it as binary, then gunzipping the result is also interesting. Oh -- that's the data that was illegal. Hence we could amusingly call this an illegal prime.