Sure -- but it won't help.
Prime sequences are used to generate psuedo-random strings in cryptology nowadays. They seem to mostly work, although if someone discovers a fast way to factor Primes, that'll break a lot of modern crypto.
Lotteries, on the other hand, use analog random number generators -- they spin balls in a cage, for instance. While both methods produce nearly random sequences, they aren't related.
Good try though :}
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No, you can apply any mathematical operation to a prime number.
You must apply a writing implement to a surface on which you are writing.
Try it! You will probably get a negative number...
The multiplicative inverse of a number is : 1/number i.e., one divided by the number. This doesn't apply to zero. Zero has no multiplicative inverse.
The number 45 does not have any meanings that are special to the extent that they cannot apply to other numbers.