Thread: "Rare" Primes View Single Post
2008-08-29, 14:30   #56
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by R.D. Silverman Although not explicitly stated, I believe that the domain is N. Now, f(x) is prime for x = 0, 4 and no other. If you accept the more general definition of prime (i.e. not restricted to just N) then f(x) will be prime i.o. (although a proof is lacking). If we allow x \in R, then f(x) is indeed prime the required number of times.
If we allow real numbers as x, then f(x) is prime 19 times - 9 times for negative x values as f(x) increases, once for x=0 where f(x) levels off at 29, and 9 more times for positive x values as f(x) decreases. There would be 10 unique primes, but 19 values of x that produce a prime f(x).