Re: [PrimeNumbers] k^n -> (k^n) + (2n-1) = prime ?!
- Note that there are some values of n for which (k^n)+(2*n-1) is NEVER prime.
For instance, if n == 63, then:
(k^n)+(2*n-1) == (k^63)+125 == (k^21)^3 + 5^3
Which of course is always composite, being divisible by (k^21)+5.
On the other extreme, (k^4)+7 seems to be a (relatively) rich source of
prime numbers... For 0 <= k <= 10000, there are 698 such primes,
compared to about 312 predicted using the prime number theorem.