A short excursion -
The well-known Euler’s Polynomial generates 40 primes at the first 40 natural numbers. It is sometimes called a prime-rich polynomial. There are many such polynomials, and although Euler’s Polynomial is perhaps the best-known, it is not the best. The best that I have heard of is , which generates 57 primes. But this morning, I was reading an article on Ulam’s Spiral when I heard of the opposite – a prime-poor polynomial. The polynomial doesn’t produce a prime until . Who knew?
And to give them credit, that prime-rich polynomial was first discovered by Jaroslaw Wroblewski & Jean-Charles Meyrignac in one of Al Zimmerman’s Programming Contests (before being found by a few other teams too).