Is there a nice cozy formula that will always spit
out primes? Try this one:
f(n) = n2 + n + 41.
Euler discovered that this formula has a long string of prime
values: it is prime for all n between 0 and 39 inclusive.
However, it is not prime for all
integers. In fact, it can be shown that no
non-constant polynomial with integral coefficients will
always spit out primes at the natural numbers.
There are formulas which always spit out primes when you
plug in a natural number... here's one (Mills, 1947):
greatest integer less than (X raised to 3n),
where X is approximately 1.3064... Surprised?
See the remark below!
The Math Behind the Fact:
It is worth pointing out that while the formula above
looks nice, it is useless... it grows too quickly,
and to determine X is tantamount to knowing the primes
in its range!
How to Cite this Page:
Su, Francis E., et al. "Formula for Primes?."
Math Fun Facts.