Prime Number Question: 10^n plus 9

[MrJackboots]

@Alive At Both Ends

In fact, there is no known formula that yields only primes, and I think most mathematicians believe none will ever be found. I don’t know if it’s been proved impossible, though.

I remember one of my math GSIs mentioning one recursive pattern that went something like this:

2^2-1=3, prime
2^3-1=7, prime
2^7-1=127, prime
2^127-1 = some fairly huge prime (on the order of 10^38)
2^(2^127-1)-1 = some quite-possibly-prime-number. It fits the Mersenne structure, but that doesn’t mean anything particularly. Nobody knows whether it’s prime or not, because nobody has the computing power to find out, and possibly never will. It’s so huge (the largest known definite prime has a relatively paltry 9.1 million digits - this one is in the range of 210^37th-illion* digits) that it doesn’t really matter whether it’s prime or not.

[psychonaut]

@Alive At Both Ends

In fact, there is no known formula that yields only primes, and I think most mathematicians believe none will ever be found. I don’t know if it’s been proved impossible, though.

Where did you get this idea? There are an infinite number of formulas which yield only primes. Here are some examples:

f(x) = 2
f(x) = 3
f(x) = 5
f(x) = 7
f(x) = 11