Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

10^n + 1

A problem that ganesh proposed started me thinking about Integers of the form:

which are prime for n=1 and n=2. After that I could not find any more primes and
I searched up to n = 2000.

Using a recurrence argument I can prove that most are composite. But I am left with

as being unknown.
I can even prove that some of these are composite but I can't eliminate them all. The question is are there any primes in the sequence 10^n +1 with n>2 ?

Last edited by bobbym (2009-06-17 00:08:39)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: 10^n + 1

It follows from the result I prove in this post that if

is prime then n is a power of 2.

I got my computer to test if

is prime for

and the only primes it found were 11 and 101. I don't have enough memory to make k any higher with my brute force algorithm.

There is a conjecture that

is prime for only finitely many n, an extension of the conjecture that only finitely many Fermat numbers are prime.