h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I need to prove that a series of nubmers are all prime numbers, I don't know how to do this mathematically, but it looks good, as far as my eyes can see.

I'll give a wrong exampl:
1 is prime, 2 is prime, 3 = 1+2 and is prime, 5 = 2+3 and is prime so the series 1,2,3,5 is prime (addin 2 last elements.

The true example:
This is of course untrue, and fails on the next step, but:
1 is prime, 11 is prime, 101 is prime, 1001 is prime, 10001 is prime etc...
so 1+10^n is prime... now how do I prove it???


Dancer

Erm, strictly speaking 1 isn't a prime number. The definition of a prime number is that it can be divided by only two other numbers, 1 and itself. For the case of 1, this isn't true. (Runs away before being shouted at for killing theory)

Wether 1 is a prime seems to be more a matter of definition. It does after all live up to the rule you gave. It can be divided only by 1 and itself.

Mersenne, Fermat and friends tried to find a formula that would always produce a prime number. Such efforts appear to be doomed to failure - nobody has ever succeeded in finding one.
See http://www.bbc.co.uk/dna/h2g2/alabaster/A670051 Mersenne primes.

My table of prime numbers includes 1.



I don't recall ever seeing an expression to calculate a prime number, let alone a progression of prime numbers. Good luck in creating one.

1 is usually not considered to be a prime number, but it is a matter of definition.

You won't be able to find a sequence of numbers like 1, 11, 101, 1001 etc that are all prime. People have been searching for a long time and have never come up with one.

I saw a program the other day about this woman. She took random rows of numbers and then colored the prime numbers black. So the squares with a normal number was white and the other sqaures where black. She made art out of them. She said so anyway, it just looked stupid to me.

Dancer, I dont want to rain on your parade, but 1001 is not prime. 77x13=1001. Sorry.

I couldn't find anything.... thought I was on to something... was wrong.. thanks.


Dancer

By the way 10^0 +1 = 2, so your sequence should go 2, 11, 101, 1001 = 7x11x13, 10001, 100001 = 11x9091, ...

In fact, every second number is divisible by 11.

How about 10^(2n)+1?

Like all such patterns this one will not give good results:

101 prime
10001 = 73 * 137
1000001 = 101 * 9901
100000001 = 17 * 5882353

and so on.

Do you have some program to test divisibility?

That is of course the problem with large numbers. I could claim 187387592659265923 is prime and probably not get contradicted if no-one has a clever program to figure it out. (By the way, I don't know if it's prime, but even though I avoided the easily testable multiples of 3, 5 and 11, the chances are it isn't).

As Gnomon points out, no patern that consistently gives primes has been discovered. I don't think the possibility has been ruled out, but anything as simple as powers +1 has almost certainly been considered.