largest known prime (1 Viewer)

[tywebb]

2^57,885,161-1 was discovered on jan. 25, 2013 to be largest known prime by curtis cooper

it has 17,425,170 digits which you can get <a href="http://www.isthe.com/chongo/tech/math/digit/m57885161/huge-prime-c.html">here</a>

 

[Sy123]

I decided to do some calculations:

I wanted to find how long it would take to scroll through the entire number, so I used this first:

http://dagobah.net/flash/Scroll_Wheel_Challenge.swf

To measure my scrolls per 30 seconds, if I'm not spazzing out on it I can manage 1000 per 30 seconds (average)
Now, there are 17, 425, 170 digits, each line of digits contains 19 * 3 digits in them (19 block of 3)
Hence the number of lines in the text is approximately: 305 704 lines.

Now one scroll on my mouse is about 6 lines of text scrollled through. Hence the number of scrolls I need to finish the text is 50 950
And the amount of time to do this number of scrolls is about 25.5 minutes lol

Useless result, but I thought it was fun to note

 

[braintic]

I'm wondering if its true that if 2^n - 1 is a prime then n must be prime?

Is so, is there any systematic way of determining which prime values of n give a prime value of 2^n - 1?

 

[seanieg89]

I'm wondering if its true that if 2^n - 1 is a prime then n must be prime?

Is so, is there any systematic way of determining which prime values of n give a prime value of 2^n - 1?

1. Yes. To prove this show that 2^{ab}-1 is divisible by 2^a-1 for positive integers a and b.

2. I guess. There are tests for primality, so this problem is a double application of them. We could for example use the ECPP primality test for p, and then the Lucas-Lehmer-Riesel test for 2^p-1. This very quickly gets out of the realm of pen and paper though of course.