Quote from: BurtW on September 12, 2013, 03:57:17 PM

Quote from: pc on September 12, 2013, 12:45:57 PM

Quote from: BurtW on September 11, 2013, 10:36:20 PM

Quote from: pc on September 10, 2013, 05:49:05 PM

A private key is just a 256-bit random number. (Well, a number between 1 and hex value FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141.)

Where did you get that God awful number? The actual value of p for secp256k1 is:

p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F

I got it from the Private Key page on the Bitcoin wiki. I don't know whether the number is right or wrong, but feel free to update the wiki (perhaps it should have a citation, even?) if the value there is wrong. I apologize for not checking my sources more thoroughly, or at least citing where I was getting my info from.

In any event, it's rather unlikely that a random 256-bit number won't be in the range. If somebody gets heads a ton of times in a row, they may want to double-check the upper bound before using it. (Or, perhaps more likely, check that their coin is fair…)

The integer p specifying the finite field F_p can be found here:

https://en.bitcoin.it/wiki/Secp256k1

which is really just copied from section 2.7.1 "Recommended Parameters secp256k1" on page 15 of this document:

http://www.secg.org/collateral/sec2_final.pdf

I will verify this and then fix the wiki if I am correct.

I just answered to your post in the dev&tech forum
It's n because G^(n+1) = G
By the way a private key above n is valid, it's just that it will equivalent to (private key)%n